Mr. Wadge's Math Shack
Welcome
Grade 12 Courses
Calculus 12
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Projects
Ch 0: PreCalculus Review
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0.0 One-Day Review
0.1 PreCalculus Review (part 1)
0.2 PreCalculus Review (part 2)
0.3 PreCalculus Review (part 3)
0.4 PreCalculus Review (part 4)
0.5 PreCalculus Review (part 5)
Ch 1 Limits and Rates of Change
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1.1 & 1.2 Tangent Problem / Limit of a Function
1.3 One-Sided Limits
1.3 (part 2) Intermediate Value Theorem
5.1 Vertical Asymptotes
5.2 Horizontal Asymptotes
1.4 Using Limits to Find Tangents
1.5 Velocity and Other Rates of Change
1.8 Review Exercises / 1.9 Chapter Test
Ch 2 Derivatives
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2.1 Derivatives
2.2 The Power Rule
2.3 The Sum and Difference Rules
2.4 The Product Rule
2.5 The Quotient Rule
2.6 The Chain Rule
2.7 Implicit Differentiation
2.8 Higher Derivatives
2.9 Review Exercises / 2.10 Chapter Test
Ch 3 Applications of Derivatives
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3.1 Velocity
3.2 Acceleration
3.3 Rates of Change in the Natural Sciences
3.5 Related Rates
3.6 Newton's Method
BONUS: Local Linear Approximation
3.7 Review Exercises / 3.8 Chapter Test
Ch 4 Extreme Values
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4.1 Increasing and Decreasing Functions (part 1 of 2)
4.1 Increasing and Decreasing Functions (part 2 of 2)
4.2 Maximum and Minimum Values
4.0 Existence Theorems
4.3 The First Derivative Test
4.4 Applied Maximum and Minimum Problems (part 1 of 2)
4.4 Applied Maximum and Minimum Problems (part 2 of 2)
4.6 Review Exercises / 4.7 Chapter Test
Ch 5 Curve Sketching
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5.0 Review
5.3 Concavity and Points of Inflection
5.4 The Second Derivative Test
5.5 A Procedure For Curve Sketching (part 1 of 2)
5.5 A Procedure For Curve Sketching (part 2 of 2)
5.6 Slant Asymptotes
5.7 Review Exercises / 5.8 Chapter Test
Ch 6 Trigonometry Review
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6.0 Review (part 1)
6.0 Review (part 2)
6.0 Review (part 3)
Ch 7 Derivatives of Trigonometric Functions
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7.1 Limits of Trigonometric Functions
7.2 Derivatives of the Sine and Cosine Functions (part 1 of 2)
7.2 Derivatives of the Sine and Cosine Functions (part 2 of 2)
7.3 Derivatives of Other Trigonometric Functions
7.4 Applications
7.5 Inverse Trigonometric Functions (part 1 of 2)
7.5 Inverse Trigonometric Functions (part 2 of 2)
7.6 Derivatives of the Inverse Trigonometric Functions
7.7 Review Exercises / 7.8 Chapter Test
Ch 8 Exponential and Logarithmic Functions
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8.1 Exponential Functions
8.2 Derivatives of Exponential Functions
8.0 Review of Logarithms
8.3 Logarithmic Functions
8.4 Derivatives of Logarithmic Functions
8.6 Logarithmic Differentiation
BONUS: Indeterminate Forms and L'Hôpital's Rule
8.7 Review Exercises / 8.8 Chapter Test
Ch 9 Area Under Curves
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9.1 Riemann Sums
9.2 The Trapezoidal Rule
9.3 Sigma Notation
9.4 Limit of Riemann Sums
Ch 10 Integration
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10.1 Antiderivatives
10.2 The Fundamental Theorem of Calculus
10.3 The Substitution Rule
10.4 Integration by Parts
Ch 11 Applications of Integrals
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11.1 The Average Value Theorem
11.2 Volume of Rotational Solids
11.3 Volume of Rotational Solids (part 2)
11.4 Volume of Rotational Solids (part 3)
11.5 Differential Equations
11.6 Slope Fields
Ch 12 Cumulative Review
