Pre-Comp Study Guide

🧬 Biology
BIOLOGY: TABLE OF CONTENTS

Unit 1: Scientific Method and Experimentation

Unit 2: Biological Macromolecules

Unit 3: Cells

Unit 4: DNA

Unit 5: Cell Cycle and Mitosis

Cell Exchange with the Environment

Unit 6: Meiosis

Unit 7: Gene Expression

Unit 8: Genetics

Unit 12: Cellular Exchange with Environment

Chemistry of Life

📀 Unit 1

Unit 1

Experimental Design
Graphs
Key Ideas

💽 Experimental Design

Experimental Design
Steps used to conduct scientific research
Observation:
Noticing something and asking a question
Inference:
An educated guess
Hypothesis:
An explanation that is tested through an experiment
(If x/independent, then y/dependent)
Experiment:
A scientific procedure to test the hypothesis
Analysis:
Interpretation of the experiment’s data
Conclusion:
The final part of the experiment
Communication:
Share the results and findings of the experiment
Vocabulary:
Independent Variable:
The variable that is being tested and changes. It must be unique and can cause a change in the dependent variable.
Dependent Variable:
The variable that is being measured. When the independent variable changes, it is also expected to change.
Constant Variable:
A variable that could affect the dependent variable, but it is kept constant/controlled
Control Group/Experimental Control:
Negative Control:
Subjects receive no treatment
Positive Control:
Subjects receive both the amount of treatment and the amount of output
Experimental Factors:
all variables, groups, or subjects involved in an experiment.

💽 Graphs

Histogram:
What it is:
A graph that shows the frequency of data within intervals (bins) using bars.
When to use it:
To display the distribution of numerical data and see patterns like skewness, peaks, or gaps.
Box Plot (or Whisker Plot):
What it is:
A graph that shows the minimum, first quartile, median, third quartile, and maximum of a data set. Outliers are often marked.
When to use it:
To summarize the distribution of data, compare groups, and identify outliers.
Dot Plot:
What it is:
A graph where each data point is represented by a dot along a number line.
When to use it:
For small to medium-sized data sets to show frequency and distribution clearly.
Bar Graph:
What it is:
A graph that uses bars of equal width to represent categories and their values.
When to use it:
To compare discrete categories or show changes over time for distinct items.
Scatter Plot:
What it is:
A graph of points representing the relationship between two numerical variables.
When to use it:
To examine correlations, trends, or patterns between two variables.
Line Graph:
What it is:
A graph that connects data points with a line to show trends over time or continuous data.
When to use it:
To display changes over time or trends in continuous data.
Pie Chart:
What it is:
A circular graph divided into slices representing parts of a whole.
When to use it:
To show percentages or proportions of a whole for categorical data.
Stacked Bar Graph:
What it is:
A bar graph where each bar is divided into segments to show subcategories in addition to the total.
When to use it:
To compare totals and also see how different parts contribute to each total.

💽 Key Ideas

Key Ideas in Biology
All living things…
Are made of cells (at least 1)
Have a genetic code in DNA
Have stages of growth and a life cycle
React to stimulus from the environment (pain, heat, etc.)
Must reproduce and pass on DNA
Maintain homeostasis (adjust internal environment)
Change over time over many generations (evolution)
Have a metabolism ( use food for energy)
Biological Levels of Organization:
Atom & Molecules
: Smallest units of matter and their combinations    (ex: water, H₂O)
Cells
: Basic units of life    (ex: red blood cell)
Tissues
: Groups of similar cells working together    (ex: muscle tissue)
Organs
: Structures made of tissues performing specific functions    (ex: heart)
Organ Systems
: Groups of organs working together    (ex: digestive system)
Organisms
: Individual living things    (ex: oak tree)
Populations
: Groups of the same species in an area    (ex: a herd of deer)
Communities
: All populations of different species in an area    (ex: forest community)
Ecosystems
: Living & non-living components in an area    (ex: coral reef)
Biome
: Areas with similar climate, landscape, and living organisms (ex: tropical)
Biosphere
: All ecosystems on Earth.    (ex: Earth)
Importance:
Interconnectedness
: Each level is connected and can affect others. For example, pollution can impact a population of fish, which can then affect the entire ecosystem.
Complexity of Life
: These levels can help scientists appreciate the complexity of life.
Research & Medicine
: Understanding these levels can lead to advancements and breakthroughs in medicine, ecology, and biotechnology.
Environmental Conservation
: Recognizing the connection between the levels assists in conservation efforts.

📀 Chemistry of Life

Chemistry of Life
Vocab:
Types of Bonds
Ionic
Bond
: form between oppositely charged ions (+ -)
Covalent
Bond
: forms when atoms share a pair of electrons
Hydrogen
Bond
: a type of covalent bond that is very weak
Van
der
Waals
Interaction
: Weak attractions between molecules due to temporary shifts in electron density.
Hydrophobic
Interaction
: The tendency of nonpolar molecules to cluster together in water, avoiding contact with polar molecules like water.
Elements:
Atom
: smallest unit of matter ( nucleus, protons, electrons, neutrons)
Molecule
: More than 1 type of atom chemically bonded
Ions
: When an atom has more or fewer electrons than it needs
Gains = positive charge
Losses = negative charge
Isotopes
: same element with different amounts of neutrons
Element
: Pure substance with 1 kind of atom
The Backbone of Life: Carbon, Hydrogen, Oxygen, Nitrogen, Phosphorus, Sulfur,
Macromolecules:
Monomer
: a single unit of a molecule
Polymerization
: the process of monomers combining to create polymers
Polymers
: made entirely of similar monomers bonded together
Cells:
Organelles
: Organs/parts in cells
Organization of Life:
(Before Cells)
Atoms
Elements
Molecules
Macromolecules
Protein
Lipid
Carbohydrate
Nucleic acid
Organelles
Cells
Important People:
Antonie Van Leeuwenhoek: first person to view
living cells
Robert Hooke: first person to view
dead cork cells

💽 Water/pH

Properties of Water
Vocab:
Properties
Hydrophobic
: Molecules or parts that repel water and don’t  dissolve easily
Hydrophilic
: Molecules that are attracted to water and dissolve easily
Amphipathic
: Molecules that have both hydrophobic and hydrophilic parts
Hydration Sphere:
A layer of water molecules that surrounds ions or polar molecules, keeping them dissolved in water.
Cohesion
: when water is attracted to water
Surface Tension: water’s surface acts like a skin due to cohesion
Ex: Paperclip on the surface doesn’t sink as long as the surface isn’t disturbed
Adhesion
: when what is attracted to other molecules
Capillary Action: the ability of water to flow through narrow spaces against gravity
Ex: Water goes from roots to leaves through the stem
Water:
Life depends on hydrogen bonds in water because it makes water flexible
Most cells are made of  70%-95% water, which is important for cellular structure and function.
Water is a polar molecule, meaning it has slightly negative oxygen and slightly positive hydrogen. This is due to hydrogen sharing electrons with oxygen.
Water is a universal solvent due to its ability to dissolve a wide range of substances
pH
Introduction to pH
pH is a measure of how acidic or basic a solution is. It is important because it affects chemical reactions, biological systems, and the environment. For example, many aquatic organisms can only survive within a narrow pH range, so changes in water acidity can harm ecosystems. Similarly, soil pH affects plant growth and nutrient availability. Understanding pH is essential for maintaining environmental balance, human health, and proper functioning of chemical processes.
Key Definitions
pH:
A scale used to measure the concentration of hydrogen ions in a solution, indicating its acidity or alkalinity.
Hydronium Ion (H₃O⁺):
A water molecule that has gained an extra hydrogen ion; represents acidity in a solution.
Hydroxide Ion (OH⁻):
Ion responsible for basicity in a solution.
Logarithmic Scale:
A scale in which each unit represents a tenfold change in concentration; the pH scale is logarithmic, so a change of 1 pH unit means a tenfold increase or decrease in H⁺ concentration.

💽 Functional Groups

1. Hydroxyl Group (–OH)
Structure:
Oxygen bonded to hydrogen (–OH)
Found In:
Alcohols, carbohydrates, sugars
Function:
Increases solubility in water; makes molecules polar
Example:
Glucose, ethanol
2. Amino Group (–NH₂)
Structure:
Nitrogen bonded to two hydrogens (–NH₂)
Found In:
Amino acids, proteins
Function:
Acts as a base; helps form proteins
Example:
Amino acids (like glycine)
3. Carboxyl Group (–COOH)
Structure:
Carbon double-bonded to oxygen and single-bonded to a hydroxyl (–COOH)
Found In:
Amino acids, fatty acids
Function:
Acts as an acid; donates hydrogen ions (H⁺)
Example:
Fatty acids, amino acids
4. Phosphate Group (–PO₄³⁻)
Structure:
Phosphorus bonded to four oxygen atoms (–PO₄³⁻)
Found In:
DNA, RNA, ATP, phospholipids
Function:
Transfers energy; adds negative charge to molecules
Example:
ATP, DNA backbone

💽 Cellular Respiration

What Is Cellular Respiration?
Cellular respiration is the process cells use to release energy from food, specifically glucose. This energy is stored as
ATP (adenosine triphosphate)
, which cells use to power all activities like movement, growth, repair, and maintaining balance. Cellular respiration happens in living organisms and is essential for survival because it provides usable energy for cells.
Basic Word Equation
Glucose + Oxygen → Carbon Dioxide + Water + Energy (ATP)
Scientific (Chemical) Equation
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP (energy)
Real-World Example
When you eat food like bread or fruit, your body breaks the glucose down through cellular respiration. The energy released is used for things like running, thinking, breathing, and even keeping your heart beating. Without cellular respiration, your cells wouldn’t have the energy needed to function.
Quick Facts
Occurs mainly in the
mitochondria
Uses
oxygen
(aerobic respiration)
Produces
ATP
, the cell’s energy currency
Happens in both
plants and animals
Opposite process of
photosynthesis
Releases
carbon dioxide
as a waste product

📀 Macromolecules

Macromolecules in Biochemistry:
The four classes of macromolecules in biochemistry are carbohydrates, proteins, nucleic acids, and lipids. Each type has its own monomer subunit which joins to other monomers in specific ways.
Carbohydrates
Carbohydrates are macromolecules made of sugars that serve as a primary source of energy for living organisms. They are composed of carbon, hydrogen, and oxygen and can also provide structural support, such as cellulose in plant cell walls.
Monomer
- Monosaccharides (ex: glucose)
CHO
- Carbon, Hydrogen, and Oxygen
Bond
Type
- Glycosidic bonds
Examples
-  Starch, cellulose, glycogen
Function
- Short-term energy storage for animals/ Provides plant structure
Monosaccharides
Glucose
: A simple sugar that is the main energy source for cells.
Fructose
: A simple sugar found in fruits that provides energy and tastes very sweet.
Galactose
: A simple sugar that combines with glucose to form lactose (milk sugar).
Disaccharides
(Two monosaccharides)
Lactose
: A disaccharide made of glucose and galactose, found in milk.
Sucrose
: A disaccharide made of glucose and fructose, commonly known as table sugar.
Maltose
: A disaccharide made of two glucose molecules, formed during the digestion of starch.
Polysaccharides
Starch
: A polysaccharide used by plants to store energy.
Dietary fiber
: Indigestible plant carbohydrates that help with digestion and gut health.
Peptidoglycan
: A polysaccharide that forms the rigid cell wall of bacteria.
Glycogen
: A polysaccharide used by animals to store energy in the liver and muscles.
Cellulose
: A structural polysaccharide that makes up plant cell walls.
Chitin
: A structural polysaccharide found in fungal cell walls and the exoskeletons of insects and crustaceans.
Glycosidic Bonding
A glycosidic bond is a covalent bond that links two sugar molecules (monosaccharides) together to form a disaccharide or polysaccharide.
This bond is formed through dehydration synthesis (also called condensation), where a water molecule (H₂O) is removed as the hydroxyl (-OH) of one sugar joins with the hydrogen (H) of another sugar.
The bond can be broken by hydrolysis, a reaction that adds water to split the disaccharide or polysaccharide back into its monosaccharide units
Lipids
Lipids are biomolecules that are insoluble in water and are important for energy storage, cell membranes, and signaling. Common types include fats, oils, phospholipids, and steroids, all essential for normal biological functions.
Monomer
- Lipids do not have true monomers. They are made from components like fatty acids and glycerol, but they are not polymers.
CHO
- Carbon, Hydrogen, and Oxygen
Bond
Type
- Ester bonds
Examples
-  Fats, oils, phospholipids, steroids, waxes
Function
- Long-term energy storage, insulation, cell membrane structure
There are three major classifications of lipids: triglycerides, phospholipids, and steroids.
Triglycerides
Structure:
1 glycerol + 3 fatty acids
Function:
Long-term energy storage; insulation and cushioning
Additional facts:
Make up fats and oils; saturated or unsaturated
Phospholipids
Structure:
1 glycerol + 2 fatty acids + phosphate group
Function:
Form cell membranes (phospholipid bilayer)
Additional facts:
Have a hydrophilic head and hydrophobic tails
Steroids
Structure:
Four fused carbon rings
Function:
Hormones, membrane stability (cholesterol)
Additional facts:
Not made of fatty acids; act as chemical messengers
Ester Bonds & Fatty Acids (Lipids)
Ester bonds:
Link fatty acids to glycerol in triglycerides and phospholipids
Formation
: Made by a dehydration reaction (water released)
Fatty acids attached by ester bonds can be:
Saturated:
No double bonds, straight chains, solid at room temperature
Unsaturated:
One or more double bonds, bent chains, liquid at room temperature
Importance:
The type of fatty acids affects lipid shape, fluidity, and function
Proteins
Proteins are biomolecules made of amino acids and are essential for structure, transport, enzymes, signaling, and defense in the body.
Monomer:
Amino acids (20 kinds)
CHO(N):
Carbon, Hydrogen, Oxygen, and Nitrogen (sometimes Sulfur)
Bond Type:
Peptide bonds (Covalent)
Examples:
Enzymes, hemoglobin, keratin, insulin, antibodies
Function:
Build and repair tissues, catalyze reactions, transport molecules, regulate processes, provide structural support
R-Group determines the amino acid type
Types of Proteins and Their Functions
Enzymes
: Speed up chemical reactions (catalysts)
Structural
proteins
: Provide support and shape (e.g., keratin in hair, collagen in connective tissue)
Transport
proteins
: Carry substances around the body or in cells (e.g., hemoglobin transports oxygen)
Hormonal
proteins
: Regulate body processes (e.g., insulin controls blood sugar)
Defensive
proteins
: Protect the body (e.g., antibodies in the immune system)
Contractile
proteins
: Enable movement (e.g., actin and myosin in muscles)
Storage
proteins
: Store amino acids or nutrients (e.g., ferritin stores iron)
Polypeptide Structure
Primary Structure
What it is: Linear sequence of amino acids in a polypeptide chain
Bond type: Peptide bonds (covalent bonds linking amino acids)
Function/Importance: Determines all higher-level structures; sequence dictates protein function
Secondary Structure
What it is: Local folding of the polypeptide chain into α-helices or β-pleated sheets
Bond type: Hydrogen bonds between the backbone atoms (not side chains)
Function/Importance: Adds stability and shape to regions of the protein
Tertiary Structure
What it is: 3D folding of the entire polypeptide chain
Bond types:
Hydrogen bonds
Ionic bonds
Disulfide bridges (covalent bonds between cysteine residues)
Hydrophobic interactions
Van der Waals Interaction
Function/Importance: Determines the protein’s overall shape and function
Quaternary Structure
What it is: Assembly of multiple polypeptide chains into a functional protein complex
Bond types: Same as tertiary
Function/Importance: Allows proteins with multiple subunits to work together (e.g., hemoglobin has 4 subunits)
Nucleic Acids
Nucleic Acids are biomolecules that store and transmit genetic information and help in protein synthesis. DNA holds the instruction for building and maintaining an organism, while RNA plays a critical role in protein synthesis and other cellular processes.
Monomer:
Nucleotides (made of a sugar, phosphate group, and nitrogenous base)
CHO(NP):
Carbon, Hydrogen, Oxygen, Nitrogen, Phosphorus
Bond Type:
Phosphodiester bonds (link nucleotides)
Examples:
DNA (deoxyribonucleic acid), RNA (ribonucleic acid)
Function:
Store genetic information, transmit instructions for protein synthesis, and regulate cellular activities
Nucleic Acids form two kinds of structures a double stranded DNA ( Deoxyribonucleic Acid) and a single stranded structure called RNA (Ribonucleic Acid)
A nucleotide has three main components:
Phosphate group
Pentose (5 carbon sugar):
DNA - Deoxyribose
RNA - Ribose
Nitrogenous Base:
DNA: Adenine, Guanmine, Cytosine, and Thymine
RNA: Adenine, Guanmine, Cytosine, and Uracil
There are three main types of RNA which we will get to in the DNA section.

