Excel in Year 12 Mathematics

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

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 of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: <i>y = f(-x)</i>

Reflection across the x-axis: <i>y = -f(x)</i>

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Even and odd functions

Factorise by taking out the greatest common factor

Factorise by grouping

Factorising difference of squares: <i>x^2 - y^2</i>

Factorising trinomials

Factoring difference of cubes

Factoring sum of cubes

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: <i>y = ax^2 + bx + c</i>

Quadratic function in vertex form: <i>y = a(x-p)^2 + q</i>

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing parabolas for given quadratic functions

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Solving quadratic equations by factorising

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solving quadratic inequalities

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Solving radical equations

Basic radical functions

Transformations of radical functions

Square root of a function

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

What is a rational function?

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Solving equations with algebraic fractions

Solving rational inequalities

Exponents: Product rule <i>(a^x)(a^y) = a^(x+y)</i>

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

Exponents: Power rule <i>(a^x)^y = a^(x * y)</i>

Exponents: Negative exponents

Exponents: Zero exponent: <i>a^0 = 1</i>

Exponents: Rational exponents

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

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

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

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving simultaneous equations by elimination

Solving simultaneous equations by substitution

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Graphing linear inequalities in two variables

Graphing simultaneous linear inequalities

Graphing quadratic inequalities in two variables

Graphing simultaneous quadratic inequalities

Applications of inequalities

What is linear programming?

Linear programming word problems

Use sine ratio to calculate angles and sides (Sin = \( \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos = \( \frac{a}{h}\) )

Use tangent ratio to calculate angles and sides (Tan = \( \frac{o}{a}\) )

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Standard angle

Coterminal angles

Reference angles

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Unit circle

Sine rule

Cosine rule

Applications of the sine rule and cosine rule

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

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

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

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

Unit Vector

Word problems on vectors

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

Fundamental counting principle

Factorial notation

Path counting problems

Permutation vs. Combination

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Binomial theorem

Introduction to probability

Organizing outcomes

Probability of independent events

Comparing experimental and theoretical probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

Definition of derivative

Power rule

Gradient and equation of tangent line

Chain rule

Derivative of trigonometric functions

Derivative of exponential functions

Product rule

Quotient rule

Implicit differentiation

Derivative of inverse trigonometric functions

Derivative of logarithmic functions

Higher order derivatives

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

Zero matrix

Identity matrix

Properties of matrix addition

Properties of scalar multiplication

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

Transforming vectors with matrices

Transforming shapes with matrices

Finding the transformation matrix

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression