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Grade 11 Mathematics

8. Absolute Value Functions (Content Coming Soon)

9. Quadratic Functions (Content Coming Soon)

9.1.

Function Notation

9.2.

Inverse of a Quadratic Function

9.3.

Factored Form of a Quadratic Function

9.4.

Vertex Form of a Quadratic Function

9.5.

Solving Using the Quadratic Formula

9.6.

Application Problems

9.7.

Systems of Equations Involving Quadratic Equations

10. Inequalities (Content Coming Soon)

10.1.

Linear Inequalities in One Variable

10.2.

Quadratic Inequalities in One Variable

10.3.

Linear Inequalities in Two Variables

10.4.

Quadratic Inequalities in Two Variables

11. Exponential Functions (Content Coming Soon)

Exponential Functions

11.5.

Transformations of Exponential Functions

12. Trigonometry (Content Coming Soon)

12.1.

Primary Trig Ratios

12.2.

Reciprocal Trig Ratios

12.3.

Common and Special Angles

12.4.

Primary Trig Ratios of Angles Between 0 and 360

Applications of Trigonometry (2D)

12.8.

Applications of Trigonometry (3D)

12.9.

Solving Trig Equations

12.10.

Proving Trig Identities

13. Sinusoidal Functions (Content Coming Soon)

13.1.

Periodic Functions and Properties

13.2.

Graphs of Sine and Cosine (Degrees)

13.3.

Transformation of Sinusoidal Functions

13.4.

Applications of Sinusoidal Functions

14. Discrete Functions (Content Coming Soon)

Pascal's Triangle and the Binomial Expansion

15. Financial Applications (Content Coming Soon)

Ordinary Simple Annuity

15.4.

Using Technology to Solve Financial Problems

15.5.

Investments and Loans with Regular Payments

15.6.

Buying and Leasing

Grade 11 Math

1. Real Number System

1.1.

Real Number System

1.2.

Interval Notation vs. Set Notation

2. Introduction to Functions

Properties of Parent Functions

2.4.

Determining Domain & Range

2.5.

Inverse Functions

3. Transformations of Functions

Stretches & Compressions

3.4.

Combining Transformations

4. Operations with Polynomials

4.1.

Review

4.2.

Adding and Subtracting Polynomials

4.3.

Binomial

\times

Binomial (Review)

4.4.

Multiplying Any Polynomials

5. Factoring Polynomials

5.1.

Common Factoring and Factoring by Grouping

5.2.

Factoring Simple Trinomials

y=x^2+bx+c

5.3.

Factoring Harder Trinomials

y=ax^2+bx+c

5.4.

Factoring Difference of Squares

5.5.

Factoring Perfect Square Trinomials

5.6.

Factoring Summary + Extra Practice

6. Radical Expressions and Functions

6.1.

Operations with Radicals

6.2.

Simplifying Radicals

6.3.

Solving Radical Equations

6.4.

Applications of Radical Functions

7. Rational Functions

7.1.

Rational Expressions and Functions

7.2.

Multiplying and Dividing Rational Expressions

7.3.

Adding and Subtracting Rational Expressions

7.4.

Solving Rational Equations

7.5.

Graphs of Rational Functions

8. Absolute Value

8.1.

Basics of Absolute Value

8.2.

Absolute Value Functions

8.3.

Solving Absolute Value Equations

9. Reciprocal Functions

9.1.

Reciprocal Functions

10. Quadratic Functions

10.1.

Quadratic Functions

10.2.

Properties of Quadratic Graphs

11. Factored Form of a Quadratic Equation

11.1.

Factored Form of a Quadratic Equation

11.2.

Determining the Factored Form of a Quadratic Equation

12. Vertex Form of a Quadratic Equation

12.1.

Vertical Stretches and Reflections

12.2.

Translations (Shifts)

12.3.

Graphing Quadratics in Vertex Form

12.4.

Determining the Quadratic Equation in Vertex Form

13. Completing the Square

13.1.

Exploring Perfect Squares

13.2.