💽 Vocab Macromolecules

Macromolecules Vocabulary
Macromolecule
: A very large molecule made up of smaller molecules, essential for life (includes carbohydrates, lipids, proteins, nucleic acids).
Polymer
: A large molecule made of repeating smaller units called monomers.
Monomer
: A small, basic unit that can join with other monomers to form a polymer.
Carbohydrate
: Macromolecule made of carbon, hydrogen, and oxygen; primary source of energy for cells.
Monosaccharide
: Simple sugar and the monomer of carbohydrates (e.g., glucose, fructose).
Disaccharide
: Two monosaccharides joined together (e.g., sucrose, lactose).
Polysaccharide
: Many monosaccharides linked together (e.g., starch, glycogen, cellulose).
Lipid
: Macromolecule made mostly of carbon and hydrogen; stores energy and makes up cell membranes (includes fats, oils, and phospholipids).
Fatty
Acid
: Long chain of carbon and hydrogen atoms; building block of many lipids.
Triglyceride
: Lipid made of one glycerol and three fatty acids; main form of stored energy.
Phospholipid
: Lipid with a hydrophilic head and hydrophobic tails; makes up cell membranes.
Steroid
: Lipid with four fused carbon rings (e.g., cholesterol, hormones).
Protein
: Macromolecule made of amino acids; performs a wide variety of functions in the body.
Amino
Acid
: Building block (monomer) of proteins.
Peptide
Bond
: Bond that links amino acids together in a protein.
Enzyme
: Protein that speeds up chemical reactions in living organisms.
Nucleic
Acid
: Macromolecule made of nucleotides; stores and transmits genetic
information
(DNA and RNA).
Nucleotide:
Monomer of nucleic acids, made of a sugar, phosphate group, and nitrogenous base.
DNA
(
Deoxyribonucleic
Acid
): Nucleic acid that stores genetic information.
RNA
(
Ribonucleic
Acid
): Nucleic acid that helps in protein synthesis.
Hydrophilic:
“Water-loving”; molecules or parts of molecules that dissolve in water (e.g., the phosphate head of a phospholipid).
Hydrophobic:
“Water-fearing”; molecules or parts of molecules that do not mix with water (e.g., fatty acid tails in lipids).
Polypeptide:
A chain of amino acids linked by peptide bonds; forms a protein when folded.
R-group (Side Chain):
Part of an amino acid that determines its properties and how it interacts with other amino acids.
Denaturation:
Process where a protein loses its shape and function due to heat, pH change, or chemicals.
Saturated Fat:
Lipid in which all carbon atoms are bonded to as many hydrogen atoms as possible; usually solid at room temperature.
Unsaturated Fat:
Lipid with one or more double bonds in the fatty acid chains; usually liquid at room temperature.
Functional Group:
Specific group of atoms in a molecule that determines its chemical properties (e.g., hydroxyl, carboxyl, amino).
Dehydration Synthesis:
Chemical reaction that joins monomers together by removing a water molecule.
Hydrolysis:
Chemical reaction that breaks polymers into monomers by adding a water molecule.

💽 Enzymes

Enzymes
What they do:
Enzymes are biological catalysts that
speed up chemical reactions
without being consumed in the process. They lower the activation energy needed for reactions to occur.
Key Terms Related to Enzymes
Substrate:
The molecule(s) that an enzyme
acts on
in a chemical reaction.
Active Site:
The specific region of the enzyme where the substrate
binds
.
Induced Fit:
The change in shape of the enzyme’s active site that occurs when the substrate binds, allowing a better fit.
Product:
The molecule(s) that are
produced
after the enzyme catalyzes the reaction.
Cofactors:
Non-protein
inorganic molecules or ions
(like Mg²⁺ or Zn²⁺) that help an enzyme function.
Coenzymes:
Organic molecules (often vitamins) that assist enzymes in catalyzing reactions.
Denatured:
When an enzyme
loses its shape and function
due to extreme temperature, pH, or chemical exposure, making it unable to bind the substrate.

📀 Cells

Cells
Endosymbiont Theory
(Explains how some eukaryotic organelles originated)
States that
mitochondria and chloroplasts
were once
free-living prokaryotes
These prokaryotes were
engulfed by a larger cell
and formed a symbiotic relationship
Over time, they became permanent organelles
Evidence:
Mitochondria & chloroplasts have
their own circular DNA
They have
double membranes
They
replicate independently
by binary fission
Their ribosomes are similar to
bacterial ribosomes
Cell Theory
All living organisms are made of
one or more cells
The cell is the
basic unit of structure and function
in living things
All cells arise from
pre-existing cells
Organelles & Cell Structures
Cell Membrane
(Prokaryotes & Eukaryotes)
Function:
Controls what enters and exits the cell
Structure:
Phospholipid bilayer with proteins (fluid mosaic)
Selectively permeable
Nucleus
(Eukaryotes only)
Function:
Stores genetic material (DNA), controls cell activities
Structure:
Double membrane called the nuclear envelope
Other:
Contains nuclear pores for transport
Nuclear Envelope
Function:
Separates nucleus from cytoplasm
Structure:
Two membranes with pores
Nucleolus
(Eukaryotes only)
Function:
Produces rRNA and assembles ribosomes
Structure:
Dense region inside nucleus
Not membrane-bound
Cytoplasm
(All cells)
Function:
Site of many chemical reactions
Structure:
Everything inside membrane except nucleus
Cytosol
Definition:
Fluid portion of cytoplasm
Contains:
Enzymes, ions, small molecules
Ribosomes
(All cells)
Function:
Protein synthesis
Structure:
rRNA + proteins
Free Ribosomes
Make proteins used
inside the cell
Bound Ribosomes
(on rough ER)
Make proteins for
secretion, membranes, or lysosomes
Endoplasmic Reticulum (ER)
(Eukaryotes only)
Rough ER
Function:
Protein synthesis & folding
Structure:
Flattened membranes with ribosomes
Smooth ER
Function:
Lipid synthesis, detoxification, Ca²⁺ storage
Structure:
Tubular membranes, no ribosomes
Mitochondria
(Eukaryotes only)
Function:
Cellular respiration, ATP production
Structure:
Double membrane, inner folds called cristae
Has own DNA and ribosomes
Golgi Apparatus
(Eukaryotes only)
Function:
Modifies, sorts, and packages proteins & lipids
Structure:
Stacked flattened sacs (cisternae)
Works closely with ER
Lysosomes
(Mostly animal cells)
Function:
Digests waste, old organelles, pathogens
Structure:
Membrane-bound sacs with enzymes
Acidic interior
Vacuoles
Animals:
Small; storage and transport
Plants:
Large central vacuole
Stores water, ions, pigments
Maintains turgor pressure
Chloroplast
(Plant cells only)
Function:
Photosynthesis
Structure:
Double membrane, thylakoids stacked into grana
Contains chlorophyll and its own DNA
Cell Wall
Plants:
Cellulose
Bacteria:
Peptidoglycan
Function:
Protection and structural support
Outside cell membrane
Nucleoid Region
(Prokaryotes only)
Function:
Contains DNA
Structure:
Not membrane-bound
DNA is circular
Flagella
Prokaryotes & some eukaryotes
Function:
Movement
Structure:
Long whip-like appendage
Pili
(Prokaryotes only)
Function:
DNA transfer (conjugation)
Structure:
Longer than fimbriae, fewer in number
Fimbriae
(Prokaryotes only)
Function:
Attachment to surfaces
Structure:
Short, numerous hair-like projections
Capsule
(Some prokaryotes)
Function:
Protection, prevents dehydration, immune evasion
Structure:
Sticky outer layer
Other:
Increases virulence
Plasmids
(Prokaryotes mainly)
Function:
Carry extra genes (e.g. antibiotic resistance)
Structure:
Small circular DNA
Other:
Replicate independently of chromosome
Centrosome
(Animal cells only; absent in most plant cells)
Function:
Main
microtubule-organizing center (MTOC)
Organizes the
mitotic spindle
during cell division
Structure:
Region of cytoplasm near the nucleus
Contains
two centrioles
arranged at right angles
Surrounded by
pericentriolar material (PCM)
Other notes:
Duplicates once per cell cycle
Essential for proper chromosome separation
Centrioles
(Animal cells only)
Function:
Help organize spindle fibers during mitosis and meiosis
Form
basal bodies
for cilia and flagella
Structure:
Cylindrical structures
Made of
9 triplets of microtubules (9×3 arrangement)
Found in pairs inside the centrosome
Other notes:
Oriented
perpendicular
to each other
Not membrane-bound
Cytoskeleton
(Eukaryotic cells)
Definition:
A network of protein fibers throughout the cytoplasm
Functions:
Maintains
cell shape
Provides
structural support
Enables
cell movement
Transports organelles and vesicles
Involved in
cell division
Three Types of Cytoskeletal Fibers
1. Microfilaments (Actin Filaments)
Protein:
Actin
Size:
Thinnest fibers
Structure:
Made of actin protein (G-actin) monomer that polymerize into filaments (F-actin)
Functions:
Maintain cell shape and support cell cortex
Involved in cell movements
Enable cytokinesis
Muscle contractions
Facilitates endocytosis and exocytosis
2. Intermediate Filaments
Protein:
Various (e.g. keratin)
Size:
Medium thickness
Structure:
Various fiber proteins (e.g. keratin, vimentin, lamin.), rope-like, strong and flexible
Functions:
Mechanical strength and stress resistant
Cell and Nuclear shape
Form nuclear lamin
3. Microtubules
Protein:
Tubulin
Size:
Thickest fibers
Structure:
Hollow tubes of tubulin dimers
Functions:
Acts as tracks for protein (kinesin & dynein)
Involved in intracellular transport
Components of cilia and flagella
Cell shape and provide structural support
Plants V.S. Animals
Both Have:
Cell membrane
Nucleus
Cytoplasm
Ribosomes
ER (rough & smooth)
Golgi apparatus
Mitochondria
Plant Cells Only
Cell wall
(cellulose) → support & shape
Chloroplasts
→ photosynthesis
Large central vacuole
→ storage & turgor pressure
Animal Cells Only
Lysosomes
→ digestion of waste
Centrosome & centrioles
→ cell division
Small vacuoles
(if present)
Eukaryotes vs. Prokaryotes
Both Have:
Cell membrane
Cytoplasm
Ribosomes
DNA (genetic material)
Eukaryotes Only
Nucleus → stores DNA and controls cell activities
Membrane-bound organelles → specialized structures (e.g., mitochondria, ER, Golgi apparatus, lysosomes, chloroplasts in plants)
Larger in size (typically 10–100 µm)
Complex internal structure
Prokaryotes Only
No nucleus → DNA located in nucleoid region
No membrane-bound organelles
Smaller in size (typically 0.1–5 µm)
Often have a cell wall (peptidoglycan in bacteria)
May have flagella or pili for movement and attachment

💽 Cellular Exchange

Cellular Exchange
Plasma Membrane
Structure & Function:
Structure:
Composed of a
phospholipid bilayer
with embedded proteins, cholesterol, and carbohydrates.
Amphipathic: a molecule with both hydrophilic and hydrophobic ends
Functions:
Regulates
entry and exit
of substances (selective permeability).
Provides
protection and support
to the cell.
Facilitates
cell signaling
via receptors.
Allows
cell recognition
through surface markers.
Anchors
cytoskeleton
for shape and movement.
Fluid Mosaic Model
Describes the plasma membrane as
flexible and dynamic
, like a mosaic of proteins floating in a lipid bilayer.
Components:
Proteins:
Integral proteins:
Span the membrane, involved in transport and signaling.
Peripheral proteins:
Attached to surface, involved in signaling, support, and recognition.
Carbohydrates:
Glycoproteins:
Proteins with sugar chains, important for cell recognition.
Glycolipids:
Lipids with sugar chains, also for recognition and stability.
Cholesterol:
Maintains membrane fluidity.
Membrane Fluidity Factors
Temperature: Higher temp → more fluid; lower temp → less fluid.
Fatty acid saturation: Unsaturated tails increase fluidity; saturated tails decrease it.
Cholesterol: Stabilizes fluidity, prevents too much rigidity or too much movement.
Types of Movement in the Membrane
Lateral movement:
Phospholipids move side to side within the same layer; very frequent, occurring millions of times per second.
Transversal (flip-flop) movement:
Phospholipids move between layers; rare because it requires energy and enzymes (flippases).
Diffusion
Definition:
Movement of molecules from
high to low concentration
down a
concentration gradient
until equilibrium is reached.
Concentration Gradient:
A difference in the concentration of a substance (such as ions, molecules, or solutes) between two areas. Substances naturally move
from areas of higher concentration to areas of lower concentration
(down the gradient) or, in active transport, are moved
against the gradient
using energy.
Transport Across Membranes
1. Passive Transport
– no energy required, molecules move down their concentration gradient.
Osmosis
Simple Diffusion:
Small, nonpolar molecules (O₂, CO₂) move directly through the membrane.
Facilitated Diffusion:
Uses
proteins
to help molecules cross.
Channels:
Allow molecules to pass through a pore.
Ligand-gated:
Open in response to a chemical signal.
Mechanical-gated:
Open when the membrane is physically stretched.
Always open (leak):
Constantly open.
Voltage-gated:
Open in response to changes in membrane potential.
Carrier Proteins:
Bind molecules, change shape, and transport them across.
Aquaporins:
Specialized channels for water.
2. Active Transport
– requires energy (ATP), moves molecules
against their concentration gradient
.
Osmosis
Pumps:
Primary:
Uses ATP directly to move ions or molecules (e.g., sodium-potassium pump).
Secondary:
Uses the energy from one molecule moving down its gradient to drive another molecule against its gradient (e.g., glucose-sodium co-transport).
Vesicular Transport:
Endocytosis:
Process of taking materials into the cell via vesicles.
Pinocytosis:
“Cell drinking”; uptake of liquids and dissolved substances.
Phagoctosis:
“Cell eating”; uptake of large particles or whole cells.
Receptor Mediated:
Specific molecules are taken in after binding to receptors.
Exocytosis:
Process of expelling materials out of the cell via vesicles.
Osmosis
Definition:
Diffusion of
water
across a semi-permeable membrane.
Osmotic Pressure:
Pressure required to stop water from moving across a membrane.
Types of Solutions & Effects on Cells:
Hypertonic:
Higher solute outside; water leaves cell →
shrinks (crenation in animal, plasmolysis in plant)
.
Hypotonic:
Lower solute outside; water enters cell →
swells (lysis in animal, turgid in plant)
.
Isotonic:
Equal solute; water moves equally →
cell maintains shape
.
Turgor Pressure:
The pressure of water inside a plant cell pushing against the cell wall, which helps the cell maintain its shape and provides structural support to the plant.
Hemolysis:
The bursting of red blood cells when they are placed in a hypotonic solution, causing water to rush into the cells and rupture them.
Secretory Pathway
Definition:
The route proteins take to be
made, modified, packaged, and transported
out of the cell or to membranes.
Steps:
Protein made by
ribosomes on rough ER
Protein enters
rough ER lumen
Transport vesicle carries protein to
Golgi apparatus
Golgi modifies, sorts, and packages proteins
Vesicles deliver proteins to:
Cell membrane (for secretion)
Lysosomes
Other parts of the cell
ER-Gogi Apparatus-Exocytosis