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12.1 Cumulative Review for Chapters 1 – 3
12.2 Cumulative Review for Chapters 4 – 7
12.3 Cumulative Review for Chapters 8 – 9
PreCalculus 12
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Term Project Options
Review of Grade 11
Chapter 1: Sequence and Series
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1.1 Arithmetic Sequences
1.2 Arithmetic Series
1.3 Geometric Sequences
1.4 Geometric Series
1.5 Infinite Geometric Series
1.6 Chapter Review
Ch2: Transformations (First Half)
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2.1 Functions and Relations (review)
2.2 Arithmetic Combinations of Functions
2.3 Composite Functions
2.5 Inverse Functions (Part 1 of 2)
2.5 Inverse Functions (Part 2 of 2)
2.7 Chapter Review
Ch2: Transformations (Second Half)
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2.4 Transformations of Graphs (Part 1 of 2)
2.4 Transformations of Graphs (Part 2 of 2)
2.6 Combined Transformations
2.7 Chapter Review
Ch3: Polynomials
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3.1 Polynomials
3.2 Graphing Polynomial Functions
3.3 Division of Polynomials
3.4 The Remainder and Factor Theorems
3.5 Polynomial Applications
3.6 Chapter Review
Ch4: Radicals & Rational Functions
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4.1 Radicals
4.2 Graphing and Solving Radical Equations
4.3 Rational Functions
4.4 Graphing Rational Functions
4.5 Chapter Review
Ch5: Logarithms
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5.1 Exponents
5.2 Logarithmic Functions and their Graphs (Part 1 of 2)
5.2 Logarithmic Functions and their Graphs (Part 2 of 2)
5.3 Properties of Logarithms
5.4 Exponential and Logarithmic Equations
5.5 Applications of Exponential and Logarithmic Functions
5.6 Chapter Review
Ch6: Trigonometry (Pt. 1)
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6.1 Angles and their Measure
6.2 Trigonometric Functions of Acute Angles
6.3 Trigonometric Function - General & Special Angles
6.4 Graphing Basic Trigonometric Functions (part 1 of 3)
6.4 Graphing Basic Trigonometric Functions (part 2 of 3)
6.4 Graphing Basic Trigonometric Functions (part 3 of 3)
6.5 Application of Periodic Functions
6.6 Chapter Review
Ch7: Trigonometry (Pt. 2)
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7.1 Trigonometric Identities and Equations
7.2 Verifying Trigonometric Identities
7.3 Trigonometric Equations (part 1 of 2)
7.3 Trigonometric Equations (part 2 of 2)
7.4 Sum and Difference Identities (part 1 of 2)
7.4 Sum and Difference Identities (part 2 of 2)
7.5 Double Angle Identities
7.6 Chapter Review
Old Curriculum Material
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7.1 Fundamental Counting Principle (part 1 of 2)
7.1 Fundamental Counting Principle (part 2 of 2)
7.2 Permutations
7.3 Combinations
7.4 Binomial Theorem
7.5 Pathway Problems
7.6 Chapter Review
Final Exam
Foundations 12
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Ch 1: Logical Reasoning and Set Theory
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1.1 Connecting Words "And", "Or", "Not"
1.2 Set Theory (Part 1 of 2)
1.2 Set Theory (Part 2 of 2)
1.3 Venn Diagrams - Part One
1.4 Venn Diagrams - Part Two
1.5 Conditional Statements
1.6 Chapter Review
Ch 2: Permutations and Combinations
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2.1 The Fundamental Counting Principle (part 1 of 2)
2.1 The Fundamental Counting Principle (part 2 of 2)
2.2 Factorial Notation and Permutations (part 1 of 2)
2.2 Factorial Notation and Permutations (part 2 of 2)
2.3 Permutations with Restrictions
2.4 Permutations with Repetitions
2.5 Combinations - Part 1
2.6 Combinations - Part 2
2.7 Problem Solving with Permutations and Combinations
2.8 Chapter Review