Completing the Square (

x^2+bx+c

)

13.3.

Completing the Square (

ax^2+bx+c

)

14. Solving Quadratic Equations

14.1.

Solving Quadratic Equations by Factoring

14.2.

Solving Quadratic Equations by Completing the Square

14.3.

Solving Quadratic Equations Using the Quadratic Formula

14.4.

Discriminant Analysis (Determining the Number of Solutions/Roots from the Quadratic Formula)

14.5.

Solving Quadratic Equations Strategies

15. Systems of Linear & Quadratic Equations

15.1.

Solving Systems of Equations

16. Inequalities

16.1.

Solving Linear Inequalities in One Variable (Review)

16.2.

Solving Inequalities in Two Variables

16.3.

Solving Quadratic Inequalities in One Variable

17. Exponential Functions

17.1.

📝Review: Basic Exponent Rules

Characteristics of Exponential Functions

17.6.

Transformations of Exponential Functions

17.7.

Applications of Exponential Functions (Growth & Decay)

18. Trigonometry

18.1.

Primary Trig Ratios (Review)

18.2.

Solving Right-Triangle Problems (Review)

18.3.

Reciprocal Trig Ratios

18.4.

Special Angles & Special Triangles (Degrees)

18.5.

Trig Ratios for Angles Between 0° and 360°

18.6.

Solving Simple Trig Equations

19. Trigonometry with Non-Right Triangles

19.1.

Sine Law

19.2.

Sine Law - Ambiguous Case

20. Trigonometric Identities & Proofs

20.1.

Reciprocal & Quotient Identities

20.2.

Pythagorean Identities

20.3.

Proofs using Trigonometric Identities

21. Sinusoidal Functions (degrees)

21.1.

Periodic and Sinusoidal Functions

21.2.

Sinusoidal Functions (Sine and Cosine Graphs)

21.3.

Transformations of Sinusoidal Functions

21.4.

Applications of Trigonometric Functions

22. Sequences & Series

Recursive Sequences and Rules for Defining Sequences

Pascal's Triangle and the Binomial Expansion

23. Financial Applications

Investments and Loans with Regular Payments (Ordinary Simple Annuities)

23.4.

Buying and Leasing

Grade 10 Math

1. Linear Relations (Review)

2. Systems of Linear Equations

2.1.

Intro to Systems of Linear Equations

2.2.

Solving by Graphing

2.3.

Solving by Substitution

2.4.

Solving by Elimination (Part 1)

2.5.

Solving by Elimination (Part 2)

2.6.

Solving a System of Linear Equations - No Solution or Many Solutions

3. Analytic Geometry

3.1.

Pythagorean Therom (Review)

3.2.

Midpoint of a Line Segment

3.3.

Length of a Line Segment

3.4.

Equation of a Circle

4. Analytic Geometry: Geometric Properties

4.1.

Classifying Triangles

4.2.

Properties of Triangles

4.3.

Classifying Quadrilaterals

4.4.

Properties of Quadrilaterals

4.5.

Properties of Circles

5. Expanding Polynomials

\times

Binomial

5.3.

Binomial

\times

Trinomial

6. Quadratic Relations

6.1.

Quadratic Relations

6.2.

Properties of Quadratic Graphs

6.3.

Quadratic

x^2

vs Exponential

2^x

Graphs

7. Factored Form of a Quadratic Equation

7.1.

Factored Form of a Quadratic Equation

7.2.

Determining the Factored Form of a Quadratic Equation

8. Factoring Polynomials

Factoring Simple Trinomials

y=x^2+bx+c

8.4.

Factoring Harder Trinomials

y=ax^2+bx+c

8.5.

Factoring Difference of Squares

8.6.

Factoring Perfect Square Trinomials

8.7.

Factoring Summary + Extra Practice

9. Vertex Form of a Quadratic Equation

9.1.

Vertical Stretches and Reflections

9.2.

Translations (Shifts)

9.3.

Graphing Quadratics in Vertex Form

9.4.

Determining the Quadratic Equation in Vertex Form

10. Completing the Square

10.1.

