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Grade 12 Math Topics

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1. Functions

1.1

Function notation

1.2

Operations with functions

1.3

Adding functions

1.4

Subtracting functions

1.5

Multiplying functions

1.6

Dividing functions

1.7

Composite functions

1.8

Inequalities of combined functions

1.9

Inverse functions

1.10

One to one functions

1.11

Difference quotient: applications of functions

2. Transformations

2.1

Transformations of functions: Horizontal translations

2.2

Transformations of functions: Vertical translations

2.3

Reflection across the y-axis: y = f(-x)

2.4

Reflection across the x-axis: y = -f(x)

2.5

Transformations of functions: Horizontal stretches

2.6

Transformations of functions: Vertical stretches

2.7

Combining transformations of functions

2.8

Even and odd functions

3. Polynomial Functions

3.1

What is a polynomial function?

3.2

Polynomial long division

3.3

Polynomial synthetic division

3.4

Remainder theorem

3.5

Factor theorem

3.6

Rational zero theorem

3.7

Characteristics of polynomial graphs

3.8

Multiplicities of polynomials

3.9

Imaginary zeros of polynomials

3.10

Determining the equation of a polynomial function

3.11

Applications of polynomial functions

3.12

Solving polynomial inequalities

3.13

Fundamental theorem of algebra

3.14

Descartes' rule of signs

4. Radical Functions

4.1

Basic radical functions

4.2

Transformations of radical functions

4.3

Square root of a function

4.4

Solving radical equations

5. Rational Functions

5.1

What is a rational function?

5.2

Point of discontinuity

5.3

Vertical asymptote

5.4

Horizontal asymptote

5.5

Slant asymptote

5.6

Graphs of rational functions

5.7

Solving rational equations

5.8

Solving rational inequalities

6. Direct and Inverse Variation

6.1

Direct variation

7. Piecewise Functions

7.1

Evaluating piecewise functions

7.2

Graphing piecewise linear functions

7.3

Graphing piecewise non-linear functions

8. Exponential Functions

8.1

Exponents: Product rule (a^x)(a^y) = a^(x+y)

8.2

Exponents: Division rule (a^x / a^y) = a^(x-y)

8.3

Exponents: Power rule (a^x)^y = a^(x * y)

8.4

Exponents: Negative exponents

8.5

Exponents: Zero exponent: a^0 = 1

8.6

Exponents: Rational exponents

8.7

Solving exponential equations using exponent rules

8.8

Graphing exponential functions

8.9

Graphing transformations of exponential functions

8.10

Finding an exponential function given its graph

9. Logarithmic Functions

9.1

What is a logarithm?

9.2

Converting from logarithmic form to exponential form

9.3

Evaluating logarithms without a calculator

9.4

Common logarithms

9.5

Natural log: ln

9.6

Evaluating logarithms using change-of-base formula

9.7

Converting from exponential form to logarithmic form

9.8

Solving exponential equations with logarithms

9.9

Product rule of logarithms

9.10

Quotient rule of logarithms

9.11

Combining product rule and quotient rule in logarithms

9.12

Evaluating logarithms using logarithm rules

9.13

Solving logarithmic equations

9.14

Graphing logarithmic functions

9.15

Finding a logarithmic function given its graph

10. Applications of Exponential and Logarithmic Functions

10.1

Exponential growth and decay by a factor

10.2

Exponential decay: Half-life

10.3

Exponential growth and decay by percentage

10.4

Finance: Compound interest

10.5

Continuous growth and decay

10.6

Logarithmic scale: Richter scale (earthquake)

10.7

Logarithmic scale: pH scale

10.8

Logarithmic scale: dB scale

10.9

Finance: Future value and present value

11. Trigonometric Ratios and Angle Measure

11.1

Angle in standard position

11.2

Coterminal angles

11.3

Reference angle

11.4

Find the exact value of trigonometric ratios

11.5

ASTC rule in trigonometry (All Students Take Calculus)