Ch 3: Probability
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3.1 Probability Terminology and Notation
3.2 Odds and Probability
3.3 Mutually Exclusive Events and the Event "A ∪ B"
3.4 Independent / Dependent Events and the Event "A ∩ B"
3.5 Solving Problems Using Tables and Diagrams
3.6 Probability Involving Permutations and Combinations
3.7 Chapter Review
Ch 4: Exponential and Logarithmic Functions
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4.1 Review and Preview (part 1 of 2)
4.1 Review and Preview (part 2 of 2)
4.2 Analyzing Exponential Functions (part 1 of 2)
4.2 Analyzing Exponential Functions (part 2 of 2)
4.3 Analyzing Logarithmic Functions (part 1 of 2)
4.3 Analyzing Logarithmic Functions (part 2 of 2)
4.4 Interpreting Graphs of Exponential and Logarithmic Functions
4.5 Modelling Data Using Exponential and Logarithmic Functions
4.6 Chapter Review
Ch 5: Polynomial and Sinusoidal Functions
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5.1 Polynomial Functions of Degree Zero, One, and Two
5.2 Polynomial Functions of Degree Three
5.3 Modelling Data Using Polynomial Functions
5.4 Angular Measure - Degrees and Radians (part 1 of 2)
5.4 Angular Measure - Degrees and Radians (part 2 of 2)
5.5 Amplitude and Period
5.6 Horizontal & Vertical Shifts
5.7 Modelling Data Using Sinusoidal Functions
5.8 Chapter Review
Ch 6: Financial Mathematics
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6.1 Simple Interest andCompound Interest
6.2 Investments Using Compound Interest
6.3 Basic Loans Using Compound Interest (part 1 of 2)
6.3 Basic Loans Using Compound Interest (part 2 of 2)
6.4 Mortgages
6.5 Buying, Renting, and Leasing
6.6 Investment Portfolios
6.7 Chapter Review
Grade 11 Classes
PreCalculus 11
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Review (what you should already know)
Ch1: Factoring and the Quadratic Function
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1.1 Factoring
1.2 Factoring (More Complicated Types)
1.3 Properties of Quadratic Functions
1.4 The Standard Form of a Quadratic Function
1.5 Chapter Review
Ch2: Quadratic Transformations
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2.1 Finding the Equation of a Parabola
2.2 General Form to Standard Form
2.3 Vertex of a Parabola
2.4 Applications of Quadratic Functions
2.5 Chapter Review
Ch3: Quadratic Equations
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3.1 Solving Quadratic Equations by Factoring
3.2 Completing the Square and Square Root Property
3.3 The Quadratic Formula
3.4 Graphing Calculator and the Discriminant
3.5 Applications of Quadratic Equations
3.6 Chapter Review
Ch4: Systems of Equations
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4.1 Graphing Non-Linear Systems of Equations
4.2 Solving Non-Linear Systems Algebraically
4.3 Graphing Linear Inequalities in Two Variables
4.4 Graphing Non-Linear Inequalities
4.5 Applications of Inequalities
4.6 Chapter Review
Ch5: Radicals
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5.1 Radical Operations (Part 1 of 2)
5.1 Radical Operations (Part 2 of 2)
5.2 Simplifying Radicals
5.3 Adding and Subtracting Radical Expressions
5.4 Multiplying and Dividing Radical Expressions (Part 1 of 2)
5.4 Multiplying and Dividing Radical Expressions (Part 2 of 2)
5.5 Radical Equations
5.6 Chapter Review
Ch6: Rational Functions
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6.1 Properties of Rational Expressions
6.2 Multiplication and Division of Rational Expressions
6.3 Sums and Differences of Rational Expressions
6.4 Mixed Operations
6.5 Rational Equations
6.6 Graphing Rational Functions
6.7 Applications of Rational Equations
6.8 Chapter Review
Ch7: Trigonometry
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7.1 Angles and their Measure
7.2 The Three Trigonometric Functions
7.3 Special Angles
7.4 & 7.5 Oblique Triangles / Law of Sines (Part 1)
7.5 Law of Sines (Part 2)
7.6 Law of Cosines
7.7 Chapter Review
Ch8: Finance
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8.1 Investments and Loans
8.2 Effective Interest Rates and Annuities
8.3 Stocks and Bonds
8.4 Instalment Loans
8.5 Canadian Mortgages
8.6 Chapter Review
Final Exam Review
Old Curriculum Material
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1.1 Absolute Value
4.3 Absolute Value Functions
4.4 Solving Absolute Value Equations
4.5 Rational Functions
4.6 Reciprocal Functions (Part 1 of 2)
4.6 Reciprocal Functions (Part 2 of 2)
4.7 Chapter Review
Foundations 11
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Ch 1: Rates and Scale Factor
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1.1 Ratios and Rates
1.2 Visualizing Rates
1.3 Similar Figures
1.4 Perimeter, Area and Surface Area of Similar Figures
1.5 Volume of Similar Figures
1.6 Chapter Review
Ch 2: Geometry
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2.1 Geometry
2.2 Proofs
2.3 Polygons
2.4 Compass and Straightedge Construction
2.5 Chapter Review
Ch 3: Non-Right Angle Triangles
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3.1 Review of Sine, Cosine and Tangent for Right Triangles
3.2 Law of Sines (Part 1 of 2)
3.2 Law of Sines (Part 2 of 2)
3.3 Law of Cosines
3.4 Applied Problems
3.5 Chapter Review
Ch 4: Analyze Puzzles and Games
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4.1 Patterns
4.2 Inductive Reasoning
4.3 Deductive Reasoning
4.4 Puzzles and Games of Strategy
4.5 Chapter Review
Ch 5: Statistics
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5.1 Mean, Median and Mode
5.2 Standard Deviation
5.3 The Normal Distribution (Part 1 of 2)
5.3 The Normal Distribution (Part 2 of 2)
5.4 Confidence Interval for Means
5.5 Chapter Review
Ch 6: Linear Systems
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6.1 Review: Graphing a Linear Equation (Part 1 of 2)
6.1 Review: Graphing a Linear Equation (Part 2 of 2)
6.2 Linear Inequalities
6.3 Linear Programming
6.4 Application of Linear Programming
6.5 Chapter Review
Ch 7: Quadratic Functions
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7.1 Quadratic Functions (Part 1 of 3)
7.1 Quadratic Functions (Part 2 of 3)
7.1 Quadratic Functions (Part 3 of 3)
7.2 General Form of a Quadratic Function
7.5 Application of Quadratic Functions & Equations (part 1 of 2)
7.0 Graphing Non-Linear Systems of Equations (Part 1 of 2)
7.0 Graphing Non-Linear Systems of Equations (Part 2 of 2)
7.6 Chapter Review
Ch8: Math Research Project
Old Curriculum Material
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7.3 Quadratic Equations
7.4 Solving Quadratic Equations (part 1 of 2)
7.4 Solving Quadratic Equations (part 2 of 2)
7.5 Application of Quadratic Functions & Equations (part 2 of 2)
Workplace 11
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Ch 1: Slope and Rate of Change
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1.1 Ratios and Proportions
1.2 Rates / Solving Problems with Proportions
1.3 Slope
1.4 Angle of Elevation
1.5 Pitch, Grade, and Drop
1.6 Calculating Slope on a Coordinate Plane
1.7 Calculating Slope from Ordered Pairs
1.8 Rate of Change
1.9 Interpolation and Extrapolation
Ch 2: Graphs and Statistics
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2.1 Broken Line Graphs
2.2 Bar Graphs
2.3 Pictographs
2.4 Histograms
2.5 Review of Percents / Circle Graphs (part 1 of 2)
2.5 Making Circle Graphs (part 2 of 2)
2.6 Graphs and Technology
2.7 Other Types of Graphs
2.8 Misleading Graphs
2.9 Mean, Median, Mode, and Range
2.10 Standard Deviation
Ch 3: Scale Factor and Representations
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3.1 Scale Factor
3.2 Scale Diagrams
3.3 One-Point Perspective
3.4 Two-Point Perspective
3.5 Exploded Views and Component Parts
3.6 Orthographic Drawings
3.7 Isometric Drawings
3.8 Oblique Drawings
Ch 4: Financial Literacy
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4.1 Financial Institutions
4.2 Bank Accounts
4.3 Bank Statements
4.4 Simple Interest
4.5 Compound Interest
4.6 Compounding Periods
4.7 Credit
4.8 Loans
4.9 Mortgages
4.10 Mortgage Payments
4.11 Investments
Grade 8, 9, 10 Classes
Foundations & PreCalculus 10
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Problem Sets
Review (what you should already know)
Ch 1: Measuring Systems, Surface Area, and Volume
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1.1 Metric Systems
1.2 Imperial Systems
1.3 Converting Metric and Imperial Systems
1.4 Surface Area and Volume of Prisms (part 1 of 2)
1.4 Surface Area and Volume of Prisms (part 2 of 2)
1.5 Surface Area and Volume of Pyramids
1.6 Surface Area and Volume of Cylinders, Cones, and Spheres
1.7 Chapter Review
Ch 2: Radicals
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2.1 Number Systems
2.2 Greatest Common Factor and Least Common Multiple (part 1 of 2)
2.2 Greatest Common Factor and Least Common Multiple (part 2 of 2)
2.3 Squares and Square Roots
2.4 Rational And Irrational Numbers
2.5 Simplifying Radicals
2.6 Exponential Notation (part 1 of 3)
2.6 Exponential Notation (part 2 of 3)
2.6 Exponential Notation (part 3 of 3)
2.7 Chapter Review
Ch 3: Polynomials
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3.1 Classifying Polynomials (part 1 of 2)
3.1 Classifying Polynomials (part 2 of 2)
3.2 Multiplying Polynomials
3.3 Removing Common Factors
3.4 Factoring x^2 + bx + c (part 1 of 2)
3.4 Factoring x^2 + bx + c (part 2 of 2)
3.5 Factoring ax^2 + bx + c
3.6 Special Factors
Algebra Tiles
3.7 Chapter Review
Ch 4: Relations and Functions
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4.1 Relations
4.2 Functions
4.3 Linear Equations
4.4 Non-Linear Equations
4.5 Graphing with a Calculator
4.6 Chapter Review
Ch 5: Linear Functions
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5.1 Slope
5.2 Rate of Change
5.3 Graphing Linear Functions
5.4 Parallel and Perpendicular Lines
5.5 Applications of Linear Relations
5.6 Chapter Review
Ch 6: Linear Equations
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6.0 Rewriting Equations
6.1 Different Forms of Linear Equations (part 1 of 2)
6.1 Different Forms of Linear Equations (part 2 of 2)
6.2 Special Cases of Linear Equations
6.3 Equations of Parallel and Perpendicular Lines
6.4 Linear Applications and Modelling
6.5 Function Notation
6.6 Chapter Review
Ch 7: Solving Linear Systems
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7.1 Solving Linear Systems by Graphing
7.2 Solving Linear Systems by Addition
7.3 Solving Linear Systems by Substitution
7.4 Problem Solving with Two Variables
7.5 Chapter Review
Ch 8: Trigonometry
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8.1 Sine, Cosine, and Tangent for Right Triangles (part 1 of 2)
8.1 Sine, Cosine, and Tangent for Right Triangles (part 2 of 2)
8.2 Relationships Between Sine, Cosine, and Tangent
8.3 Special Angles
8.4 Applications of Trigonometry
8.5 Compound Trigonometry Applications
8.6 Chapter Review
Math 9
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Ch 1: Square Roots, Powers, and Exponent Laws
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1.1 Square Roots
1.2 Square Roots of Big & Small Numbers
1.3 Estimating Square Roots
1.4 Powers
1.5 Order of Operations
1.6 Exponent Rules
1.7 Power Rules
1.8 Review
Ch 2: Finance
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2.1 Salary and Wages
2.2 Commission
2.3 Tips and Piecework
2.4 Deductions
2.5 Simple Interest
2.6 Budgeting
Ch 3: Rational Numbers
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3.1 Rational Numbers
3.2 Operations with Integers
3.3 Operations with Decimals
3.4 Dividing Decimals
3.5 Multiplying and Dividing Fractions
3.6 Adding Fractions
3.7 Subtracting Fractions
3.8 Adding and Subtracting Negative Rational Numbers
3.9 Order of Operations with Rational Numbers
3.10 Review
Ch 4: Polynomials
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4.1 Defining Polynomials
4.2 Simplifying Polynomials
4.3 Adding & Subtracting Polynomials
4.4 Multiplying Polynomials
4.5 Dividing Polynomials
4.6 Order of Operations with Polynomials
Ch 5: Linear Equations
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5.1 One-Step Equations
5.2 Two-Step Equations
5.3 Using the Distributive Property
5.4 Combining Like Terms
5.5 Variables on Both Sides of an Equation
5.6 Clearing Fractions
5.7 Solving ANY Linear Equation
5.8 Writing Algebraic Equations
Ch 6: Proportional Reasoning
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6.1 Congruent Triangles
6.2 Similar Triangles (Part 1 of 2)
6.2 Similar Triangles (Part 2 of 2)
6.3 Similar Polygons
6.4 Scale Factor
6.5 Scale Diagrams
6.6 Unit Conversions
Ch 7: Statistics
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7.1 Statistics
Ch 8: Linear Relations
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8.1 Patterns (part 1 of 2)
8.1 Patterns (part 2 of 2)
8.2 Modeling Real-Life Situations
8.3 Cartesian Plane
8.4 Graphing a Table of Values
8.5 Interpolation and Extrapolation
Math 8
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Ch 1: Integers
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1.1 Multiplying Integers
1.2 Dividing Integers
1.3 Adding Integers
1.4 Subtracting Integers
Practice
Ch 2: Fractions
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2.1 Basic Fraction Skills
2.2 More Fraction Skills
2.3 Multiplying Fractions
2.4 Multiplying Mixed Fractions
2.5 Dividing Fractions
2.6 Dividing Mixed Fractions
2.7 Adding and Subtracting Fractions
2.8 Adding Mixed Fractions
2.9 Subtracting Mixed Fractions
2.10 Order of Operations with Fractions
Practice
Ch 3: Percent, Proportions, Ratio, and Rate
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3.1 Converting Fractions, Decimals, & Percents
3.2 Solving Proportions
3.3 Percents
3.4 Common Percent Problems
3.5 Ratios
3.6 Rates
3.7 Proportion Problems
Handouts
Ch 4: Square Roots and the Pythagorean Theorem
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4.1 Perfect Squares and Square Roots
4.2 Estimating Square Roots
4.3 Cube and Cube Roots
4.4 The Pythagorean Theorem
4.5 The Pythagorean Theorem (continued)
4.6 Applications of the Pythagorean Theorem
Practice
Ch 5: Probability and Statistics
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5.1 Probability
5.2 Probability with Cards
5.3 Tree Diagrams
5.4 Independent and Dependent Events
5.5 Dependent Events
5.6 Measures of Central Tendency
Ch 6: Linear Equations and Relations
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6.1 Algebraic Expressions
6.2 Solving One-Step Equations
6.3 Solving Two-Step Equations
6.4 The Distributive Property
6.5 The Cartesian Plane
6.6 Linear Relations
6.7 Linear Models
Ch 7: Geometry
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7.1 Area Review
7.2 Area of Composite Shapes
7.3 Volume of Prisms
7.4 Volume of Composite Shapes
7.5 Surface Area of Prisms
7.6 Surface Area of Cylinders
7.7 Surface Area of Composite Shapes
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2.9 Subtracting Mixed Fractions
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