Exploring Perfect Squares

10.2.

Completing the Square (

x^2+bx+c

)

10.3.

Completing the Square (

ax^2+bx+c

)

11. Solving Quadratic Equations

11.1.

Solving Quadratic Equations by Factoring

11.2.

Solving Quadratic Equations by Completing the Square

11.3.

Solving Quadratic Equations Using the Quadratic Formula

11.4.

Discriminant Analysis (Determining the Number of Solutions/Roots from the Quadratic Formula)

11.5.

Solving Quadratic Equations Strategies

12. Congruent & Similar Polygons/Triangles

13. Trigonometry of Right Triangles

13.1.

Pythagorean Therom (Review)

13.2.

Primary Trig Ratios (

\sin

\cos

\tan

)

13.3.

Finding Side Lengths in a Right Triangle

13.4.

Finding Angle Measures in a Right Triangle

13.5.

Solving Right Triangles

13.6.

Right Triangle Word Problems

14. Trigonometry of Acute Triangles

15. Measurements

Working with the SI & Imperial Systems

16. Algebra - Factors & Multiples of Numbers

16.1.

Prime Factorization

16.2.

The Greatest Common Factor (GCF) & Least Common Multiple

17. Relations & Functions

18. Arithmetic Sequences

18.1.

Arithmetic Sequences

Grade 12 Pre-Calculus

1. Functions (Basics)

1.1.

Interval Notation vs. Set Notation

1.2.

Domain & Range

1.3.

Basic Functions Review

1.4.

Basic Functions & Graph Properties

Operations with Functions

2. Transformations

2.1.

Vertical & Horizontal Translations

2.2.

Vertical & Horizontal Reflections

2.3.

Vertical & Horizontal Expansions & Compressions

2.4.

Combining Transformations

2.5.

Inverse Functions & Transformations

3. Polynomial Functions

3.1.

Polynomials

3.2.

Polynomial Graphs & Characteristics

3.3.

Factoring

3.4.

Factoring & Graphing Polynomials

3.5.

Transformations of Cubic & Quartic Functions

3.6.

Dividing Polynomials

3.7.

Factoring Polynomials (Degree 3+)

3.8.

Solving Linear & Quadratic Equations

3.9.

Solving General Polynomial Equations

3.10.

Applications of Polynomial Functions

4. Radical Functions

4.1.

Radical Functions

4.2.

Transformations of Radical Functions

4.3.

Solving Radical Equations

4.4.

Applications of Radical Functions

5. Rational Functions

Graphing Rational Functions

5.4.

Solving Rational Equations

5.5.

Applications of Rational Functions

6. Inequalities

6.1.

Solving Linear Inequalities

6.2.

Solving Polynomial Inequalities (Number Line)

6.3.

Solving Polynomial Inequalities (Graphs)

6.4.

Solving Rational Inequalities (Number Line & Graphs)

7. Trigonometric Ratios (Radians)

7.1.

Radians

7.2.

Trigonometric Ratios in Radians

7.3.

Special Angles & Unit Circle in Radians

7.4.

Solving Simple Trigonometric Equations

8. Trigonometric (Sinusoidal) Graphs

8.1.

Graphs of Sinusoidal Functions

8.2.

Transformations of Sinusoidal Functions

8.3.

Graphs of Reciprocal Trigonometric Functions

8.4.

Equivalent Sinusoidal Functions (Radians)

8.5.

Applications of Trigonometric Functions

9. Trigonometric Identities & Proofs

9.1.

Equivalent Trigonometric Expressions

9.2.

Reciprocal & Quotient Identities

9.3.

Pythagorean Identities

9.4.

Sum & Difference Identities

9.5.

Double & Half Angle Identities

9.6.

Proofs using Trigonometric Identities

10. Trigonometric Equations

10.1.

Solving Linear Trigonometric Equations

10.2.

Solving Quadratic Trigonometric Equations

11. Exponential Functions

Solving Exponential Equations

11.5.

Characteristics of Exponential Functions

11.6.