📀 DNA and Replication

DNA (Deoxyribosenucleic Acid)
Function
Stores
genetic information
Controls
protein synthesis
Passed from cell to cell during
cell division
Determines traits of an organism
Structure of DNA
DNA is a
double helix
(twisted ladder shape)
Hydrogen Bond between the two strands
Triple Hydrogen bond between Guanmine and Cytosine
Double Hydrogen Bond between Thymine and Adenine
Made of repeating units called
nucleotides
Each nucleotide contains:
Deoxyribose sugar
Phosphate group
Nitrogenous base
Nitrogenous Bases
Adenine (A)
Thymine (T)
Cytosine (C)
Guanine (G)
Complementary Base Pairing
A pairs with T (2 hydrogen bonds)
C pairs with G (3 hydrogen bonds)
Ensures accurate DNA replication
Antiparallel Structure
DNA strands run in
opposite directions
One strand runs
5′ → 3′
Other strand runs
3′ → 5′
5′ and 3′ Prime Ends
5′ end: phosphate group attached to 5th carbon
3′ end: hydroxyl (–OH) group on 3rd carbon
DNA polymerase can only add nucleotides to the
3′ end
This directionality is crucial for replication
Watson and Crick Model
Proposed the
double helix model
in 1953
Described complementary base pairing
Explained how DNA can
replicate accurately
Rosalind Franklin
Used
X-ray diffraction
Produced Photo 51
Provided critical evidence for the
helical structure
Her work was essential to the Watson–Crick model
Stages of DNA Replication
Initiation
begins at a specific DNA sequence called the origin of replication. Helicase binds at the origin and unwinds the DNA, forming a replication bubble. Two replication forks develop at either end of the bubble and move in opposite directions. Primase then lays down RNA primers on both template strands to allow DNA synthesis to start.
Elongation
occurs as DNA polymerase extends from the RNA primers, adding complementary nucleotides in the 5′ → 3′ direction. The leading strand is synthesized continuously toward the replication fork, while the lagging strand is synthesized away from the fork in short segments called Okazaki fragments. DNA ligase later joins these fragments to form a continuous strand.
Termination
happens when the replication forks meet or reach the ends of the chromosome. RNA primers are replaced with DNA, and DNA ligase seals any remaining gaps. In eukaryotic cells, telomerase extends the telomeres to ensure the ends of chromosomes are fully replicated. The result is two identical DNA molecules, each made of one original strand and one newly synthesized strand.
DNA Replication Enzymes
Helicase
Unwinds and separates the DNA double helix by breaking the hydrogen bonds between complementary base pairs, forming the replication fork.
Primase
Synthesizes short RNA primers on the DNA template strands, providing a free 3′-OH group needed for DNA polymerase to begin DNA synthesis.
DNA Polymerase
Adds complementary DNA nucleotides to the growing strand in the 5′ → 3′ direction. It synthesizes the leading strand continuously and the lagging strand discontinuously as Okazaki fragments, and also proofreads for errors.
DNA Ligase
Joins Okazaki fragments on the lagging strand by forming phosphodiester bonds, producing a continuous DNA strand.
Telomerase
Extends the telomeres at the ends of linear chromosomes in eukaryotic cells, preventing the loss of genetic information during replication.
Chargaff’s Rule
%A = %T
%C = %G
Total purines = total pyrimidines
Supports complementary base pairing
Semi-Conservative Replication
Each new DNA molecule contains:
One
original (parental)
strand
One
newly synthesized
strand
Ensures genetic continuity

💽 Vocab DNA/Replication

DNA and Replication:
Vocabulary-
DNA (Deoxyribonucleic Acid)
: Molecule that stores genetic information in all living organisms.
Nucleotide
: Building block of DNA and RNA, made of a sugar, phosphate group, and nitrogenous base.
Nitrogenous
Base
: Part of a nucleotide that forms the “rungs” of the DNA ladder; includes adenine (A), thymine (T), cytosine (C), and guanine (G).
Double
Helix
: Twisted ladder shape of DNA, formed by two strands of nucleotides.
Complementary
Base
Pairing
: Rule that A pairs with T and C pairs with G in DNA.
Chargaff’s
Rule
: In DNA, the amount of A equals T and the amount of C equals G, which explains complementary base pairing.
Replication
: Process by which DNA copies itself before cell division.
Semi-Conservative Replication
: Each new DNA molecule has one original strand and one newly synthesized strand.
Origin of Replication
: Specific location on DNA where replication begins.
Chromatin
: Uncoiled, loose form of DNA in the nucleus during interphase; condenses into chromosomes during cell division.
Helicase
: Enzyme that unwinds and separates the two DNA strands.
Primase
: Enzyme that synthesizes a short RNA primer to start DNA replication.
RNA
Primer
: Short segment of RNA added by primase to provide a starting point for DNA synthesis.
DNA
Polymerase
III
: Enzyme that adds new nucleotides to the growing DNA strand and proofreads for errors.
Ligase
: An enzyme that joins Okazaki fragments on the lagging strand to make a continuous strand.
Telomerase
: Enzyme that adds repetitive nucleotide sequences to the ends of chromosomes (telomeres) to protect them from shortening.
Leading
Strand
: DNA strand synthesized continuously toward the replication fork.
Lagging
Strand
: DNA strand synthesized in small fragments away from the replication fork.
Okazaki
Fragments
: Short segments of DNA synthesized on the lagging strand.
Sister
Chromatids
: Two identical copies of a single chromosome connected by a centromere, formed during DNA replication.

📀 Cell Cycle and Mitosis

Cell Cycle & Mitosis
The (eukaryotic) cell cycle is a series of events a eukaryotic cell goes through. It allows the cell to grow, duplicate DNA, and divide. It is divided into 2 main phases:
Interphase
- The longest phase where cells grow, duplicate DNA, and prepare for cell division. It is separated into 3 subphases:
G1 Phase (Gap 1)
- The first and longest phase in interphase where the cell grows.
Key events:
-Cell grows- The size of the cell increases.
-Protein synthesis- Essential proteins are made.
-Duplication of organelles- Organelles are duplicated for daughter cells.
-R-point (Restriction Point) or G1 Checkpoint- A checkpoint that decides if a cell goes to G0 or continues in the cycle.
S Phase (Synthesis Phase)
- The second phase in interphase where the cell’s DNA is duplicated.
Key events:
-DNA replication- The cell’s DNA is duplicated.
-Duplication of chromosomes- The chromosomes in the cell are duplicated to form sister chromatids.
-Duplication of Centrosomes- The centrosomes are duplicated to later help with chromosome separation.
-Intra-S checkpoint- A mechanism that checks for errors and damages in the DNA during DNA replication and stops the cycle if an error is detected.
G2 Phase (Gap 2)
- The last phase in interphase where cells continue to grow and prepare for division.
Key events:
-Cell growth- The cell continues to grow.
-Preparation- The cell makes proteins and organelles needed for division.
-DNA damage checkpoint or G2/M checkpoint- A checkpoint that stops the cycle if damaged or unreplicated DNA is detected.
M phase (Mitotic phase)
- A phase in the cell cycle where a cell divides into 2 daughter cells. This phase is separated into 2 subphases:
Mitosis (Nuclear Division)
- A type of cell division that results in 2 diploid, genetically identical daughter cells. This happens in somatic/body cells. This step has 4 stages:
-
Prophase
- First stage of mitosis
Key Events:
Chromosomes condense
Nuclear envelope and nucleolus break down
Centrosomes move to opposite ends of the cell and
spindle fibers form
-
Metaphase
- Second stage of mitosis
Key Events:
Sister chromatids move to the metaphase plate(cell’s equator)
Spindle fibers attach to chromosomes
Metaphase Checkpoint helps ensure that all chromosomes are in their correct places
-
Anaphase
- Third stage of mitosis
Key Events:
Sister chromatids are separated and pulled to opposite poles by spindle fibers
Cell elongates/Cytokinesis starts
-
Telophase
- Last stage of mitosis
Key Events:
Nuclear membrane and nucleolus reappear creating 2 nuclei
Chromosomes decompress into chromatin
Spindle fibers break down
Cytokinesis continues
Cytokinesis (Cytoplasmic Division)
- The division of the cytoplasm, organelles, and cell membrane in cell division. This is the last step in cell division and usually starts in late anaphase.
Types of Cytokinesis:
-Animal cells:
At the equator of the cell, a contractile ring (made of actin and myosin) forms
The contractile ring tightens which results in a cleavage furrow that pinches the cell membrane inward until the cell splits
-Plant cells (Pinching isn’t possible because of the stiff cell wall):
The Golgi apparatus sends out vesicles with cell wall materials which gather at the center of the cell.
The vesicles combine to form a cell plate
The cell plate develops into a new cell wall which splits the cell
Key ideas:
The G0 phase is where cells are in a resting state(not dividing, but instead performing normal functions) and is not part of the cell cycle. It is where a cell goes if it is not signaled to go to the S phase after G1 (R-Point). Some cells can go back to the cell cycle after going to G0 because  of an occurrence of a traumatic event, while other cells stay in G0 permanently.
The main purposes of cell division are growth/development, repair/maintenance, reproduction, and genetic continuity.
Video Resources:
Mitosis: The Amazing Cell Process that Uses Division to Multiply! (Updated)
The Cell Cycle (and cancer) [Updated]

💽 Vocab Cell Cycle and Mitosis

Cell Cycle Vocabulary
Cell Cycle:
Series of events a cell goes through as it grows, prepares for division, and divides.
Interphase:
Stage where a cell grows, performs normal functions, and prepares for division.
G1 phase:
Cell grows and performs normal functions.
S phase (Synthesis):
DNA is replicated so the cell has two copies of each chromosome.
G2 phase:
Cell continues to grow and prepares for mitosis.
Mitosis:
Division of the nucleus into two identical nuclei.
Cytokinesis:
Division of the cytoplasm, resulting in two separate daughter cells.
Chromatin:
The uncoiled, loose form of DNA found in the nucleus during interphase; it condenses into chromosomes during cell division.
Chromosome:
Tightly packed structure of DNA in the nucleus.
Chromatid:
One of two identical halves of a replicated chromosome.
Centromere:
Region where two sister chromatids are joined.
Spindle Fibers:
Protein fibers that help separate chromosomes during mitosis.
Centrosome:
Structure that organizes spindle fibers during cell division.
Prophase:
First stage of mitosis; chromosomes condense, spindle fibers form, and nuclear membrane begins to break down.
Metaphase:
Stage when chromosomes line up in the center of the cell.
Anaphase:
Stage when sister chromatids are pulled apart to opposite ends of the cell.
Telophase:
Stage when chromosomes arrive at opposite ends, nuclear membranes reform, and chromosomes begin to uncoil.
Daughter Cells:
Two genetically identical cells produced at the end of mitosis and cytokinesis.
Nucleosome:
The basic unit of DNA packaging in a eukaryotic cell, consisting of a segment of DNA wrapped around a core of histone proteins.
Sister Chromatids:
Two identical copies of a single chromosome that are connected by a centromere, formed during DNA replication.

📀 Meiosis

Meiosis
Meiosis is a type of cell division where a diploid parent cell (Germline cells) is divided into four genetically unique haploid cells (Sperm or egg [Gametes]). This is a type of nuclear division and is crucial for sexual reproduction. Meiosis usually happens after interphase in the cell cycle in the place of mitosis. It is divided into 4 sections with 2 main sections (Meiosis I and II):
Meiosis I (Reduction Division)- The first process that happens in meiosis where the diploid parent cell is divided into 2 genetically unique haploid cells. It is also called reduction division because the number of chromosomes is reduced by half. This process has four stages:
Prophase I- First stage in meiosis I
Key Events:
Chromatin condenses into chromosomes.
Homologous Pairing (Synapsis) happens where homologous chromosomes from each parent pair up and form a structure with four chromatids (Bivalent/Tetrad).
Crossing over happens where alleles of non-sister chromatids switch places making new gene combinations.
Nuclear envelope and nucleolus break down.
Centrosomes move to opposite poles of the cell and the
Meiotic spindle starts to form.
Metaphase I- Second stage in meiosis I
Key Events:
Homologous pairs move to the metaphase plate (cell’s equator) in a random order (Independent assortment).
Spindle fibers attach to homologous chromosomes.
Anaphase I- Third stage in meiosis I
Key Events:
Homologous pairs are pulled apart to separate poles of the cell by spindle fibers.
Cytokinesis starts.
Telophase I- Final stage in meiosis I
Key Events:
Nuclear membrane and nucleolus reappear creating 2 nuclei.
Chromosomes relax/decompress into chromatin.
Spindle fibers/the meiotic spindle break down.
Cytokinesis continues.
Cytokinesis- This is the division of the cytoplasm, organelles, and cell membrane. This is the same process that happens at the end of mitosis.
Meiosis II (Equational Division)- The third process that happens in meiosis where the 2 haploid cells from meiosis I are divided into 4 genetically unique haploid daughter cells. It is sometimes called equational division because it is similar to mitosis. There are 4 main stages that happen in both cells:
Prophase II- First stage of meiosis II
Key Events:
Chromatin condenses into chromosomes.
Nucleolus and nuclear envelope break down.
Centrosomes move to opposite ends of the cell and start to form the meiotic spindle/spindle fibers.
Metaphase II- Second stage of meiosis II
Key Events:
Chromosomes move to the metaphase plate.
Spindle fibers attach to chromosomes.
Anaphase II- Third stage of meiosis II
Key Events:
Sister chromatids are pulled to opposite ends of the cell by spindle fibers.
Cytokinesis begins.
Telophase II- Fourth stage of meiosis II
Key Events:
Nucleus and nuclear envelope reform.
Chromosomes decondense into chromatin.
The meiotic spindle/spindle fibers breakdown.
Cytokinesis continues.
Cytokinesis (2nd time)- This is again the division of the cytoplasm, organelles, and cell membrane. This is the same process that happens at the end of mitosis.
Video Resource:
Meiosis (Updated)

💽 Comparison of Mitosis and Meiosis

Comparison of Mitosis and Meiosis
Video Resource:
Mitosis vs. Meiosis: Side by Side Comparison

📀 Gene Expression

Gene Expression
What is Gene Expression?
Gene expression is the process by which the information stored in a gene (a specific sequence of DNA) is used to produce a functional biological product. In most cases, this product is a protein, although some genes code for functional RNA molecules such as rRNA and tRNA. Gene expression allows cells to carry out specialized functions and respond to their environment.
The flow of genetic information follows the central dogma of molecular biology, which states that genetic information flows from DNA to RNA to protein. Gene expression occurs through transcription and translation. In eukaryotic cells, RNA processing occurs between these two stages and is essential for producing a functional mRNA molecule.
Transcription
Definition
Transcription is the process by which the nucleotide sequence of a gene in DNA is copied into a complementary RNA sequence, specifically messenger RNA (mRNA).
Where it happens
Eukaryotes:
Transcription occurs in the nucleus, separating it from translation
Prokaryotes:
Transcription occurs in the cytoplasm, and transcription and translation can occur simultaneously
What transcription produces
mRNA
, which carries the genetic code to the ribosome
Other RNA molecules such as
tRNA
and
rRNA
, which are essential for translation
What is Required for Transcription
DNA template strand
, which contains the gene being expressed
RNA polymerase
, an enzyme that catalyzes RNA synthesis
RNA nucleotides
(adenine, uracil, cytosine, guanine)
Promoter region
, a specific DNA sequence that signals where transcription should begin
Transcription factors
(in eukaryotes), which help RNA polymerase bind to the promoter
Steps of Transcription
Initiation
RNA polymerase binds to the promoter region of the gene
In eukaryotes, transcription factors bind first and recruit RNA polymerase
The DNA double helix unwinds, exposing the template strand
Elongation
RNA polymerase moves along the DNA template strand in the
3’ → 5’ direction
RNA nucleotides are added to the growing mRNA strand in the
5’ → 3’ direction
Complementary base pairing occurs:
DNA adenine pairs with RNA uracil
DNA thymine pairs with RNA adenine
DNA cytosine pairs with RNA guanine
DNA guanine pairs with RNA cytosine
A phosphodiester bond forms between adjacent RNA nucleotides
Termination
RNA polymerase reaches a termination sequence
The mRNA molecule is released
The DNA strands re-anneal to reform the double helix
RNA Processing (Eukaryotes Only)
The RNA produced by transcription is called pre-mRNA and is not immediately functional. It must undergo several modifications to become mature mRNA capable of being translated.
RNA Processing Includes:
Addition of a
5’ cap
Addition of a
poly-A tail
RNA splicing
5’ Cap
A chemically modified guanine nucleotide added to the 5’ end of the mRNA
Protects the mRNA from enzymatic degradation
Helps the mRNA bind to ribosomes
Plays a role in the export of mRNA from the nucleus
Poly-A Tail
A long sequence of adenine nucleotides added to the 3’ end
Increases the stability and lifespan of mRNA
Prevents degradation by exonucleases
Helps ribosomes recognize and bind to the mRNA
RNA Splicing
Definition
RNA splicing is the process by which introns (non-coding regions) are removed from pre-mRNA and exons (coding regions) are joined together to form a continuous coding sequence.
Introns
Non-coding nucleotide sequences
Often involved in regulation of gene expression
Removed before translation
Exons
Coding nucleotide sequences
Remain in mature mRNA
Determine the amino acid sequence of the protein
Spliceosome
A large complex made of proteins and small nuclear RNAs (snRNAs)
Recognizes splice sites and catalyzes intron removal
Alternative Splicing (Extra)
Allows different exons to be combined in different ways
Enables a single gene to produce multiple proteins
Increases protein diversity in complex organisms
Translation
Definition
Translation is the process by which the nucleotide sequence of mRNA is decoded to produce a polypeptide chain, which later folds into a functional protein.
Where it happens
Occurs at ribosomes in the cytoplasm
Can occur on free ribosomes or ribosomes attached to the rough endoplasmic reticulum
What is Required for Translation
mRNA
, containing codons that specify amino acids
Ribosomes
, composed of rRNA and proteins
tRNA
, which carries specific amino acids
Amino acids
, the building blocks of proteins
Energy
, supplied by ATP and GTP
Key Molecules in Translation
mRNA
Contains codons, each made of three nucleotides
Determines the order of amino acids in the protein
tRNA
Each tRNA is specific to one amino acid
Contains an anticodon complementary to an mRNA codon
Ensures correct amino acid placement
Ribosome (rRNA)
Has a large and small subunit
Contains A (aminoacyl), P (peptidyl), and E (exit) sites
Catalyzes peptide bond formation
Steps of Translation
Initiation
The small ribosomal subunit binds to the mRNA
The start codon AUG is recognized
A tRNA carrying methionine binds to the start codon
The large ribosomal subunit joins to form a complete ribosome
Elongation
tRNA molecules enter the A site of the ribosome
Amino acids are linked by peptide bonds
The ribosome moves along the mRNA in the 5’ → 3’ direction
The polypeptide chain increases in length
Termination
Occurs when a stop codon (UAA, UAG, or UGA) enters the A site
Release factors bind instead of tRNA
The completed polypeptide is released
Ribosomal subunits separate
Codons
Codon
A sequence of three mRNA nucleotides
Specifies a particular amino acid or stop signal
Anticodon
A three-nucleotide sequence on tRNA
Complementary to the mRNA codon
Start Codon
AUG
Codes for methionine
Establishes the reading frame
Stop Codons
UAA, UAG, UGA
Signal the end of translation
Do not code for amino acids
Genetic Code Characteristics
Universal
in almost all organisms
Degenerate
, meaning multiple codons code for the same amino acid
Non-overlapping
, each nucleotide belongs to only one codon
Read in triplets
Overall Summary
Gene expression allows DNA to control cell structure and function
Transcription copies DNA into RNA
RNA processing produces stable, functional mRNA
Translation converts mRNA into protein
Codons determine the amino acid sequence
Introns are removed, and exons are expressed

