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Grade 12 Math Topics

Functions

Function notation

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Inequalities of combined functions

Inverse functions

One to one functions

Difference quotient: applications of functions

Transformations

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

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

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

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Even and odd functions

Polynomial Functions

What is a polynomial function?

Polynomial long division

Polynomial synthetic division

Remainder theorem

Rational zero theorem

Characteristics of polynomial graphs

Multiplicities of polynomials

Imaginary zeros of polynomials

Determining the equation of a polynomial function

Applications of polynomial functions

Solving polynomial inequalities

Fundamental theorem of algebra

Descartes' rule of signs

Radical Functions

Basic radical functions

Transformations of radical functions

Square root of a function

Solving radical equations

Rational Functions

What is a rational function?

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Solving rational equations

Solving rational inequalities

Direct and Inverse Variation

Direct variation

Piecewise Functions

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Exponential Functions

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

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

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

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Logarithmic Functions

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Applications of Exponential and Logarithmic Functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Trigonometric Ratios and Angle Measure

Angle in standard position

Coterminal angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Graphing Trigonometric Functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Applications of Trigonometric Functions

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Solving Trigonometric Equations

Solving first degree trigonometric equations

Determining non-permissible values for trig expressions

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Inverse Trigonometric Functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Finding exact value of inverse reciprocal trig functions

Permutations and Combinations

Fundamental counting principle

Factorial notation

Path counting problems

Permutation vs. Combination

Problems involving both permutations and combinations

Pascal's triangle

Binomial theorem

Conics

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

Imaginary and Complex Numbers

Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

Vectors

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

Scalar multiplication

Equivalent vectors

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

Word problems on vectors

Introduction to Matrices

Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

Properties of Matrices

Identity matrix

Properties of matrix addition

Properties of scalar multiplication

Properties of matrix multiplication

Determinants and Inverses of Matrices

The determinant of a 2 x 2 matrix

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

The inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

Transformations with Matrices

Transforming vectors with matrices

Transforming shapes with matrices

Finding the transformation matrix

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