Transformations of Exponential Functions

11.7.

Applications of Exponential Functions

12. Logarithmic Functions

Solving Logarithmic Equations

12.4.

Using Logarithms to Solve Exponential Equations

12.5.

Characteristics of Logarithmic Functions

12.6.

Transformations of Logarithmic Functions

12.7.

Applications of Logarithmic Functions

13. Combination of Functions

13.1.

Combining Families of Functions

13.2.

Sum & Difference of Functions

13.3.

Product & Quotient of Functions

13.4.

Composition of Functions

13.5.

Solving Equations & Inequalities Graphically

14. Rates of Change

14.1.

Average Rate of Change & the Secant Line

14.2.

Instantaneous Rate of Change & the Tangent Line

14.3.

Graphs & Rates of Change

14.4.

Rates of Change of Polynomials

14.5.

Rates of Change of Trigonometric Functions

14.6.

Rates of Change of Exponential Functions

14.7.

Rates of Change of Logarithmic Functions

15. Permutations and Combinations [BC/AB]

16. Conics [BC/AB]

16.1.

Introduction to Conics

Grade 9 Math

1. Rational Numbers

1.1.

Review - Order of Operations

1.2.

Intro to Rational Numbers

Mixed Numbers (Adding & Subtracting)

1.6.

Mixed Numbers (Multiplying & Dividing)

1.7.

Fractions, Decimals, and Percentages

1.8.

Roots & Radicals

2. Powers & Exponents

2.1.

Review: Powers & Exponents

2.2.

Intro to Exponent Rules

2.3.

Exponent Rules for Fractions & Products

2.4.

Product Rule for Multiplying Powers

2.5.

Quotient Rule for Dividing Powers

2.6.

Exponent Rule for Power of a Power

2.7.

Simplifying & Evaluting Expressions with Powers

2.8.

Zero & Negative Exponents

3. Polynomial Expressions

3.1.

Definitions/Terminology

3.2.

The Meaning of

x

x^2

x^3

, and

\sqrt x

3.3.

Adding & Subtracting Polynomials

3.4.

Multiplying a Polynomial by a Monomial (Distributive Law)

3.5.

Dividing a Polynomial by a Monomial

3.6.

Simplifying Polynomial Expressions Practice Questions

4. Solving Equations

4.1.

One-Step Equations with 1 Unknown

4.2.

Multi-Step Equations with 1 Unknown

4.3.

Solving Equations Practice Questions

5. Solving Inequalities

5.1.

Representing Inequalities

5.2.

Solving Inequalities

6. Relations

Direct & Partial Variation

7. Analytic Geometry: Equation of a Line

7.1.

Intro to the Equation of a Line

7.2.

Slope of a Line

7.3.

Different Forms of the Equation of a Line

7.4.

Graphs of Lines

7.5.

Parallel & Perpendicular Lines

7.6.

Finding the Equation of a Line

7.7.

Solving by Graphing

8. Investigating Relationships

8.1.

Plotting & Interpreting Data

8.2.

Correlation, Interpolation & Extrapolation

Interpreting Graphs & Situations

9. Angles

9.1.

Interior Angles of Polygons

9.2.

Exterior Angles of Polygons

10. 2D Geometry - Properties of 2D Figures

10.1.

Conjectures & Hypotheses

10.2.

Properties of Polygons

11. 2D Geometry - Measurements

Optimal Area & Perimeter of a Rectangle

12. 3D Geometry - Measurements

12.1.

Surface Area & Volume of a Prism

12.2.

Surface Area & Volume of a Cylinder

12.3.

Surface Area & Volume of a Right Pyramid

12.4.

Surface Area & Volume of a Right Cone

12.5.

Surface Area & Volume of a Sphere

12.6.

Optimize Surface Area & Volume

12.7.

Surface Area & Volume of Composite Shapes

13. Circle Geometry

13.1.

Introduction to Circles

13.2.

Measuring and Circles

13.3.

Circles and Polygons

13.4.

Angles and Segments in Circles

14. Data Analysis

14.1.

Intro to Data & Mathematical Modelling

14.2.

Data Collection

14.3.

Measures of Central Tendency - Mean, Median, Mode

14.4.

Measures of Spread - Quartiles & Box Plots

14.5.

Probability in Society (Under Construction)

15. Financial Literacy

Simple & Compound Interest

15.5.

Appreciation & Depreciation

15.6.

Making Financial Decisions (Under Construction)

15.7.

(Bonus) Savings VS Investments

Algebra I (Common Core)

1. Foundations of Algebra

1.1.

📝Review: Working With Numbers

1.2.

📝Review: Integers, Decimals

1.3.

📝Review: Fractions, & Mixed Numbers

1.4.

📝Review: Ratios, Rates, and Proportions

1.5.

📝Review: Percentages

1.6.

📝Review: Powers & Exponents

1.7.

Scientific Notation

1.8.

📝 Review: Roots & Radicals

1.9.

The Language of Algebra

2. Quantities and Units

Working with the SI & Imperial Systems

3. Solving One-Variable Equations

Solving Equations & Formulas

4. Solving One Variable Inequalities

4.1.

Representing Inequalities

4.2.

Solving Inequalities

4.3.

Solving Compound Inequalities

4.4.

Solving Inequalities Involving Absolute Values

5. Relations & Functions

Plotting & Interpreting Data

5.4.

Interpreting Graphs & Situations

6. Linear Functions (Equation of a Line)

6.1.

Intro to the Equation of a Line

6.2.

Slope of a Line

6.3.

Different Forms of the Equation of a Line

6.4.

Graphs of Lines

6.5.

Parallel & Perpendicular Lines

6.6.

Finding the Equation of a Line

6.7.

Line of Best Fit

7. Systems of Linear Equations

Solving by Substitution

7.4.

Solving by Elimination (Part 1)

7.5.

Solving by Elimination (Part 2)

7.6.

Solving a System of Linear Equations - No Solution or Many Solutions

8. Linear Inequalities in 2 Variables

8.1.

Solving Linear Inequalities

8.2.

Systems of Linear Inequatlities

9. Exponents & Radicals

9.1.

Integer Exponents

9.2.

Intro to Exponent Rules

9.3.

Exponent Rules for Fractions & Products

9.4.

Product Rule for Multiplying Powers

9.5.

Quotient Rule for Dividing Powers

9.6.

Exponent Rule for Power of a Power

9.7.

Rational Exponents

9.8.

Expressions with Exponents & Radicals

10. Exponential Functions

10.1.

Characteristics of Exponential Functions

10.2.

Transformations of Exponential Functions

10.3.

Applications of Exponential Functions (Growth & Decay)

11. Absolute Value Functions

11.1.

Piecewise Functions

11.2.

Basics of Absolute Value

11.3.

Absolute Value Functions

11.4.

Solving Absolute Value Equations

12. Sequences

Recursive Sequences and Rules for Defining Sequences

13. Polynomial Expressions

13.1.

Definitions/Terminology

13.2.

Adding & Subtracting Polynomials

13.3.

Monomial

\times

Polynomial (Distributive Method)

13.4.

Binomial

\times

Binomial

13.5.

Binomial

\times

Trinomial

13.6.

Special Products of Binomials

13.7.

(Extension) Dividing a Polynomial by a Monomial

14. Factoring Polynomials

Factoring Simple Trinomials

y=x^2+bx+c

14.4.

Factoring Harder Trinomials

y=ax^2+bx+c

14.5.

Factoring Difference of Squares

14.6.

Factoring Perfect Square Trinomials

14.7.

Factoring Summary + Extra Practice

15. Quadratic Functions

15.1.

Quadratic Relations

15.2.

Properties of Quadratic Graphs

15.3.

Factored Form of a Quadratic Equation

15.4.

Determine the Factored Form of a Quadratic

15.5.

Transformations of Quadratic Functions (Graphing)

15.6.

Vertex Form of a Quadratic Equation

15.7.

Determine the Vertex Form of a Quadratic

16. Completing the Square

16.1.