📀 Genetics

Genetics
What Genetics Is
Genetics is the study of how traits are passed from parents to their children. Traits are characteristics like eye color, hair type, height, or even blood type. These traits are controlled by
genes
, which are sections of DNA in our cells. Think of genes like instructions or recipes that tell your body how to make certain features.
How Traits Are Inherited
Every person has
two copies of each gene
, one from their mother and one from their father.
Each gene can have
different versions
, called
alleles
. For example, the gene for eye color may have a brown allele and a blue allele.
The combination of alleles you inherit is your
genotype
. This is like your genetic “code.”
How your genotype shows up in real life—like the color of your eyes—is called your
phenotype
.
Dominant and Recessive Alleles
Dominant alleles
are stronger. If you have one dominant allele and one recessive allele, the dominant trait will appear.
Recessive alleles
are weaker. They only show up if you have
two copies
of the recessive allele.
Example:
B = brown eyes (dominant)
b = blue eyes (recessive)
If your genotype is
Bb
, your eyes will be brown (phenotype) because the B allele is dominant.
Only if your genotype is
bb
will you have blue eyes.
Homozygous vs. Heterozygous
Homozygous
: Both alleles are the same (BB or bb).
Heterozygous
: Two different alleles (Bb).
This matters because heterozygous individuals can carry a recessive trait without showing it.
Mendelian Genetics
Gregor Mendel discovered predictable patterns of inheritance by studying pea plants. He proposed three main laws:
Law of Segregation:
Each organism has two alleles for every gene. During gamete formation, the alleles separate so each gamete receives only one allele.
Example: A pea plant with genotype Bb will produce gametes with either B or b, not both.
Law of Independent Assortment:
Alleles for different traits separate independently during gamete formation.
Example: A plant’s gene for seed shape (round or wrinkled) does not affect its gene for seed color (yellow or green).
Law of Dominance:
Some alleles are dominant and mask the presence of recessive alleles.
Example: In pea plants, the allele for tall plants (T) is dominant over short plants (t). A plant with Tt will be tall.
Non-Mendelian Genetics
Not all inheritance follows Mendel’s simple patterns. Non-Mendelian genetics includes:
Incomplete Dominance:
Neither allele is completely dominant, resulting in a blend of traits.
Example: A red flower (RR) crossed with a white flower (rr) produces pink flowers (Rr).
Codominance:
Both alleles are expressed equally.
Example: In AB blood type, both A and B alleles are expressed.
Polygenic Inheritance:
Traits controlled by multiple genes, producing a wide range of phenotypes.
Example: Human height or skin color.
Multiple Alleles:
Some genes have more than two possible alleles.
Example: Blood type alleles (A, B, O).
Sex-Linked Traits:
Traits controlled by genes on sex chromosomes.
Example: Color blindness is often X-linked and affects males more than females because males have only one X chromosome.

💽 Vocab Genetics

Genetics:
Vocabulary-
Chromosome:
Long, tightly packed structure of DNA found in the nucleus of the cell
Gene:
Section of DNA on a chromosome that controls a specific trait
Trait:
Physical or biological characteristic, such as height, eye color, or blood type
Allele:
Version of a gene
Autosome:
Chromosome that is not a sex chromosome
Sex Chromosome:
Chromosome that determines biological sex
Complete Dominance:
When one allele completely masks another
Incomplete Dominance:
When neither allele is completely dominant, resulting in a blend of traits
Dominant Allele:
Allele that always shows its trait, even with only one copy present
Recessive Allele:
Allele that only shows its trait if both copies are recessive
Genotype:
Genetic makeup of an organism
Phenotype:
Physical traits of an organism, determined by its genotype
Heterozygous:
Having two different alleles for a trait
Homozygous:
Having two identical alleles for a trait
Probability:
Chance of a particular outcome occurring
Carrier:
Person with one copy of a recessive allele who does not show the trait but can pass it on
Punnett Square:
Diagram used to predict the probability of offspring inheriting particular traits from their parents
Mendelian Genetics:
Study of inheritance based on Gregor Mendel’s principles
Non-Mendelian Genetics:
Patterns of inheritance that do not follow Mendel’s laws, such as incomplete dominance, codominance, and polygenic traits
Genetic Disorder:
Disease or condition caused by abnormalities in an individual’s DNA
Gene Therapy:
Technique that uses genes to treat or prevent diseases by replacing, inactivating, or introducing genes into a person’s cells
Genetic Mutation:
Change in the DNA sequence that can affect an organism’s traits or health
Karyotypes:
Visual representation of all chromosomes in a cell, organized by size and shape
Locus:
Specific location of a gene on a chromosome
Stem Cell:
Undifferentiated cell capable of developing into different types of specialized cells
Recessive Genetic Disorder:
Disorder caused by two copies of a mutated gene, one from each parent
Dominant Genetic Disorder:
Disorder caused by only one copy of a mutated gene
Sex-Linked:
Traits or disorders associated with genes located on the sex chromosomes
Y-Linked:
Traits or disorders caused by genes located on the Y chromosome, passed from father to son
X-Linked:
Traits or disorders caused by genes on the X chromosome, often affecting males more than females
Pedigree:
Diagram showing the inheritance of traits across generations in a family
True Breeding / Pure Breeding:
Organisms that always produce offspring with the same traits when self-pollinated or mated with the same type
Hybrid:
Offspring resulting from the crossbreeding of parents with different traits

🤫 History
HISTORY
Questions

Unit 1 Notes

Unit 2 Notes

Unit 3 Notes

Unit 1 - Colonial Era NOTES

Unit 1 Notes-

The Colombian Exchange:
The
Colombian Exchange
was the exchange of
goods
,
plants
,
animals
,
people
, and
diseases
between
Europe
Africa
The Americas
Began after Christopher Columbus’s voyage in
1492
The Americas: North America, South America
Afro-Eurasia: Europe, Asia, Africa
Old World →  New World (went to America)
Animals: Horses, Cows, Pigs, Sheep
Plants: Wheat, Rice, Sugarcane, Coffee
Diseases: Smallpox, Measles,  Influenza
Impact on the Americans
Horses changed Native American life (transportation, hunting)
New Crops improved farming
Diseases killed millions of Native Americans who had no immunity
Old World →  New World (went to Europe & Africa)
Plants: Corn, Potatoes, Tomatoes, Cocoa, Tobacco
Impact on Europe & Africa:
Improved diets and population growth
New cash crops increased trade and wealth
Tobacco became a major colonial export
Effects of the Colombian Exchange
Positive Effects
Increased food supply
Growth of global trade
New agricultural products
Economic growth for Europe
Negative Effects
Spread of deadly diseases
Enslavement of Africans increased
Destruction of Native American populations and cultures
Connection to Slavery
Labor was needed to grow cash crops like sugar and tobacco
Led to the
Transatlantic Slave Trade
Enslaved Africans were forcibly brought to America
Connection to Colonial Economies
Helped create the
plantation system
Encouraged European nations to establish colonies
Increased wealth for European empires
Importance
Permanently connected the Eastern and Western Hemispheres
Changed diets, economies, and populations worldwide
Played a major role in the development of colonial America
Key Vocabulary
Colombian Exchange:
Transfer of goods, people, animals, plants, and diseases between the Old World and the New World
Old World:
Europe, Africa, Asia
New World:
The Americas
Cash Crop:
Crop grown to be sold for profit
Transatlantic Slave Trade:
Forced movement of Africans to America
Reasons for Colonization:
Christopher Columbus-
After waiting 17 years, the king and queen of Spain gave Columbus ships and money to make his journey.
He hoped to reach Asia by sailing across the Atlantic.
Christopher Columbus sailed the ocean blue in 1492
1492- Made the Atlantic crossing with the Nina, Pinta, and Santa Maria.
Many of his crew wanted to return home
In October 1492, Columbus landed on a small island in the Bahamas. He believed that he had reached Asia
Columbian Exchange-
Exchange of goods, ideas, disease, etc., between the Eastern and Western Hemispheres
Mercantilism
: European economic policy that stated that colonies existed for the good of the mother country. Raw materials like gold and furs were taken out of the New World to enrich the mother country.
I.e. Left North America: beans, corn, cacao, peanuts, pumpkins, squash, sweet potato, tobacco, tomatoes, turkey.
Left Africa: banana, cattle, citrus fruit, coffee beans, grapes, horses, onions, peaches, pigs, rice, sugarcane, wheat
Spanish-
The Spanish explored the North American continent for 3 main reasons:
To spread their religion- Christianity (God)
To expand their empire (Glory)
To find riches (Gold)
Spanish explorers called America the New World
French-
Explored North America for 3 reasons:
Searched for a Northwest Passage- a water route across the North American Continent
a source of wealth through the fur trade with the Native Americans
To convert Native Americans to Christianity
Louisiana Territory, and some islands in the Caribbean
Dutch-
The Dutch East India Company was chartered in 1602 to trade in Asia
The Dutch West India Company was established in 1621 to colonize and trade in America.
The Hudson river named after the English Captain
England-
Explored North America for three reasons:
In search or sources of wealth
convert Native Americans to Christianity
Claim land for England
England saw the North American natural resources as means for gaining wealth and international stature. Explorers risked their lives for fame, curiosity, and pride for their nation.
Early English unsuccessful colonies in North America included Newfoundland in Canada and Roanoke Island near North Carolina.
The English colonial Era began in 1607 with the first permanent settlement at Jamestown
This success will lead to the founding of the 13 English colonies in America
English Colonies:
Roanoke-
Sir Walter Raleigh
Previously, Raleigh had attempted to find El Dorado (the city of gold) in South America
Find El Dorado, forces Spain out of the Americas
There is no El Dorado
Granted permission to found a colony in North America
Sir Walter Raleigh is given a royal charter to the Virginia colony by Queen Elizabeth II
Forms the joint-stock company “The Virginia Company”
Virginia is named after the Virgin Queen
First Roanoke colony is abandoned in one year—1585
1587:  Reestablished under John White
1585-1506: Anglo-Spanish war
Spain begins amassing the Spanish Armanda—a huge naval fleet to escort a land invasion of England
Think they moved to Croatian Island but forced to move back to england
Jamestown-
First permanent English colony
Located in Jamestown, Virginia
1607– a group of merchants formed the Virginia Company of London
Settled in Jamestown, named after King James I
Many of the settlers spent their time looking for gold and did not prepare for the winter
First winter was harsh
Many settlers faced starvation and disease
Called “The Starving Time”
Settler John Smith helped colonists survive
Established a work ethic
“He that shall not work, shall not eat”
John Rolfe
Helped settlers discover that Jamestown was ideal for
growing tobacco
because of the fertile soil
Became one of the South’s largest cash crops
First Africans arrived in Jamestown in 1619
Carried on a Dutch ship and sold into slavery
Helped with planting and harvesting of the crops
Pilgrim/ Puritan/ Great Migration-
The Plymouth Company is given permission to settle in North America
The pilgrims were a group of radical Protestants called Puritans
Plymouth colony established in 1620 in Massachusetts
Plymouth settlers agreed a pact for self-government called the Mayflower compact
agreement formed a council government
In England, a group of Puritans, or Separatists, were being persecuted for their religious beliefs
1607: left England for the Netherlands for more religious freedom
Few years later, noticed children were becoming more Dutch than English
Difficult to find work
Decided to come to the New World for religious freedom and the chance at a better life
Called themselves Pilgrims— they were on a journey with religious purpose
1620 winter— landed in today Massachusetts after a two-month long journey
Called their settlement Plymouth
Landed in winter
Caused hardships since they could not plant crops and almost starved to death
Puritans that stayed in England= continued to be persecuted
Wanted to “purify” the Church of England of certain practices and beliefs that were too much like the Catholic Church
Group of wealthy Puritans received a charter for a settlement in the Massachusetts Bay Area
1630: Left England and the
Great Puritan Migration
began
1640: Over ten thousand Puritans had migrated to Massachusetts
Spread out all over New England to
Connecticut
,
Rhode Island
, and
New Hampshire
Three Colonial Regions:
New England Colonies-
Colonies:
Massachusetts
Connecticut
Rhode Island
New Hampshire
Geography & Climate
Rocky soil
Dense forest
Cold winters, short growing season
Economy
Fishing and whaling
Shipbuilding
Lumber and Trade
Small farms (subsistence farming)
Government & Society
Town meetings (direct democracy)
Representative government
Strong focus on education
Mostly Puritan influence (some religious intolerance early on)
Middle Colonies
Colonies
New York
Pennsylvania
New Jersey
Delaware
Geography & Climate
Fertile valleys
Mild climate
Good rivers and harbors
Economy
Farming (wheat, barley, oats)
Known as the
“Breadbasket Colonies”
Trade and manufacturing
Busy ports and cities
Government & Society
Representative assemblies
Religious tolerance
Culturally diverse population
Southern Colonies
Colonies
Virginia
Maryland
North Carolina
South Carolina
Georgia
Geography & Climate
Fertile soil
Hot, humid climate
Many rivers for transportation
Economy
Plantation system
Cash crops:
Tobacco, rice, indigo
Heavy reliance on enslaved labor
Government & Society
Mostly royal or proprietary colonies
The Church of England is dominant
Wealthy plantation owners have political power
Key Comparisons
Feature
New England
Middle Colonies
Southern Colonies
Climate
Cold
Mild
Hot
Soil
Rocky
Fertile
Fertile
Main Economy
Trade, fishing
Farming & Trade
Plantations
Farms
Small
Medium
Large
Labor
Family
Free workers
Enslaved Labor
Religion
Puritan
Tolerant
Anglican
Tips
Fishing/Shipbuilding=New England
Wheat/Breadbasket=Middle Colonies
Plantations/Tobacco=Southern Colonies
Government, Geography, and Society:
Magna Carta
Signed in 1215 by King John of England
First document to limit royal power
Key Principles:
No taxation without representation
right to a fair trial
rule of law apply to all
Influenced American Constitution
English Bill of Rights
Built upon Magna Carta’s Principles
Key freedoms established
Free speech in Parliament
Regular elections
No excessive punishments
Rights to petition the government
Direct influence on the Bill of Rights
Mayflower Compact
First written framework for America
Signed by 41 male pilgrims
created by a civil body
Established:
Rule by majority
Equal law for all
Common good/individual interest
House of Burgesses
Established in 1619 in Jamestown
First representative assembly in America
Made local law and set taxes
Member elected by property owning colonist
Pattern for future colonial government
Fundamental Orders of Connecticut
Founded by Thomas Hooker
Government by the people
Written constitution
Leaders
John Winthrop
“City upon the hill”
Governor of Massachusetts bay
Thomas Hooker
Champion of democracy
Founded colonist colony
John W
Reasons to Leave England
Religious freedom
Economic opportunities
Land ownership
escape persecution
Adventure and new beginnings
Promise of self government
Summary of Notes:
Reasons for European Colonization
Economic opportunity (land, trade, wealth)
Religious freedom (especially for English settlers)
Political freedom and self-government
3 G’s: Gold, God, Glory (especially Spain)
English Colonies Overview
The English colonies were divided into three regions:
New England Colonies
Middle Colonies
Southern Colonies
New England Colonies
Colonies: Massachusetts, Connecticut, Rhode Island, New Hampshire
Geography & Climate
Rocky soil
Dense forests
Cold winters, short growing season
Economy
Fishing & whaling
Shipbuilding
Lumber & Trade
Small farms
Government & Society
Town meetings (direct democracy)
Representative government
Strong focus on education
Religious freedom (varied by colony, stricter in Massachusetts)
Middle Colonies
Colonies: New York, Pennsylvania, New Jersey, Delaware
Geography & Climate
Fertile valleys
Mild climate
Good harbors and rivers
Economy
Farming (wheat, barley, oats)
Known as the “Breadbasket Colonies”
Trade and manufacturing
Urban centers and ports
Government & Society
Representative assemblies
Religious tolerance
Diverse population and cultures
Southern Colonies
Colonies: Virginia, Maryland, North Carolina, South Carolina, Georgia
Geography & Climate
Fertile soil
Hot, humid climate
Many rivers (used for transportation)
Economy
Plantation system
Cash crops: tobacco, rice, indigo
Heavy reliance on enslaved labor
Government & Society
Mostly royal or proprietary colonies
Church of England dominant
Large gap between wealthy plantation owners and poor farmers
Key Colonial Economies
Cash Crops: Crops grown to sell for profit
Plantations: Large farms growing cash crops
Transatlantic Slave Trade: Enslaved Africans brought to the Americas to work on plantations
Important Settlements & Dates
1607 – Jamestown
First permanent English settlement
Located in Virginia
Founded for economic reasons
1620 – Plymouth
Founded by Pilgrims
Located in Massachusetts
Important Documents
Mayflower Compact (1620)
Agreement signed by Pilgrims
First form of self-government in the colonies
Established majority rule
English Bill of Rights (1689)
Limited the power of the king
Protected individual rights
Influenced the American Bill of Rights
The Great Awakening
Religious revival movement
Emphasized personal faith and individual choice
Encouraged questioning authority
Helped support ideas of democracy and self-government
French Colonization
Focused on fur trade
Converted Native Americans to Christianity
Explored waterways and trade routes
Sought a passage to Asia
Spain in the Americas
Settled for Gold, God, and Glory
Built missions and colonies
Sought wealth and religious conversion
Key Vocabulary
Colony: A settlement controlled by another country
Representative Government: Elected officials make decisions for the people
Self-Government: People govern themselves
Religious Tolerance: Acceptance of different religious beliefs
Plantation: Large farm focused on cash crops

Unit 1-Practice Questions

Questions:
Why did many people choose to settle in the English Colonies?
What was the Mayflower Compact?
How did the 1st great awakening contribute to the rise of the representative government in the colonies?
Which factor contributed the most to the transatlantic slave trade?
What were some of the factors of the Middle colonies?
What were some of the factors of the New England colonies?
What were some of the factors of the Southern colonies?
Why did the French decide to settle in America?
What were the 3 G’s?
Which European country settled for the 3 G’s?
What is the significance of 1607?
What is the significance of 1620?
Where is Jamestown located?
What is a cash crop and what were they grown on?
Where was tobacco grown?
What current document did the English Bill of Rights influence today?
Explain two reasons why the Southern colonies relied heavily on enslaved labor.
How did geography and climate shape the economy of the New England Colonies?
Describe the importance of representative assemblies in the English colonies
Why were rivers important to the development of the Southern Colonies?
Compare the economies of the Middle Colonies and the Southern Colonies.
How did religious beliefs influence settlement patterns in the English colonies?
Why was Jamestown considered a risky location for a colony at first?
Explain how the Mayflower Compact helped influence later democratic ideas in America.
What role did cash crops play in the growth of colonial economies?
Why did European nations compete to establish colonies in North America?
Multiple Choice Practice Questions
Which colony is known for town meetings and self government?
Virginia
Massachusetts
South Carolina
Georgia
The Middle Colonies were often called the “breadbasket” because they:
Had many bakeries
Produced large amounts of grain
Imported food from Europe
Focused on fishing
Which crop was MOST associated with the Southern colonies?
Wheat
Corn
Tobacco
Fur
Which group signed the Mayflower Compact?
Puritans
Quakers
Pilgrims
Anglicans
Which factors MOST contributed to the success of plantation farming in to South?
Rocky soil
Cold climate
Fertile soil and long growing seasons
Small family farms
Which document influenced the American Bill of Rights?
Magna Carta
Mayflower Compact
English Bill of Right
Articles of Confederation
Which colony was founded primarily for economic reasons?
Plymouth
Massachusetts Bay
Jamestown
Pennsylvania
Why did Spain settle much of the Americas?
Fur trade and farming
God, Gold, and Glory
Religious freedom
Self-government
Which region had the most religious tolerance?
New England Colonies
Middle Colonies
Southern Colonies
Spanish Colonies
Which year marks the founding of the first permanent English settlement in North America?
1492
1607
1620
1776

Unit 1-Practice Questions Answer Key

Questions Answer Key:
Why did many people choose to settle in the English Colonies?
They wanted religious freedom and a new beginning, otherwise they would face religious persecution
What was the Mayflower Compact?
An agreement signed by the pilgrims that was the first form of self-government; 1620
How did the 1st great awakening contribute to the rise of the representative government in the colonies?
The 1st great awakening contributed by emphasizing individual opinions and religious freedom.
Which factor contributed the most to the transatlantic slave trade?
The Columbia’s exchange contributed the most
What were some of the factors of the Middle colonies?
Fertile valleys, waterways, urban centers
mild climate, all year round agriculture
representative systems, individually founded colonies
”breadbasket”, farm small grains & dairy, trading at ports
religious tolerance, equality, diverse populations
New York, Pennsylvania, New Jersey, Delaware
What were some of the factors of the New England colonies?
Rocky soil and dense forest
What were some of the factors of the Southern colonies?
Why did the French decide to settle in America?
What were the 3 G’s?
Which European country settled for the 3 G’s?
What is the significance of 1607?
What is the significance of 1620?
Where is Jamestown located?
What is a cash crop and what were they grown on?
Where was tobacco grown?
What current document did the English Bill of Rights influence today?
Explain two reasons why the Southern colonies relied heavily on enslaved labor.
How did geography and climate shape the economy of the New England Colonies?
Describe the importance of representative assemblies in the English colonies
Why were rivers important to the development of the Southern Colonies?
Compare the economies of the Middle Colonies and the Southern Colonies.
How did religious beliefs influence settlement patterns in the English colonies?
Why was Jamestown considered a risky location for a colony at first?
Explain how the Mayflower Compact helped influence later democratic ideas in America.
What role did cash crops play in the growth of colonial economies?
Why did European nations compete to establish colonies in North America?
Multiple Choice Practice Questions
Which colony is known for town meetings and self government?
Virginia
Massachusetts
South Carolina
Georgia
The Middle Colonies were often called the “breadbasket” because they:
Had many bakeries
Produced large amounts of grain
Imported food from Europe
Focused on fishing
Which crop was MOST associated with the Southern colonies?
Wheat
Corn
Tobacco
Fur
Which group signed the Mayflower Compact?
Puritans
Quakers
Pilgrims
Anglicans
Which factors MOST contributed to the success of plantation farming in the South?
Rocky soil
Cold climate
Fertile soil and long growing seasons
Small family farms
Which document influenced the American Bill of Rights?
Magna Carta
Mayflower Compact
English Bill of Right
Articles of Confederation
Which colony was founded primarily for economic reasons?
Plymouth
Massachusetts Bay
Jamestown
Pennsylvania
Why did Spain settle much of the Americas?
Fur trade and farming
God, Gold, and Glory
Religious freedom
Self-government
Which region had the most religious tolerance?
New England Colonies
Middle Colonies
Southern Colonies
Spanish Colonies
Which year marks the founding of the first permanent English settlement in North America?
1492
1607
1620
1776

Unit 2 - The American Revolution NOTES

Unit 2 Notes-

Colonization of North America:
Europeans Exploration:
Exploration began in the
late 1400s
, with
Christopher Columbus’s arrival
in the Americas in
1492
.
The nations wanted
land, wealth, trade, and power
in the New World
Spain, France, the Netherlands, and England
all competed for territory and influence
Europeans Exploration:
People came to the English colonies for
economic opportunities, religious freedom, and adventure
.
Economic Opportunity:
A chance to
own land and make money
from farming and trade
Religious Freedom:
Some groups wanted to practice their
religion without interference
Adventure and Opportunity:
A new start
in a new land
The First English Colonies:
Jamestown (1607):
First permanent English settlement
in North America
Located in
Jamestown, Virginia
Settlers struggled at first with
disease, hunger, and conflict with Native Americans
Plymouth (1620):
Established by the Pilgrims
, who came seeking religious freedom
They created the
Mayflower Compact
, an early form of representative government, where settlers agreed to make laws for the good of the colony
Found in
present-day  Massachusetts
The Road to Revolution:
Growing Tensions:
Taxes and trade regulations
imposed by the British Government to
pay debts from the French and Indian War
Lack of colonial representation
in the British Parliament
Unreasonable acts
imposed on the colonists
Acts Passed by Parliament:
Royal Proclamation of 1763:
After the French and Indian War, Britain
banned settlement and exploration west of the Appalachian Mountains
to reduce conflict with Native Americans
The colonists were very
angry
because many wanted to
move west and profit from land
Helped
build resentment
toward British control
Sugar Act of 1764:
Britain placed a
tax on imported sugar and molasses
to raise money and cut down on smuggling
The colonists protested because Britain was
taxing them without giving them representation
in Parliament
This was
one of the first laws that upset colonists
Stamp Act of 1765:
Required colonists to buy a stamp for all
legal papers, newspapers, and printed materials
It was the
first direct tax
on the colonies
Representatives from
nine of the thirteen colonies
met at the
Stamp Act Congress in New York
to make a petition against the act
Colonists protested,
“
No taxation without representation
,”
and the act was repealed, but anger stayed high
Quartering Act of 1765:
Colonists had to
house British soldiers
in their homes
This was seen as a
violation of privacy
and other rights, and the colonists started to resent the government
Declaratory Act of 1766:
Passed right after the Stamp Act was repealed
Said
Parliament could make laws for the colonies
“in all cases whatsoever.”
Colonists saw this as
Britain asserting total control
Townshend Acts of 1767:
Taxes were placed on everyday items such as
glass, lead, paint, paper, and tea
Fines
were placed on colonists who were caught
smuggling
these items into their homes
This led to
boycotts of British goods, protests, and tensions being further increased
Tea Act of 1773:
Allowed the British East India Company to sell tea cheaply, undercutting colonial merchants
Caused the
Boston Tea Party
Made it so that only the  British East India Company was allowed to sell tea
Boston Tea Party:
On
December 16, 1773
, the
Sons of Liberty
disguised themselves as Native Americans. They boarded three British ships in the Boston Harbor and dumped
342 chests of tea
into the harbor as a way to protest British taxation.
The Coercive (Intolerable)  Acts of 1774  :
The Boston Harbor was closed
until all the tea that was dumped was paid for
Town meetings were limited to
one a year
Any British official accused of breaking a law could be
tried in Great Britain
instead of the colonies
This led to the
First Continental Congress
in September of that year
Battles of the Revolution:
Lexington and Concord (April 19, 1775):
First Battle
of the American Revolution
British troops marched to
seize colonial weapons
Colonial militia known as the
Minutemen
resisted
Colonists won
and showed that they could fight back
Bunker Hill (June 17, 1775):
Colonists defended
Breed’s Hill
The British
attacked three times
The
British won
but suffered heavy casualties
Battle of Trenton (December 26, 1776):
Washington
led troops across the Delaware River
Surprise attack
on Hessian soldiers
The
colonists won
Boosted morale after many defeats
Battle of Princeton  (January 3, 1777):
Washington attacked
British forces after Trenton
The
colonists won
and strengthened American confidence
Forced the British to retreat
from much of New Jersey
⭐Battle of Saratoga (September-October 1777):
Known as the
turning point
in the Revolution, as the French joined the colonists in the war
British General Burgoyne was surrounded and led to the
British surrender
Battle of Valley Forge (Winter 1777-1778):
Continental Army suffered extreme hardship
Trained by Baron von Steuben
Army became for disciplined and unified
Showed perseverance
Battle of Monmouth (June 28, 1778):
First major battle after French alliance
Extremely hot
during the battle
It was  a
draw
Proved the Continental Army had improved
⭐Battle of Yorktown (September-October 1781):
Last major battle
of the American Revolution
American and French forces
trapped British General Cornwallis
British navy
blocked by French flee
t
The
Americans and French won
Treaty of Paris (1783):
Basic Facts (MUST MEMORIZE):
Signed September 3, 1783
Marked the official end
of The American Revolutionary War
Involved the

United States and Great Britain

Made the British recognize the

United States as an independent nation

American Negotiators:
Benjamin Franklin
John Adams
John Jay
Why the British agreed:
Defeated at Yorktown
War was
expensive and unpopular
France and Spain
were also fighting Britain
Britain wanted to
protect trade with the U.S
Main Terms of the Treaty:
Recognition of Independence
British Troop withdraw from the territory
Fishing rights were granted to the Americans off the coast of Newfoundland
Americans agreed to repay pre-war debts owed to British merchant

Unit 2- Questions

Questions:
What happened during the Revolutionary Era?
What is a Boycott and what did colonists boycott?
What are the Stamp Act, Quartering Act, and Sugar Act? What did they contribute to?
Why did Britain tax the colonists?
Explain the Proclamation of 1763.
What was one result of the Treaty of Paris of 1783?
What is the signature of the Battle of Saratoga?
Explain Unalienable Rights
Who is John Paul John’s?
What happens after the colonists dump tea into the Boston Harbor?
Which act required colonists to pay a tax on printed materials?
Explain the Boston Tea Party.
Explain the Articles of Confederation
Who is Crispus Attucks?
What is Shay’s Rebellion?
How did the American colonies react to the Intolerable Acts?
The 1st Continental Congress sent what to the King?
Explain the Battle of Yorktown
Explain the Battle of Saratoga
Explain Valley Forge
Who wrote the Declaration of Independence?
Who is John Hancock?
Why did the phrase “no taxation without representation” anger colonist so much?
How did the French and Indian War directly lead to tensions between Britain and the colonies?
Compare the Patriots and Loyalists. How did their views differ?
Why was the Proclamation of 1763 difficult for colonists to accept?
Explain how boycotts were an effective form of protest against British rule.
Why was the Stamp Act especially upsetting compared to other taxes?
How did the Intolerable acts push the colonies closer to war?
Why was the First Continental Congress important even though it did not declare independence?
Explain why Saratoga is considered at turning point in the war?
How did French support change the outcome of the American Revolution?
What weakness of the Articles of Confederation became clear after the war?
Why did events like Shays’ Rebellion worry American leaders?
How did Valley Forge strengthen the Continental Army despite harsh conditions?
Explain the significance of Yorktown in ending the war
How do unalienable rights connect to the Declaration of Independence?
Multiple Choice Questions:
Which event directly caused Britain to pass the Intolerable Acts?
Stamp Acts protests
Boston Tea Party
Battle of Lexington
Treaty of Paris
In which battle did the French come to the colonists aid?
Battle of Yorktown
Battle of Saratoga
Battle of Lexington
Battle of Princeton
What was significant about the Battle of Monmouth?
Not a battle
The Continental Army lost
First major battle after French alliance
Last battle of the revolution
The stamp act was the first ________ on the colonists.
War
Reason for conflict
Direct Tax
Massacre
How often were town meetings allowed after the Intolerable Acts were passed?
1
6
2
3
European exploration of the Americas began in the late 1400s because the European nations wanted________.
To escape wars in Europe
Land, wealth, trade, and power
To spread democracy
To form alliances with Native Americans
Which countries compete for territory and influence in the New World
Spain, Portugal, Germany, England
France, England, Italy, Spain
Spain, France, the Netherlands, adn England
England, Russia, Spain, and Sweden
Jamestown is significant because it was
The first colony with religious freedom
Founded by the Pilgrims
The first permanent English settlement in North America
Located in Massachusetts
Plymouth colony was founded in 1620 primarily for
Economic profit
Military defense
Religious freedom
exploration
Colonists were angry about British tak=xes mainly because
They were too low
They were unfairly enforced
Colonists had no representation in Parliament
They only affected merchants

Unit 2- Questions Answers

Questions:
What happened during the Revolutionary Era?
The American colonies protested British control, taxes, and laws, fought a war against Britain, and eventually gained independence, creating the United States of America.
What is a Boycott and what did colonists boycott?
A boycott is refusing to buy goods as a form of protest. Colonists boycotted British goods, especially tea, paper, glass, and other taxed items.
What are the Stamp Act, Quartering Act, and Sugar Act? What did they contribute to?
Acts that taxed sugar, molasses, printed materials, and required colonists to house soldiers.
Why did Britain tax the colonists?
To pay off debts from the French and Indian War and maintain British troops in the colonies.
Explain the Proclamation of 1763.
It banned colonists from settling west of the Appalachian Mountains to reduce conflict with Native Americans, which angered colonists who wanted land.
What was one result of the Treaty of Paris of 1783?
Britain officially recognized the United States as an independent nation.
What is the signature of the Battle of Saratoga?
It was the turning point of the war because it convinced France to help the colonists.
Explain Unalienable Rights
Rights that cannot be taken away, such as life, liberty, and the pursuit of happiness.
Who is John Paul John’s?
A naval hero of the American Revolution known for fighting the British navy and saying, “I have not yet begun to fight.”
What happens after the colonists dump tea into the Boston Harbor?
Britain passes the Intolerable (Coercive) Acts to punish Massachusetts.
Which act required colonists to pay a tax on printed materials?
The Stamp Act.
Explain the Boston Tea Party.
In 1773, colonists dumped British tea into the Boston Harbor to protest the Tea Act and taxation.
Explain the Articles of Confederation
The first U.S government; it created a weak central government with little to no power.
Who is Crispus Attucks?
The first person killed in the Boston Massacre.
What is Shay’s Rebellion?
A rebellion by farmers protesting high taxes and debt, showing the weakness of the Articles Confederation.
How did the American colonies react to the Intolerable Acts?
They united and formed the First Continental Congress.
The 1st Continental Congress sent what to the King?
A petition asking him to repeal unfair laws.
Explain the Battle of Yorktown
American and French forces trapped British General Cornwallis, leading to British surrender and ending the war.
Explain the Battle of Saratoga
American forces surrounded British troops, leading to surrender and French support.
Explain Valley Forge
A harsh winter camp where soldiers suffered but became stronger and better trained.
Who wrote the Declaration of Independence?
Thomas Jefferson
Who is John Hancock?
President of Continental Congress, famous for his large signature.
Why did the phrase “no taxation without representation” anger colonists so much?
They were taxed but had no voice in Parliament.
How did the French and Indian War directly lead to tensions between Britain and the colonies?
Britain went into debt and taxed the colonies to pay for the war.
Compare the Patriots and Loyalists. How did their views differ?
Patriots wanted independence, and loyalists wanted to stay loyal to Britain.
Why was the Proclamation of 1763 difficult for colonists to accept?
Colonists wanted western land they felt they earned.
Why was the Stamp Act especially upsetting compared to other taxes?
They hurt British businesses and showed colonial unity.
How did the Intolerable acts push the colonies closer to war?
It was the first direct tax affecting daily life.
Why was the First Continental Congress important even though it did not declare independence?
They punished all of Boston and removed self-government.
Explain why Saratoga is considered a turning point in the war?
It united colonies politically for the first time.
How did French support change the outcome of the American Revolution?
It brought French military support
What weakness of the Articles of Confederation became clear after the war?
France provided soldiers, ships, money, and weapons.
Why did events like Shays’ Rebellion worry American leaders?
It showed the government was too weak to maintain order.
How did Valley Forge strengthen the Continental Army despite harsh conditions?
Training and discipline improved despite hardship.
Explain the significance of Yorktown in ending the war
It forced Britain to give up the war.
How do unalienable rights connect to the Declaration of Independence?
The Declaration says government exists to protect them.
Multiple Choice Questions:
Which event directly caused Britain to pass the Intolerable Acts?
Stamp Acts protests
Boston Tea Party
Battle of Lexington
Treaty of Paris
In which battle did the French come to the colonists' aid?
Battle of Yorktown
Battle of Saratoga
Battle of Lexington
Battle of Princeton
What was significant about the Battle of Monmouth?
Not a battle
The Continental Army lost
First major battle after French alliance
Last battle of the revolution
The stamp act was the first ________ on the colonists.
War
Reason for conflict
Direct Tax
Massacre
How often were town meetings allowed after the Intolerable Acts were passed?
1
6
2
3
European exploration of the Americas began in the late 1400s because the European nations wanted________.
To escape wars in Europe
Land, wealth, trade, and power
To spread democracy
To form alliances with Native Americans
Which countries compete for territory and influence in the New World
Spain, Portugal, Germany, England
France, England, Italy, Spain
Spain, France, the Netherlands, and England
England, Russia, Spain, and Sweden
Jamestown is significant because it was
The first colony with religious freedom
Founded by the Pilgrims
The first permanent English settlement in North America
Located in Massachusetts
Plymouth colony was founded in 1620 primarily for
Economic profit
Military defense
Religious freedom
exploration
Colonists were angry about British taxes mainly because
They were too low
They were unfairly enforced
Colonists had no representation in Parliament
They only affected merchants

Unit 3 - The Constitution NOTES

Unit 3 Notes-

The Structure:
Use: “
P
lease,
L
et's
E
at
J
ello
S
oon
A
fter
S
ummer
R
eturns” to memorize the main structure
P
reamble
L
egislative Branch - Article I (1)
E
xecutive Branch- Article II (2)
J
udicial Branch - Article III (3)
S
tates Relations- Article IV (4)
A
mendment Procedures - Article V (5)
S
upremacy Clause - Article VI (6)
R
atification - Article VII (7)
Branches of the Government:
The
three branches
of the United States Government includes the,
Legislative, Executive, and Judicial Branch
Legislative Branch:
Creates
the laws through the congress
Congress includes the
Senate and House of Representatives
Senate: A group with
100 members
(2 from each state). It reviews and votes laws proposed by congress, approves treaties with other countries, and confirms presidential appointments (like judges and cabinet members). Each member serves
6 years.
House of Representatives: A group with
435 members
based on each state's population. It introduces most bills such as money and tax bills. Represents people through more detail as each representative serves
2 year terms.
Has the power to impeach officials
Executive Branch:
Enforces and carries
out the law,
signs
bills into laws or vetos (denies) them,
commands
the military, works with other countries, and
appoints
new judges and officials. ( with Senate approval)
Includes the
President, Vice President, Cabinet members, and Federal agencies
President
: The
leader
of the country and head of the executive branch. The person who goes to foreign countries and acts as the face of the country.
Vice President:
Person who
assists
the presidents,  steps in for the president when they die or become unfit for the position, and presides over the Senate.
Cabinet Members:
A group of
advisors
made up of the heads of executive departments who help the President run the government. Includes heads of departments such as defense, Education, and treasury.
Federal Agencies:
Government
organizations
that carry out laws and provide services such as FBI, EPA, CDC, CIA,ETC
Judicial Branch:
Interprets and explains
the law by, deciding if laws follow the constitution, resolving disputes between the states or people, protecting individual rights, and overturning laws that violate the constitution
Includes the
Supreme Court and other lower federal courts
Supreme Court:
The
main court
of the United States. Includes
9 justices
who are appointed for
life terms.
They hear the most important cases throughout the nation.
Justices:
Judges of the Supreme Court who hears cases and makes the final decisions.
Federal Courts:
Lower courts that hear cases involving federal laws
Principles of  the Constitution:
Use:
P
lease
R
emember,
I L
ove
S
onic
C
hilli
F
ries
P
opular Sovereignty:
A government where people have the right to vote and change their government if it abuses their power
R
epublicanism:
A form of government in which the people exercise their power by voting for a political representative
I
ndividual Rights:
People having rights, liberties, and privileges
L
imited Government:
Government has limited power. They must follow the law
S
eparation of Powers:
When the power is divided among the three branches of government (Legislative, Executive, and Judicial)
C
hecks and Balances:
When the branches have the power to check the other branches. This prevents any one branch from overpowering the others.
F
ederalism:
The power to govern is shared between the national and state government
(could also remember:
ps
.
i
l
ove
c
heeks
fr :)
)
Amending the Constitution:
There are currently
27 amendments
to the U.S Constitution as of 2025
The first 10 amendments are known as the
Bill of Rights
which guarantees basic human rights and regulations
The process is
complex
on purpose to ensure the changes are carefully inspected and considered
For the changes to be made to the constitution, the congress or states must propose it
By Congress:
Atleast ⅔ of both the House and Senate must approve of the change
By the States:
⅔ of the states legislatures call for a national convention
After the change is proposed ¾ of the states (38 out of 50)
States can ratify by:
State legislatures or State conventions
Bill of Rights:
Amendment 1:
Freedom of
religion, speech, press, assembly, and petitions
Amendment 2:
The right to
keep and bear arms.
Amendment 3:
No soldiers can
live in people's homes
without permission
Amendment 4:
Protection from
unreasonable searches and seizures
Amendment 5:
Rights of the accused:
Due process, no self-incrimination, no double jeopardy
Amendment 6:
Right to a
fair, speedy, and public trial
with a jury and a lawyer
Amendment 7:
Right to a
jury trial in a civil cases
Amendment 8:
No cruel or unusual punishment
or excessive fines
Amendment 9:
People have
rights not listen in the constitution
Amendment 10:
Powers not given to the federal government belongs to the
states or the citizens of the country
Religion:(1st Amendment)
The First Amendment
contains the guarantees related to religion.,”The Congress shall make no law respecting an establishment of religion”
(Establishment Clause)
The government can’t establish a national religion or national church
We have the national right to
believe anything in religion
, but not to act on or practice that belief
Establishment Clause:
The government cannot create or support an official religion
Free Exercise Clause:
People are
free to practice their religion
as they choose, as long as it does not break the law
Citizenship:(14th Amendment)
Anyone
born in the United States
or
legally naturalized
is a U.S citizen
Citizens are
guaranteed equal protection
under the law
The government must follow
due process
,
as they must treat people fairly and follow the law
Natural Born Citizen:
A person who is
born
in a country or
born to parents of a country
Naturalized Citizen:
A person who
becomes a citizen through the naturalization process
,
this includes, taking and passing a citizenship test, applying for citizenship, and taking the oath of citizenship

Unit 3-Practice Questions

Open-Ended Questions:
Why did the Framers create three branches of government?
What is the Preamble, and why is it important?
What does Article I of the Constitution explain?
What is Congress, and what are its two parts?
How does the Senate represent the states?
How does the House of Representatives represent the people?
Why do members of the house serve shorter terms than the Senators?
What is one power of the Senate and one power of the House of Representatives?
What is the main role of the Executive Branch?
Why is the President considered the “face” of the United States?
Why does the President need Senate approval to appoint judges and officials?
What is the main job of the Judicial Branch?
Why are Supreme Court justices appointed for life?
What is the purpose of checks and balances?
How does separation of powers protect against abuse of power?
What is popular sovereignty, and why is it important in a democracy?
What does federalism mean?
Why is the process of amending the Constitution difficult?
What is the Bill of Right, and why was it added to the Constitution?
Why is freedom of religion important to individual rights?
What does the Establishment Clause prevent the government from doing?
WHat does the Free Exercise Clause prevent the government from doing?
What does the 14th Amendment say about citizenships?
What is the difference between a natural-born citizen and a naturalized citizen?
Why is equal protection under the law important for citizens?
What was the 1st Amendment, and why was it important?
Multiple Choice Questions:
Which branch of government is responsible for making laws?
A. Executive
B. Judicial
C. Legislative
D. Federal
How many members are in the U.S. Senate?
A. 50
B. 100
C. 435
D. 538
Which part of Congress introduces most money and tax bills?
A. Senate
B. House of Representatives
C. Supreme Court
D. Cabinet
Which branch includes federal agencies like the FBI and EPA?
A. Legislative
B. Executive
C. Judicial
D. State
Which Article explains how the Constitution can be amended?
A. Article III
B. Article IV
C. Article V
D. Article VI
Which principle means the government must follow the law?
A. Popular Sovereignty
B. Republicanism
C. Limited Government
D. Federalism
Which amendment protects against unreasonable searches and seizures?
A. 1st
B. 4th
C. 5th
D. 8th
Which clause prevents the government from creating an official religion?
A. Free Exercise Clause
B. Supremacy Clause
C. Establishment Clause
D. Due Process Clause
How many states must ratify a constitutional amendment?
A. 25
B. 34
C. 38
D. 50
Which amendment explains powers not given to the federal government belong to the states or the people?
A. 9th
B. 10th
C. 8th
D. 7th

Unit 3-Practice Questions Answer Key

Open-Ended Questions:
Why did the Framers create three branches of government?
To prevent one group from having too much power and to protect liberty.
What is the Preamble, and why is it important?
The Preamble explains the goals of the Constitution, such as justice, liberty, and unity.
What does Article I of the Constitution explain?
Article I explains the Legislative Branch and how laws are made.
What is Congress, and what are its two parts?
Congress is the lawmaking body; it includes the Senate and the House of Representatives
.
How does the Senate represent the states?
Each Senate has two Senators, so all states are represented equally.
How does the House of Representatives represent the people?
House representation is based on the state population, so it reflects the people.
Why do members of the house serve shorter terms than the Senators?
Shorter terms keep Representatives more accountable to voters.
What is one power of the Senate and one power of the House of Representatives?
Senate approves treaties or confirms appointments; House: introduces money bills or impeaches officials.
What is the main role of the Executive Branch?
To enforce and carry out the laws.
Why is the President considered the “face” of the United States?
The President represents the U.S in foreign relations and leads the nation.
Why does the President need Senate approval to appoint judges and officials?
To provide checks and balances and limit executive power.
What is the main job of the Judicial Branch?
To interpret laws and decide if they follow the Constitution.
Why are Supreme Court justices appointed for life?
To keep them independent from political pressure.
What is the purpose of checks and balances?
To prevent one branch from becoming too powerful.
How does separation of powers protect against abuse of power?
It divides power so no single branch controls everything.
What is popular sovereignty, and why is it important in a democracy?
It means power comes from the people; citizens can vote and change government.
What does federalism mean?
Power is shared between national and state governments
Why is the process of amending the Constitution difficult?
To ensure changes are carefully reviewed and widely supported.
What is the Bill of Right, and why was it added to the Constitution?
It protects individual freedoms; it was added to limit government power.
Why is freedom of religion important to individual rights?
It protects people's ability to believe freely without government control.
What does the Establishment Clause prevent the government from doing?
It prevents the government from creating or supporting an official religion
What does the Free Exercise Clause prevent the government from doing?
It protects people's right to practice their religion as long as it follows the law.
What does the 14th Amendment say about citizenships?
Anyone born in the U.S or legally naturalized is a citizen.
What is the difference between a natural-born citizen and a naturalized citizen?
Natural-born citizens are born citizens; naturalized citizens become citizens through a legal process.
Why is equal protection under the law important for citizens?
It ensures all citizens are treated fairly under the law.
What was the 1st Amendment, and why was it important?
Multiple Choice Questions:
Which branch of government is responsible for making laws?
A. Executive
B. Judicial
C. Legislative
D. Federal
How many members are in the U.S. Senate?
A. 50
B. 100
C. 435
D. 538
Which part of Congress introduces most money and tax bills?
A. Senate
B. House of Representatives
C. Supreme Court
D. Cabinet
Which branch includes federal agencies like the FBI and EPA?
A. Legislative
B. Executive
C. Judicial
D. State
Which Article explains how the Constitution can be amended?
A. Article III
B. Article IV
C. Article V
D. Article VI
Which principle means the government must follow the law?
A. Popular Sovereignty
B. Republicanism
C. Limited Government
D. Federalism
Which amendment protects against unreasonable searches and seizures?
A. 1st
B. 4th
C. 5th
D. 8th
Which clause prevents the government from creating an official religion?
A. Free Exercise Clause
B. Supremacy Clause
C. Establishment Clause
D. Due Process Clause
How many states must ratify a constitutional amendment?
A. 25
B. 34
C. 38
D. 50
Which amendment explains powers not given to the federal government belong to the states or the people?
A. 9th
B. 10th
C. 8th
D. 7th

🔢 Algebra II
To the reader:
Within this section of the Study Guide, you will find: a study guide of everything that has been taught, resources for further studying, and a full mock Algebra II Pre-Comp Test.
Good luck, have fun, and I wish you the best on your math journey.
Benjamin Dong
Table of Contents
1 Linear Functions and Systems
2 Quadratic Functions and Equations
3 Polynomial Functions
4 Rational Functions
5 Rational Exponents and Radical Functions
6 Exponential and Logarithmic Functions
7 Trigonometric Functions
8 Mock Pre-Comp

Unit 1 - Linear Functions and Systems

Linear Functions and Systems
Key Features of Functions
What defines a function?
A function is a rule in mathematics that assigns each possible input with exactly ONE output.
Domain
The domain of a function is the set of all possible x-values that can be input into a function.
For example, the function
has the domain of
, since if
were less than
, the function would not be defined.
Range
The range of a function is the set of all possible y-values that can be output from a function.
For example, the function
has the range of
, since square roots are only defined for non-negative numbers.
X-Intercepts / Zeroes
An x-intercept occurs when the graph touches the x-axis.
This can be mathematically defined as when:
Y-Intercepts
A y-intercept occurs when the graph touches the y-axis.
This can be mathematically defined as:
Intervals where the graph is positive
When
Intervals where the graph is negative
When
Intervals where the graph is increasing
If, when looking from left to right on the graph, the function is going up, then the graph is increasing.
Intervals where the graph is decreasing
If, when looking from left to right on the graph, the function is going down, then the graph is decreasing.
Practice Problem
For this function, find the following: domain, range, x- and y-intercepts, and the intervals where the graph is positive, negative, increasing, and decreasing.
Answers
(in white text)
:
>
Domain: [-6,7] | Range: [-4,7] | x-intercepts: -5, -2, 5 | y-intercept: 5 | positive: [-6,-5) U (-2,5) |
>
negative: (-5,-2) U (5,7] | increasing: (-3,2) | decreasing: (-6,-3) U (2,7)
Transformations of Functions
Translations
. Shifts
up by
. 🔴
. Shifts
down by
. 🔵
. Shifts
right by
. 🟢
. Shifts
left by
. 🟣
In the following graph, the black graph is f(x), and the other graphs are translations of f(x).
Reflections
| reflects over the x-axis 🔴
| reflects over the y-axis 🔵
In the following graph, the black graph is f(x), and the other graphs are reflections of f(x).
Dilations
| dilates the function vertically by a factor of
| dilates the function horizontally by a factor of
.
(I will not provide a graph for this one. Just move the points after you graph them. Thank you!)
Piecewise
-Defined Functions
A piecewise function is defined as multiple functions built together with each function taking up a specific x-interval.
To graph it, take the intervals for where each function is defined and draw it in that interval.
If the interval is inclusive (≥ or ≤), draw a circle and fill it in at the end of the function. If the interval is exclusive (> or <), draw a circle but don’t fill it in.
(Author’s Note: This was a pretty short lesson, lol. Just keep moving.)
Arithmetic Sequences/Series
In an arithmetic sequence, each term is the sum of the preceding term plus a constant “d”.
where a
n
is the nth term, n is the index, and d is the common difference.
Recursive Formula
Explicit Formula
Summation Formula
a
n
=a
1
(n=1)
a
n
=a
n-1
+d (n>1)
a
n
=a
1
+(n-1)d
Sigma: ∑
We typically define ∑ as “the mathematical sum”.
In short,
.
Solving Equations and Inequalities by Graphing
Graphs:
To solve equations/inequalities, graph each function, and identify the x-coordinates of the intersection. At this point, equations would already be solved. Just plug in the y-value into a function to get the full coordinate.
However, for inequalities, you need to find the intersection of the two functions. It’s pretty much the same, just shade the respective parts for each function and see where they overlap.
Algebraically:
Set the two functions equal to each other and solve for x. For inequalities, look between every interval where the two functions meet and pick a point to see if the entire interval satisfies the equation.
Linear Systems
A linear system is a set of two or more lines that can intersect at 0, 1, or infinite points.
A linear inequality is a set of two or more inequalities whose intersection is a region.
Solving both of these has been previously defined.
Congratulations! You have reached the end of:

Unit 1 - Linear Functions

This study session should have taken about:
10 minutes - just reading
30 minutes - reading + practice problems

Unit 2 - Quadratic Functions and Equations

Quadratic Functions
Click on the arrow to the left of the ‘Unit 2 - Quadratic Functions’. This will open to the sub-topics. Click on them for the context.
2.1 - Vertex Form
Vertex Form of Quadratic Functions:
In practice, any quadratic function can be written using the following form. The ‘parent’ function of any quadratic function is f(x) = x^2.
Here is a demonstration of how vertex form works.
YT VID 1
Starting from our parent function, one can trace any quadratic function
upward(+ a) pro texas longhorns ‘horns up’                  downward(- a) anti texas longhorns ‘horns down’
(Texas at Austin Longhorn mascot)                          (Texas A&M player)
Practice Question:
.  Find vertex, axis of symmetry, maximum/minimum, domain, and range of f(x).
Answers right below in white text:
Vertex:
(8, 4.5)
Axis of Symmetry(AOS):
x = 8
Max or Min:
Min
Max/Min of f(x):
4.5
Domain:
(-∞, ∞)
Range:
[4.5, ∞)
2.2 - Standard Form
2-2: Standard Form of Quadratic Function
The standard form of a quadratic equation is given as:
.
When one plugs in x=0 to this, this person will get f(0) = a(0)
2
+ b(0) + c. This simplifies to f(0) = c. This means that the y-intercept is whatever the constant ‘c’ is. In our function
, we can write this as
.
We have successfully written the standard form to vertex form. The vertex is then
. Again, ‘a’ controls vertical stretch.
Show what you know:
Find the
y-intercept
and the
vertex
of 5x
2
- 22x + 94.
Right below this for answers:
y-intercept: (0,94)
vertex: (2.2, 69.8)
2.3 - Factored Form
2-3 Factored Form of a Quadratic Function:
The ‘factored form’ is the third and final form of the quadratic function.
It consists of a constant ‘a(a appears in all forms of the quadratic, by the way),’ that controls the vertical stretch/compression.
You have to
remember t
his. Otherwise, you begin to bald(trust me, it happened to me).
Anyways, where this gets different is the rest. In the factored form, p and q right here are
x-intercepts
. Note that x-intercepts are often called by some other name, including roots, zeros, and solutions. The reason we write it like this is because of the
zero product property
. The zero product property states that anything multiplied to zero is zero. Self-explanatory! Due to this property(and given ‘a’ isn’t 0), either x - p = 0 or x - q = 0. This means that x = p or x = q when f(x) = 0. That is how we get that the roots are (p, 0) and (q, 0)
Standard Form to Factored Form
The easiest way to from standard to factored consists of using the x-method
practice problem for demonstration:
factor completely: f(x) = 2x
2
+ 24x + 70
YT VID2
The X-method in factoring is especially useful for standard form. First, we put a • c in the top square, then b on the bottom square. We then try to find two factors that multiply to the top square and add to the bottom square.
Practice problem for demonstration:
Factor
.
In the video, if it wasn’t clear, I was taking pairs that multiplied to -24(a•c).
YT VID3
To summarize…
Factored form is the third and final form of quadratic functions. It looks like this:
. ‘a’ controls the vertical stretch/compression, while p and q are the x-intercepts(also called roots, solutions, zeros). Finally, we can convert from standard form to factored form to find zeros using the x method.
2.4 - Complex Numbers
2-4 Complex Numbers -
Complex Numbers and Operations:
What are complex numbers, again?
solve:
x
2
+ 16 = 0
x
2
= -16
x = 4√(-1)
Wait, what is the square root of -1?
If we recall correctly, x^2> 0. But that was for real numbers. Now, I will introduce
complex numbers
.
The complex number i is the basis for all of this.
i
is the square root of -1.
Powers of i
:
(n is an integer, positive and negative, btw)
Adding/subtracting complex numbers
:
Treat
like x, and combine like terms.
You wouldn’t combine 5 and 5x, so don’t combine 5 and 5
.
Multiplying complex numbers:
Multipl
ying complex numbers is pretty hard, but not too hard. I think it is best shown through video.
Write
as a complex number in the form of
.
YT VID 5
As you saw, FOIL(front, outer, inner, last) is the biggest trick, sprinkled in with the powers of i.
As a general rule,
.
Now, here is the hardest part about complex numbers.
Dividing complex numbers:
Dividing numbers is much more complicated and takes many more steps. I’m not going to throw a problem at you just yet. As a general rule,
. But how does one even get to this point?
YT VID6
The biggest thing to take away is that to kickstart rationalizing the denominator,
one must multiply numerator and denominator
by
the conjugate of the denominator
.
Check YOUR Understanding:
add:
(8+4i)+(-11+5i)
answer:
-3 + 9i
subtract:
(7+13i)-(-18+9i)
answer:
25 + 4i
multiply:
(8+4i)(-11+5i)
answer:
-108 - 2i
divide:
(7+13i)/(-18+9i)
answer:
(27+19i)/45
2.5 - Completing the Square
2-5 Completing the Square
Completing the square is an alternative to factoring and in some ways a precursor to the quadratic formula.
Let's say we have an arbitrary quadratic function.
As we know, the x-intercept of a function is when f(x) is 0. So, we can now write this as
. After this, we can simplify and solve for x. Actually, going down this path directly leads to finding the
quadratic formula
, a foolproof way to a) see how many real roots there are and b) find them.
Demonstration Problem:
Find the roots for the function
Answer:
Factoring into
Using the complete the square method(make a perfect square trinomial)
Notice how we add and then subtract by 2.25 to keep the function the same
Simplify further
Set f(x)=0 →
.
Solve for x:
As you see,
factoring would not have worked here
, especially because of the glaring radical in the roots. This is a great but tedious way to solve all functions.
There is somewhat of a problem here, however:
What if there is a negative in the radical?
This is a little tricky, but we didn’t do 2.4 in vain. Remember that
If we have a situation where the step before taking the root of everything
2.6
2.7

Unit 3 - Polynomial Functions

Polynomial Functions
Pre-Note: A Polynomial Function is a function where all terms are a constant coefficient multiplied by a positive integer exponent of x.
Graphing Polynomial Functions
Identify the leading term and degree.
It gives a basic idea of what the function will look like such as number of turning points and end behavior.
If the degree is even, then both ends of the function have the same end behavior. Given this, if a is positive, then
and
.
Or else it will be
and
If the degree is odd, positive a gives
and
, while negative a gives
and
.
Find the x- and y-intercepts.
To find the x-intercepts, solve the equation to find the roots.
To find the y-intercept, plug in x = 0 to the function.
Find some other points.
Plug in some other x-values to have a few more coordinates to work with.
Sketch!
Sketch a decent graph of the function given all of this information.
Four-Functions (except division) on Polynomials
To add and subtract polynomials, just combine like terms (same degree) and sum each of those groups together. (i.e. (x
2
+6x-7) + (-3x
2
-5x+2) = (-3+1)x
2
+ (6-5)x + (-7+2)
To multiply polynomials, use the distributive property. Then, combine like terms and sum each of those groups together.
Polynomial Identities
Identities
a
2
- b
2
= (a - b)(a + b)
(a + b)
2
= a
2
+ 2ab+ b
2
a
3
- b
3
= (a - b)(a
2
+ ab + b
2
)
a
3
+ b
3
= (a + b)(a
2
- ab + b
2
)
Binomial Expansion:
The expansion contains n+1 terms.
The coefficients of each term are numbers from the nth row of Pascal's Triangle.
The exponent of a is n in the first term and decreases by 1 in each successive term.
The exponent of b is 0 in the first term and increases by 1 in each successive term.
The sum of the exponents in any term is n.
Dividing Polynomials
Methods of Division:
Long Division
You divide the highest-degree term of the dividend by the highest-degree term of the divisor, subtract, bring down the next term, and repeat.
Synthetic Division
Write coefficients of the dividend in order.
Bring down the first coefficient.
Multiply it by c (from x-c), add to the next coefficient, repeat.
Remainder Theorem
Factor Theorem
Zeroes of Polynomial Functions
Theorems about the Roots of Polynomials
Transformations of Polynomials

Unit 4 - Rational Functions

4.1 - Inverse
Variation
and the
Reciprocal
Function
4.1.1 - The Inverse Variation
The inverse variation is one where the relation between x and y can be represented as
, where k is a constant. Unlike direct variation, where
(again, where k is a constant), x and y
multiply
to a certain constant. In this way, x and y