11.6

Unit circle

11.7

Converting between degrees and radians

11.8

Trigonometric ratios of angles in radians

11.9

Radian measure and arc length

12. Graphing Trigonometric Functions

12.1

Sine graph: y = sin x

12.2

Cosine graph: y = cos x

12.3

Tangent graph: y = tan x

12.4

Cotangent graph: y = cot x

12.5

Secant graph: y = sec x

12.6

Cosecant graph: y = csc x

12.7

Graphing transformations of trigonometric functions

12.8

Determining trigonometric functions given their graphs

13. Applications of Trigonometric Functions

13.1

Ferris wheel trig problems

13.2

Tides and water depth trig problems

13.3

Spring (simple harmonic motion) trig problems

14. Trigonometric Identities

14.1

Quotient identities and reciprocal identities

14.2

Pythagorean identities

14.3

Sum and difference identities

14.4

Cofunction identities

14.5

Double-angle identities

15. Solving Trigonometric Equations

15.1

Solving first degree trigonometric equations

15.2

Determining non-permissible values for trig expressions

15.3

Solving second degree trigonometric equations

15.4

Solving trigonometric equations involving multiple angles

15.5

Solving trigonometric equations using pythagorean identities

15.6

Solving trigonometric equations using sum and difference identities

15.7

Solving trigonometric equations using double-angle identities

16. Inverse Trigonometric Functions

16.1

Finding inverse trigonometric function from its graph

16.2

Evaluating inverse trigonometric functions

16.3

Finding inverse reciprocal trigonometric function from its graph

16.4

Finding exact value of inverse reciprocal trig functions

17. Permutations and Combinations

17.1

Fundamental counting principle

17.2

Factorial notation

17.3

Path counting problems

17.4

Permutation vs. Combination

17.5

Permutations

17.6

Combinations

17.7

Problems involving both permutations and combinations

17.8

Pascal's triangle

17.9

Binomial theorem

18. Conics

18.1

18.2

18.3

18.4

19. Imaginary and Complex Numbers

19.1

Introduction to imaginary numbers

19.2

Complex numbers and complex planes

19.3

Adding and subtracting complex numbers

19.4

Complex conjugates

19.5

Multiplying and dividing complex numbers

19.6

Distance and midpoint of complex numbers

19.7

Angle and absolute value of complex numbers

19.8

Polar form of complex numbers

19.9

Operations on complex numbers in polar form

20. Vectors

20.1

Introduction to vectors

20.2

Magnitude of a vector

20.3

Direction angle of a vector

20.4

Scalar multiplication

20.5

Equivalent vectors

20.6

Adding and subtracting vectors in component form

20.7

Operations on vectors in magnitude and direction form

20.8

Unit vector

20.9

Word problems on vectors

21. Introduction to Matrices

21.1

Notation of matrices

21.2

Adding and subtracting matrices

21.3

Scalar multiplication

21.4

Matrix multiplication

21.5

The three types of matrix row operations

21.6

Representing a linear system as a matrix

21.7

Solving a linear system with matrices using Gaussian elimination

22. Properties of Matrices

22.1

Zero matrix

22.2

Identity matrix

22.3

Properties of matrix addition

22.4

Properties of scalar multiplication

22.5

Properties of matrix multiplication

23. Determinants and Inverses of Matrices

23.1

The determinant of a 2 x 2 matrix

23.2

The determinant of a 3 x 3 matrix (General & Shortcut Method)

23.3

The inverse of a 2 x 2 matrix

23.4

The inverse of 3 x 3 matrices with matrix row operations

23.5

The inverse of 3 x 3 matrix with determinants and adjugate

23.6

2 x 2 invertible matrix

23.7

Solving linear systems using Cramer's Rule

23.8

Solving linear systems using 2 x 2 inverse matrices

24. Transformations with Matrices

24.1

Transforming vectors with matrices

24.2

Transforming shapes with matrices

24.3

Finding the transformation matrix

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