Exploring Perfect Squares

16.2.

Completing the Square (

x^2+bx+c

)

16.3.

Completing the Square (

ax^2+bx+c

)

17. Solving Quadratic Equations

17.1.

Solving Quadratic Equations by Factoring

17.2.

Solving Quadratic Equations by Completing the Square

17.3.

Solving Quadratic Equations Using the Quadratic Formula

17.4.

Discriminant Analysis (Number of Solutions)

17.5.

Solving Quadratic Equations Strategies

18. Radical Equations and Functions

18.1.

Solving Radical Equations

18.2.

Applications of Radical Functions

18.3.

Graphs of Radical Functions

19. Rational Expressions and Functions

19.1.

Rational Expressions and Functions

19.2.

Multiplying and Dividing Rational Expressions

19.3.

Adding and Subtracting Rational Expressions

19.4.

Solving Rational Equations

19.5.

Graphs of Rational Functions

20. Data Analysis

20.1.

Measures of Central Tendency - Mean, Median, Mode

20.2.

Measures of Spread - Quartiles & Box Plots

20.3.

Measure of Variability

20.4.

Percentiles

20.5.

Skewness and Symmetry

21. Displaying & Summarizing Quantitative Data

21.1.

Boxplots and Five-Number Summary

Geometry (Common Core)

1. Foundations of Geometry

1.1.

Points, Lines, & Planes

1.2.

Line Segments and Rays

1.3.

Measuring and Constructions

1.4.

Midpoint of a Line Segment

1.5.

Length of a Line Segment

1.6.

Angles

2. Reasoning and Proofs

3. Lines

3.1.

Pairs of Lines

3.2.

Angles from Intersecting Lines

3.3.

Equations of Parallel & Perpendicular Lines

4. Transformations of Shapes in 2D

5. Triangles

5.1.

Angles of Triangles

5.2.

Classifying Triangles

5.3.

Properties of Triangles

6. Congruent & Similar Triangles

6.1.

Congruent Triangles

6.2.

Congruent Triangles (SAS)

6.3.

Congruent Triangles (SSS)

6.4.

Congruent Triangles (ASA)

6.5.

Similar Triangles

7. Quadrilaterals

7.1.

Classifying Quadrilaterals

7.2.

Properties of Quadrilaterals

8. Polygons

8.1.

Similar Polygons

8.2.

Interior Angles of Polygons

8.3.

Exterior Angles of Polygons

9. Trigonometry of Right Triangles

9.1.

Pythagorean Therom (Review)

9.2.

Primary Trig Ratios (

\sin

\cos

\tan

)

9.3.

Finding Side Lengths in a Right Triangle

9.4.

Finding Angle Measures in a Right Triangle

9.5.

Solving Right Triangles

9.6.

Right Triangle Word Problems

10. Trigonometry of Acute Triangles

11. Circles

11.1.

Introduction to Circles

11.2.

Measuring and Circles

11.3.

Circles and Polygons

11.4.

Angles and Segments in Circles

11.5.

Equation of a Circle

12. 2D Measurements

12.1.

Area & Perimeter

12.2.

Optimal Area & Perimeter of a Rectangle

13. 3D Measurements

13.1.

Surface Area & Volume of a Prism

13.2.

Surface Area & Volume of a Cylinder

13.3.

Surface Area & Volume of a Right Pyramid

13.4.

Surface Area & Volume of a Right Cone

13.5.

Surface Area & Volume of a Sphere

13.6.

Surface Area & Volume of 3D Figures (coming soon)

13.7.

Optimize Surface Area & Volume

14. Probability and Counting

14.1.

Introduction to Probability

14.2.

Tools for Probability

14.3.

Basic Rules of Probability

14.4.

Probability of Independent Events

14.5.

Probability of Dependent Events (Conditional Probability)

Counting and Probability

15. The Binomial Distribution

15.1.

Randomness and Probability

15.2.

Joint Distribution

15.3.

Binomial Distribution

Algebra II (Common Core)

1. Review of Basic Functions

1.1.

Properties of Parent Functions

1.2.

Determining Domain & Range

2. Transformations of Functions

Stretches & Compressions

2.4.

Combining Transformations

3. Quadratic Equations & Complex Numbers

3.1.

Completing the Square (

x^2+bx+c

Solving Quadratic Equations with Complex Solutions

3.4.

Solving Quadratic Inequalities in One Variable

3.5.

Solving Quadratic Inequalities in Two Variables

3.6.

Solving Quadratic Systems

4. Polynomial Functions

4.1.

Polynomials

4.2.

Polynomial Graphs & Characteristics

4.3.

Factoring

4.4.

Factoring & Graphing Polynomials

4.5.

Dividing Polynomials

4.6.

Factoring Polynomials (Degree 3+)

4.7.

Fundamental Theorem of Algebra

4.8.

Transformations of Cubic & Quartic Functions

4.9.

Solving General Polynomial Equations

4.10.

Solving Polynomial Inequalities (Number Line)

4.11.

Solving Polynomial Inequalities (Graphs)

4.12.

Applications of Polynomial Functions

5. Radical Expressions and Functions

5.1.

Operations with Radicals

5.2.

Simplifying Radicals

5.3.

Solving Radical Equations

5.4.

Transformations of Radical Functions

5.5.

Applications of Radical Functions

6. Exponential Functions

6.1.

📝Review: Basic Exponent Rules

6.2.

Integer Exponents

6.3.

Rational Exponents (Coming Soon)

6.4.

Exponent Rules

6.5.

Solving Exponential Equations

6.6.

Characteristics of Exponential Functions

6.7.

Transformations of Exponential Functions

6.8.

Applications of Exponential Functions (Growth & Decay)

7. Logarithmic Functions

Solving Logarithmic Equations

7.4.

Using Logarithms to Solve Exponential Equations

7.5.

Characteristics of Logarithmic Functions

7.6.

Transformations of Logarithmic Functions

7.7.

Applications of Logarithmic Functions

8. Rational Functions

8.1.

Rational Expressions and Functions

8.2.

Multiplying and Dividing Rational Expressions

8.3.

Adding and Subtracting Rational Expressions

8.4.

Solving Rational Equations

8.5.

Reciprocal Functions

8.6.

Graphs of Rational Functions

8.7.

Graphing Rational Functions

8.8.

Solving Rational Inequalities (Number Line & Graphs)

8.9.

Applications of Rational Functions

9. Combination of Functions

9.1.

Combining Families of Functions

9.2.

Sum & Difference of Functions

9.3.

Product & Quotient of Functions

9.4.

Composition of Functions

9.5.

Solving Equations & Inequalities Graphically

10. Trigonometric Ratios (Radians)

10.1.

Radians

10.2.

Trigonometric Ratios in Radians

10.3.

Special Angles & Unit Circle in Radians

10.4.

Solving Simple Trigonometric Equations

11. Trigonometric (Sinusoidal) Graphs

11.1.

Graphs of Sinusoidal Functions

11.2.

Transformations of Sinusoidal Functions

11.3.

Graphs of Reciprocal Trigonometric Functions

11.4.

Equivalent Sinusoidal Functions (Radians)

11.5.

Applications of Trigonometric Functions

12. Trigonometric Identities & Proofs

12.1.

Equivalent Trigonometric Expressions

12.2.

Reciprocal & Quotient Identities

12.3.

Pythagorean Identities

12.4.

Sum & Difference Identities

12.5.

Double & Half Angle Identities

12.6.

Proofs using Trigonometric Identities

12.7.

Inverse Trigonometric Functions

13. Sequences & Series

Pascal's Triangle and the Binomial Expansion

14. Probability and Counting

14.1.

Introduction to Probability

14.2.

Tools for Probability

14.3.

Basic Rules of Probability

14.4.

Probability of Independent Events

14.5.

Probability of Dependent Events (Conditional Probability)

14.6.

Probability Problems

14.7.

Summary of Key Definitions

14.8.