Unit 5 - Rational Exponents and Radical Functions

Unit 6 - Exponential and Logarithmic Functions

Unit 7 - Trigonometric Functions

🙂
Mock Pre-Comp

📑 English
ENGLISH: TABLE OF CONTENTS
Literature
Writing
Grammar
Ever since Mr. Kies has left us, we, the students, must become our own teachers and teach ourselves, for Ms. Burleigh and her “boyfriend” will not.
✍️ Writing
📚 Literature
Diction
Diction
: How words are used and chosen to convey tone, while also giving information on the author, like background, enunciation, and clarity.
Formal Diction
: Proper grammar, no use of slang, and is very professional. It is like an employee talking to their manager, with respect and dignity.
Informal Diction
: Casual and everyday speech. Like talking to a friend.
Colloquial Diction
: Informal, regional, everyday language, consisting of slang, contractions (can’t, won’t, etc), and regional phrases (y’all, soda, pop).
Elevated Diction
: Formal tone, used to create a signified, dignified, or grand tone. It is commonly used in research papers, formal speeches, and poetry.
Denotation
: Exact, dictionary meaning of a word.
Connotation
: Associated feelings, ideas, or cultural meanings that go beyond the literal definition of a word.
Figurative Language
Figurative Language
Metaphor
: Compares two things without using “like” or “as”, typically stating that one thing is another.
Simile
: Compares two things using “like” or “as”.
Personification
: Giving a non-human organism or object the ability to do what humans do, like actions and emotions.
Hyperbole
: An exaggeration of something to make it stand out more. Hyperboles are not meant to be taken literally.
Understatement
: The opposite of a hyperbole, making something seem less than what it is. Just like hyperboles, understatements are not meant to be taken literally.
Euphemism
: A word that is less harsh or mild that is used to substitute for a word that is considered too harsh or blunt when someone is referring to something unpleasant.
Oxymoron
: A figure of speech that consists of two opposites, like “dry rain” or jumbo shrimp”.
Pun
: A play on words where one uses words that sound alike or a word that has multiple meanings for humor.
Paradox
: A statement, situation, or idea that seems contradictory, but has more meaning, or a person with seemingly opposite traits. This is different from an oxymoron because it is usually larger scaled and more about people, ideas, and situations.
Irony
Irony
Irony
:
Dramatic Irony
: Irony where the audience knows of something or the situation of the character/s that the character/s of the story do not.
Situational Irony
: When the opposite event happens from what is expected.
Verbal Irony
: When the speaker says something that contradicts what they actually mean.
🧾 Grammar
GRAMMAR: TABLE OF CONTENTS
Verbs
Nouns
Complements
Modifiers
Pronouns
Verbals
Noun Identification Chart
Conjunctions
Sentence Classification
Verbs
Verbs
Definition:
Words used to describe an action or a state of being.
Types of verbs:
Action Verbs
:
Express physical or mental action
Transitive Verbs
:
Verbs followed by a word/words receiving the action. that answer the question
“What?”
or
“Whom?”
Ex)
“Bob
hit
Tim.”
(Who is receiving the action of being hit? Tim is being hit.)
Intransitive Verbs
:
Verbs that
DO NOT
have a word/words receiving the action that answer “What?” or “Whom?”
Ex)
“Tim
cries
.”
(Nobody is receiving the action of crying; it is intransitive.)
Linking Verbs
:
Connect a subject to a predicate nominative or predicate adjective.
Predicate Adjective:
Renames or Identifies
the subject
Ex)
“Tim
was
sad.”    (
“Was” links Tim to the adjective. “sad,” indicating that “sad” is the predicate adjective.)
Predicate Nominative:
Describes or Modifies
the subject
Ex)
“Bob
is
a bully.”    (
“Is” links Bob to a bully, meaning that “a bully” is the predicate nominative.)
Common LVs:
Forms of “to be”: (am, is, are, was, be, etc.)
Sensory Verbs: (feel, look, sound, taste, etc.)
Helping/Auxiliary Verbs
:
Assist the main verb
(linking or action) in a sentence.
Ex)
“Bob
is
being
mean.”    (
“Being” is the linking verb, while “is” is the helping verb.)
Verb Phrases:
Definition
: Phrases with an auxiliary verb(s) and a main verb (action/linking).
The phrases are named after the type of main verb.
Nouns
Nouns
Definition:
Words used to identify things, places, people, and ideas.
6 Types of nouns
:
Subject
:
A noun at the beginning of the sentence, not offset by commas. It is what or whom the sentence is about.
Ex)
“
Bob
is in trouble.”
Direct Object
:
A noun that receives the actions of a transitive verb. It needs a transitive verb.
Ex)
“Bob hit
Tim
.”     (
Who is receiving the action of being hit? Tim is being hit.)
Indirect Object
:
A noun that receives the direct object. There cannot be an indirect object without a direct object.
Ex)
“Bob gave
therapy
a try.”     (
What is being given? A try. What is being given a try? Therapy.)
Predicate Nominative
:
A noun that renames the subject after a linking verb.
Ex)
“Bob is
a bully
.”    (
“Is” links Bob to a bully, so “a bully” is the predicate nominative.)
Object of the Preposition
:
A noun in a prepositional phrase that completes the phrase.
Ex)
“In
the corner
, Tim was still crying.”
Appositive
:
Provides additional details of another noun that can be essential/restrictive or non-essential/non-restrictive. Appositive phrases contain an appositive and any words modifying it.
Essential/Restrictive
:
Are
NOT
offset by commas and usually specify a certain noun.
Ex)
“
My brother
Bob
is in loads of trouble.”
Non-essential/Non-restrictive
:
Are offset by commas, and the sentence can function without them.
Ex)
“
My brother
,
who is in lots of trouble
,
is named Bob.”
Tricks to Use:
(S/V/I/O)
is used to identify the subject, verb, indirect object, and direct object. If a sentence has all of the above, then it will
ALWAYS appear in that order.
The
“Pronoun Trick”
is a way to test if a word or group of words is a noun.
You replace the word or group of words with a pronoun
, this, or that, and if the sentence still functions, then it is a noun.
Complements
Complements
Definition:
Completes the meaning of a word. It may be one word or a group of words.
Types of Complements:
Object Complements
:
Identifies or describes
a direct object. It usually completes the meaning of a direct object and answers the question “What?” after a direct object. It can be nouns, pronouns, or adjectives.
Ex)
“The mayor appointed Ken
treasurer
.”
Subject Complements
:
Complete the meaning
of linking verbs. They rename or describe the subject. They must always occur right after a linking verb; hence, they need a linking verb. There are 2 types of Subject Complements:
Predicate Nominative
:
A noun that renames the subject after a linking verb.
Ex)
“Bob is
a bully
.” “Is” links Bob to a bully, so “a bully” is the predicate nominative.
Predicate Adjective
:
Describes the subject.
Ex)
“Tim is
sad
.” The verb “is” links Tim to the adjective “sad,” indicating that “sad” is the predicate adjective.
Modifiers
Modifiers
Definition:
Modify words in a sentence. What else do you think they do?
2 types of modifiers are Adjectives & Adverbs
Adjectives:
Definition:
Modifies a noun or pronoun. It answers:
“What kind?”
,
“Which one?”
,
“How many?”
, or
“How much?”
. It usually comes before a noun or pronoun it modifies.
Ex)
“Bob was a
troubled
kid.”
Proper Adjective
: Formed from a proper noun.
Ex)
“
Italian
bread.”
Articles
: A, an, and the.
Ex)
“
A
dog and
an
octopus.”
Pronouns as Adjectives:
Although these are pronouns, in special cases, they can be used as adjectives
Demonstrative Pronouns
: They point out specific places/people include
this, that, these, and those.
Ex)
“
That
dog and
this
octopus.” Demonstrative Pronouns.
Interrogative Pronouns
: They ask questions and include
what, which, who, whom, and whose.
Ex)
“
Which
dogs are here?” Interrogative Pronoun.
Indefinite Pronouns
: They don’t specify who or what they are talking about.
(Anyone, Someone, etc.)
Ex)
“
Some
dogs and
many
octopus.” Indefinite Pronouns.
Adverbs:
Definition:
Words that modify verbs, adjectives, or other adverbs. Many adverbs
end in -ly.
Adverbs answer the questions
“When?”
,
“Where?”
,
“How?”
, and
“To what extent?”
.  Adverbs make writing clearer and more exact.
Ex)
“Bob ate
quickly
.”
Prepositions:
(Adjectives & Adverbs)
Definition:
Words that show relationships of a noun or pronoun to another word in the sentence.
Common prepositions are locational and time-based.
Common Prepositions:
Locational: in, at, under, above, next to, between
Time-based: on, since, during, before, after, by
Directional: to, toward, into, across, past, around
Ex)
“The octopus is one of the most intelligent creatures
from
the sea.”
Prepositional Phrases
:
Begins with
a preposition
and ends with
a noun or pronoun
(Object of the Preposition).
Prep. Phrase as an Adjective
: it modifies a noun or pronoun
(“Which?” or “How many?”)
Ex)
“The octopus is one of the most intelligent creatures
from the sea.
”
(
This is an adjective phrase since it modifies “creatures.”
Prep. Phrase as an Adverb
: it modifies a verb, adjective, or adverb
(Where? When? Why? To what extent?)
Ex)
“
After getting into water
, an octopus swims.”    (
This is an adverbial phrase since it tells when the octopus swims or since it modifies “swims.”)
**All prepositions are part of a phrase**
Degrees of Comparison:
Definition:
Various forms of adverbs and adjectives to compare 2 or more things.
Positive Modifiers
:
Basic form of the modifier. Not a comparison.
Ex)
“Bob walks
fast
.”
Comparative Modifiers
:
Compares how verbs are accomplished. (‘-er’ or more/less)
Ex)
“Bob walks
faster
than Tim.”
Superlative Modifiers
:
Ultimate level. (‘-est’ or most/least)
Ex)
“Bob walks
fastest
.”
Pronouns
Pronouns
Definition:
Words used in place of one or more nouns
Functions:
Refer to a noun, otherwise known as an
antecedent
, that usually comes before the pronoun.
Make writing clearer, smoother, and less repetitive.
Be in place as an adjective.
Ex)
Bobby
feels
he
messed up.”    (
“He” is the pronoun, and “Bobby” is the antecedent.)
Types of Pronouns:
Personal Pronouns
:
Refer to people or things
. The 3 categories of personal pronouns are 1st, 2nd, and 3rd person.
First-person pronouns
: Refers to the person who is speaking. (Narrator)
Ex)
“
I
am a person.”
Second-Person Pronouns
: Refers to the person who is being spoken to.
Ex)
“
You
are a person.”
Third-Person Pronouns
:
Refers to anything else.
Ex)
“
He
or
she
is a person.”
Singular
Plural
First
I, Me
We, Us
Second
You
You
Third
He, Him, She, It
They, Them
Reflexive Pronouns
:
Personal pronouns that have -self or -selves added to certain personal pronouns. They refer back to the subject like a mirror that reflects, hence “Reflexive.”
(Myself, himself, herself, ourselves, themselves, and yourself.)
Ex)
“I am me,
myself
, and I.”
Intensive Pronouns
:
Formed by adding -self or -selves. Intensive pronouns add
emphasis
to other nouns or pronouns, so they usually follow the word they intensify.
Ex)
He
himself
is a person.”
Possessive Pronouns
:
Indicate
possession or ownership
of a noun or pronoun. They technically are determiners. Possessive pronouns with a noun: “my, your, our, his, her, its, and their.” Possessive pronouns on their own: “mine, yours, ours, his, hers, and theirs.”
Ex)
“That dog is
my
dog, which is
yours
too.”
Interrogative Pronouns
:
Pronouns that are used to
ask a question
. “What, which, who, whom, and whose” are all interrogative pronouns.
Ex)
“
Who
is that?”
Demonstrative Pronouns
:
A pronoun that points to a specific person, place, or thing. They consist of “This, that, these, and those.”
Demonstrative pronouns can also function as ADJECTIVES.
Ex)
“
That
is a person.”    (
“That” is a demonstrative pronoun that is acting as a subject.)
Ex)
“He is
that
person.”    (
Now, “that” is a demonstrative pronoun since it is modifying the word “person.”)
Indefinite Pronouns
:
Pronouns that don’t refer to a specific thing or person. Some words are “somebody, everyone, another, and everything.”
Ex)
“
Somebody
is lost.”
Relative Pronouns
:
Pronouns that connect a noun or pronoun to a dependent clause that provides more information about it. These consist of
“who, whom, whose, which, and that.”
Ex)
“He is a person
who
has two legs.”    (
Who is a relative pronoun since it introduces the clause “who has two legs,” describing “person.”)
Verbals
Verbals
Definition:
verbs in certain forms that don’t function as the simple predicate.
Rules:
Can not be the simple predicate
Can be used as its own or part of a verbal phrase
Their function overrides “verb.”
3 Types:
Gerunds
:
verbs ending in
-ing and acting like a noun
. Gerund phrases are a gerund and all of its modifiers and/or complements.
Gerunds as the 6 functions of a Noun:
Subject
:
Sewing
has never interested Steve.
Direct Object
: Steve doesn’t enjoy
sewing
.
Indirect Object
: Steve gave
sewing
a chance.
Predicate Nominative
: Now, Steve’s favorite hobby is
sewing
.
Object of the Preposition
: He often unwinds by
sewing
.
Appositive
: His favorite hobby,
sewing
, takes up his time.
To test if a verb is a gerund, you can use the
‘Pronoun Trick’
by replacing the verb with it, this, or that. If you are testing for a gerund phrase, you MUST make sure that you
replace the whole phrase with the pronoun,
or it won’t work.
Ex)
Golfing
is fun. —>
It
is fun.
Participles
: verbs
that act as adjectives
. It modifies a noun or pronoun. Participles tend to be embedded, meaning they are not obvious to find. Participial phrases are the participle and its complements and/or modifiers. It is usually found at the beginning of the sentence.
Forms of Participles:
Present
: ends in -ing.
Ex)
“I fell in the
swimming
pool.”
Past
: ends in -ed.
Ex)
“The predicate adjective is
embedded
.”
Infinitive
:
a verb form that
“to” usually precedes it,
and is a
noun, adjective, or adverb
. An infinitive phrase is an infinitive and its complements and/or modifiers.
Noun
: DO, IO, Appositive, Object of Preposition, Subject, PN
Ex)
To love
someone unconditionally is difficult.
(“To love” is the subject)
Adjective
:
modifying nouns and pronouns, answering the questions “What kind?”, “Which one?”, or “How many?”:
Ex)
He saw an opportunity
to escape
.
(“to escape” is modifying “opportunity”)
Adverb
:
modifying verbs, adjectives, and other adverbs, answering “When?”, “Where?”, “How?”, or “To what extent?”
Ex)
She rose
to speak
.
(“to speak” is modifying “rose”)
Steps to identify an infinitive
:
Pronoun Trick
- if it passes, it is a noun. If it fails…
Which or how many?
- answers “Which?” or “How many?” If it fails…
It's an adverb. - It’s an adverb.
;-;
Infinitives with “to” omitted: “see”, “hear”, “feel”, “watch”, “help”, “know”, “dare”, “need”, “make”, “let”, and “please”.
Ex)
They
helped (to) move
the couch.
**“To” plus a noun or pronoun is a prepositional phrase, not an infinitive.**
Noun Identification Chart:
Noun Identification Chart
:
Conjunctions
Conjunctions
Definition
: words or word phrases that connect other words, phrases, and clauses
Coordinating Conjunctions
:
(FANBOYS)
: For, And, Nor, But, Or, Yet, So
Subordinating Conjunctions
: after, although, as if, because, if, since, so that, than, unless, until, where, while.
Correlative Conjunctions
: conjunctions that work similarly to coordinating conjunctions, but work in pairs. Both conjunctions function as correlative.
These include:
Both… and
Not only… but also
Neither… nor
Either… or
Sentence Classification
Sentence Classification
Clause
:
contains a
subject
and a predicate.
Simple Subject
: the main noun or pronoun in a clause. The simple subject does the action of the action verb or is described/renamed by a linking verb
Main/Independent Clause
: a clause that can stand alone in a sentence; it expresses a complete thought
Subordinate/Dependent Clause
: a clause that contains a subject and a verb, but it cannot stand alone. It depends on another clause to function. It is usually found at the beginning of a sentence, separated by commas. Subordinate clauses commonly begin with relative pronouns or adverbs.
Predicate
:
contains the verb or verb phrase and usually anything after the verb
Simple Predicate
: the main verb or verb phrase
Complete Predicate
: all the words that tell what the subject does, including the simple predicate. Adverb phrases at the beginning of the sentences are also part of the complete predicate.
Within a sentence, every part of the sentence is either part of the subject or the predicate.
Common Mistakes
:
When there are multiple clauses, treat each clause as its own combination of subjects and predicates
Not recognizing when there is a compound subject or compound predicate, especially with correlatives.
Ex)
Neither the boy who fell off the swing set last week nor Steve
had known the muffin man.
Adjective phrases modifying the subject usually come before the simple predicate.
The object of the preposition can be mistaken for the subject
Types of Sentences
Simple Sentence
: contains one independent clause and no subordinate clauses. It may have a compound subject, a compound verb, and any number of phrases.
Compound Sentence
: contains two or more independent clauses and no subordinate clauses that are joined by a comma and a coordinating conjunction or semicolon.
Complex Sentence
: contains one independent clause and at least one subordinate clause.
Compound-Complex Sentence
: contains two or more independent clauses and at least one subordinate clause.
Misplaced Modifiers
Misplaced Modifiers
Misplaced Modifier
: A modifier or modifier phrase that is incorrectly put in a sentence, making it so that the sentence is unclear. A common misplaced modifiers are limiting words, such as “only.”
Ex)
“He threw the book to the person made of leather.” “He threw the book made of wood to the table.”
“Made of leather” could be modifying the person or the book, leaving the reader unclear of the meaning. So, the sentence should be reiterated to: “He threw the book made of wood to the person.”
Noun-Verb Agreement
Noun-Verb Agreement
Noun-Verb Agreement: a noun’s verb must agree with the plurality or singularity of a noun.
Singular Nouns:
The boy reads.
The girl runs.
The kid jumps.
Plural Nouns:
The boys read.
The girls run.
The kids jump.
Collective Nouns: Nouns that sum up a group of things, but itself can be plural or singular. Examples include “School/s,” “flock/s,” “group/s,” etc.”

🌮 Spanish(for fun)
(this is not required, Mr. Kies said that theres no precomp or comp but hes gonna look into making the teachers make a final worth 20% of our grade)
SPANISH: TABLE OF CONTENTS
Leccion Preliminar
Como te llamas?
De donde eres?
¿Cuántos años tienes?
El Salon de Clases
Los Días de la Semana
Lección 1: Hola, ¿qué tal?
Contextos
Estructura
Lección 2: En la clase

#️⃣ Algebra I
ALGEBRA 1:
Table of Contents:

Unit 1

1.1
1.2
1.3
1.4
1.5
1.6
1.7

Unit 2

2.1
2.2
2.3
2.4
2.5
2.6
2.7

Unit 3

Unit 1 Notes

Unit 1:

1.1: Operations on Real Numbers
Vocabulary:
Real Number:
A number that can be placed on the number line. Includes both rational and irrational numbers
Natural Numbers:
Any counting number starting from 1 (Ex: 1, 2, 3, …)
Whole Numbers:
Natural numbers including 0 ( Ex :0, 1, 2, 3, …)
Integers:
Whole numbers and their opposites, including zero (Ex: …, −3, −2, −1, 0, 1, 2, 3, …)
Rational Number:
A number that can be written as a fraction where the denominator is not zero (Ex: 3/4, −5, 0.25, 0.666…)
Includes: Integers, Terminating Decimals, Repeating Decimals
Irrational Number:
A number that cannot be written as a fraction; its decimal form is non-terminating and non-repeating (Ex:
, π)
Subset:
A set whose elements are all contained within another set
Classify:
To place a number into all sets to which it belongs
Terminate (Decimal):
A decimal that ends (Ex: 0.75)
Repeat (Decimal):
A decimal in which a digit or group of digits repeats forever (Ex: 0.333…)
Approximate:
A value that is close to the exact value but not exact (Ex:√5 ≈ 2.24)
Equivalent:
Having the same value, even if written in different forms (Ex:1/2 = 0.5)
ALL REAL NUMBER CHART
Understand Sets and Subsets:
A
set
is a collection of objects, such as numbers. An
element of a set
is an object that is in the set.
Write a set by listing the elements, enclosed in curly braces
The goal is to find the
overlap
Example Problems:
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ←
Main set
B = {2, 4, 6, 8, 10} ←
Subset of EVEN numbers
C = {5, 10}←
Subset of MULTIPLES of 5
Steps:
Find the numbers in all of the subsets (Write down the all the numbers listed (ex: 1 - 10, write 1,2,3..10) ) FInd the numbers in that set that are required ( ex: even numbers from 1-10, write down 2,4,6,8)
Lastly, if it asks for multiples of numbers (ex: multiple of 3) or anything after, write down the required numbers from the
second
set, not the original one
1.2: Solving Linear Equations:
Vocab:
Linear Equation:
An equation whose graph is a straight line and whose variables are only to the first power. (Ex: 2x + 3 = 11, y = −4x + 7)
Variable:
A symbol (usually a letter) that represents an unknown number (Ex: x, y, z)
Coefficient:
The number that multiplies a variable (Ex: 3x → coefficient is 3)
Constant:
A number without a variable (Ex: 2x + 5 → constant is 5)
Pratice Questions

Unit 2 Notes

Unit 2:

Vocabulary:
Slope-intercept form:
The linear formula
y = mx+b
, where
m
is the slope of the line and
b
is the y-intercept. The Slope-intercept form is useful when the slope and the
y-intercept
of the line are unknown
Point-slope form:
The linear formula
y - y1 = m(x - x1)
where
m
is the slope  and
(x1 , y1)
, is a specific point and
(x , y)
in any point on the line. The point-slope form is useful when you know the slope and a point that is not
( 0, b)
Standard Form:
The linear equation
Ax + By = C
, where
A
,
B,
and
C
are integers. The standard form is useful for graphing vertical or horizontal lines, for finding the
x-
and
y- intercept
, and representing certain situations in terms of constraints

Unit 3 Notes