Counting Techniques

14.9.

Counting and Probability

15. The Binomial Distribution

15.1.

Randomness and Probability

15.2.

Joint Distribution

15.3.

Binomial Distribution

16. Sampling and Estimating

16.1.

Intro to Sampling Distribution

16.2.

Sampling Distribution for a Mean

16.3.

Sampling Distribution for a Proportion

16.4.

Finite Population Sampling

16.5.

Introduction to Confidence Intervals

16.6.

Confidence Interval for a Mean

16.7.

Confidence Interval for a Proportion

16.8.

Margin of Error and Sample Size

17. Vectors (Extension Topic)

17.1.

Basics of Vectors

17.2.

Vector Operations and Linear Combinations

17.3.

Vector Properties

17.4.

Length of a Vector (Vector Norm)

18. Matrices (Extension Topic)

18.1.

Basics of Matrices

18.2.

Matrix Multiplication

Matrix Inverse Algorithm

18.6.

Solving Matrix Equations

18.7.

Basics of Determinants

19. Systems of Linear Equations (Extension Topic)

19.1.

Basics of Systems of Linear Equations

19.2.

Augmented Matrix

19.3.

Reduced Row Echelon Form (RREF)

19.4.

Reducing a Matrix (Gauss-Jordan Elimination)

19.5.

Solving Linear Systems

19.6.

Solving a System of Linear Equations Using Matrices

Grade 12 Calculus

1. Review

1.1.

Functions

1.2.

Linear Equations (Lines)

2. Rate of Change

2.1.

The Slope of Tangent Lines

\frac{0}{0}

2.5.

Evaluating

\frac{0}{0}

Limits -- by Factoring

2.6.

Evaluating

\frac{0}{0}

Limits -- with Radicals

2.7.

Evaluating

\frac{0}{0}

Limits -- with Absolute Values

2.8.

Evaluating

\frac{0}{0}

Limits -- with Substitution

2.9.

Continuity

2.10.

Extra Thinking Questions

3. Derivatives of Polynomials

3.1.

Introduction to Derivatives & Differentiability

Composite Functions (Chain Rule)

3.6.

Extra Thinking Questions

4. Derivative Applications

4.1.

Higher Order Derivatives -- Displacement, Velocity & Acceleration

4.2.

Maximum & Minimum on a Closed Interval

4.3.

Optimization Problems

5. Curve Sketching

5.1.

Increasing & Decreasing Intervals

5.2.

Critical Points & Local Max/Min

5.3.

Asymptotes

5.4.

Inflection Points & Concavity

5.5.

Curve Sketching

6. Derivatives of Exponential (& Logarithmic) Functions

6.1.

Review of Exponential Functions

y=b^x

6.2.

Derivative of Exponential Functions

y=b^x

6.3.

Review of Exponential Functions

y=e^x

6.4.

Derivative of Exponential Functions

y=e^x

6.5.

Optimization Problems w/ Exponential Functions

6.6.

Hyperbolic Functions (Bonus)

6.7.

Derivative of Logarithmic Functions (Bonus)

7. Derivative of Trigonometric Functions

7.1.

Review of Trig Functions

7.2.

Derivative of Trig Functions

7.3.

Optimization Problems w/ Trig Functions

8. Vectors

8.1.

Introduction to Vectors

8.2.

Magnitude of a Vector

9. Vector Products

9.1.

Dot Product

9.2.

Dot Product Applications

9.3.

Cross Product

9.4.

Cross Product Applications

10. Equations of Lines & Planes

10.1.

Equations of Lines in

R^2

R^3

10.2.

Equations of Planes in

R^3

11. Intersections of Lines & Planes

11.1.

Intersection of 2 Lines

11.2.

Intersection of a Line & Plane

11.3.

Intersection of 2 Planes

11.4.

Intersection of 3 Planes

12. Distance Between Lines & Planes

12.1.

Distance from a Point to a Line in

R^2

12.2.

Distance from a Point to a Plane in

R^3

12.3.

Distance from a Point to a Line in

R^3

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