# Year 12 Maths Help & Practice

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##### 1Introduction to Relations and Functions

##### 2Functions

##### 3Transformations of Functions

- 3.1Transformations of functions: Horizontal translations
- 3.2Transformations of functions: Vertical translations
- 3.3Reflection across the y-axis:
*y = f(-x)* - 3.4Reflection across the x-axis:
*y = -f(x)* - 3.5Transformations of functions: Horizontal stretches
- 3.6Transformations of functions: Vertical stretches
- 3.7Combining transformations of functions
- 3.8Even and odd functions

- 3.1Transformations of functions: Horizontal translations
##### 4Factorising Polynomial

##### 5Quadratic Functions

- 5.1Characteristics of quadratic functions
- 5.2Transformations of quadratic functions
- 5.3Quadratic function in general form:
*y = ax^2 + bx + c* - 5.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 5.5Completing the square
- 5.6Converting from general to vertex form by completing the square
- 5.7Shortcut: Vertex formula
- 5.8Graphing parabolas for given quadratic functions
- 5.9Finding the quadratic functions for given parabolas
- 5.10Applications of quadratic functions

- 5.1Characteristics of quadratic functions
##### 6Polynomial Functions

##### 7Radicals

##### 8Radical Functions

##### 9Exponents

##### 10Rational Functions

##### 11Exponential Functions

- 11.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 11.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 11.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 11.4Exponents: Negative exponents
- 11.5Exponents: Zero exponent:
*a^0 = 1* - 11.6Exponents: Rational exponents
- 11.7Graphing exponential functions
- 11.8Graphing transformations of exponential functions
- 11.9Finding an exponential function given its graph

- 11.1Exponents: Product rule
##### 12Logarithmic Functions

- 12.1What is a logarithm?
- 12.2Converting from logarithmic form to exponential form
- 12.3Evaluating logarithms without a calculator
- 12.4Common logarithms
- 12.5Natural log: ln
- 12.6Evaluating logarithms using change-of-base formula
- 12.7Converting from exponential form to logarithmic form
- 12.8Solving exponential equations with logarithms
- 12.9Product rule of logarithms
- 12.10Quotient rule of logarithms
- 12.11Combining product rule and quotient rule in logarithms
- 12.12Evaluating logarithms using logarithm rules
- 12.13Solving logarithmic equations
- 12.14Graphing logarithmic functions
- 12.15Finding a logarithmic function given its graph

- 12.1What is a logarithm?
##### 13Applications of Exponential and Logarithmic Functions

- 13.1Exponential growth and decay by a factor
- 13.2Exponential decay: Half-life
- 13.3Exponential growth and decay by percentage
- 13.4Finance: Compound interest
- 13.5Continuous growth and decay
- 13.6Logarithmic scale: Richter scale (earthquake)
- 13.7Logarithmic scale: pH scale
- 13.8Logarithmic scale: dB scale
- 13.9Finance: Future value and present value

- 13.1Exponential growth and decay by a factor
##### 14Solving Simultaneous Equations

- 14.1Determining number of solutions to linear equations
- 14.2Solving simultaneous equations by graphing
- 14.3Solving simultaneous equations by elimination
- 14.4Solving simultaneous equations by substitution
- 14.5Money related questions in linear equations
- 14.6Unknown number related questions in linear equations
- 14.7Distance and time related questions in linear equations
- 14.8Rectangular shape related questions in linear equations

- 14.1Determining number of solutions to linear equations
##### 15Inequalities in Two Variables

##### 16Introduction to Trigonometry

- 16.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 16.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 16.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 16.4Combination of SohCahToa questions
- 16.5Solving expressions using 45-45-90 special right triangles
- 16.6Solving expressions using 30-60-90 special right triangles
- 16.7Word problems relating ladder in trigonometry
- 16.8Word problems relating guy wire in trigonometry
- 16.9Other word problems relating angles in trigonometry

- 16.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 17Trigonometric Ratios and Angle Measure

##### 18Bearings

##### 19Graphing Trigonometric Functions

##### 20Applications of Trigonometric Functions

##### 21Trigonometric Identities

##### 22Conics

##### 23Imaginary and Complex Numbers

- 23.1Introduction to imaginary numbers
- 23.2Complex numbers and complex planes
- 23.3Adding and subtracting complex numbers
- 23.4Complex conjugates
- 23.5Multiplying and dividing complex numbers
- 23.6Distance and midpoint of complex numbers
- 23.7Angle and absolute value of complex numbers
- 23.8Polar form of complex numbers
- 23.9Operations on complex numbers in polar form

- 23.1Introduction to imaginary numbers
##### 24Vectors

##### 25Sequences and Series

##### 26Permutations and Combinations

##### 27Introduction to Probability

##### 28Probability

##### 29Derivatives

- 29.1Definition of derivative
- 29.2Power rule
- 29.3Gradient and equation of tangent line
- 29.4Chain rule
- 29.5Derivative of trigonometric functions
- 29.6Derivative of exponential functions
- 29.7Product rule
- 29.8Quotient rule
- 29.9Implicit differentiation
- 29.10Derivative of inverse trigonometric functions
- 29.11Derivative of logarithmic functions
- 29.12Higher order derivatives

- 29.1Definition of derivative
##### 30Introduction to Matrices

##### 31Properties of Matrices

##### 32Determinants and Inverses of Matrices

- 32.1The determinant of a 2 x 2 matrix
- 32.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
- 32.3The inverse of a 2 x 2 matrix
- 32.4The inverse of 3 x 3 matrices with matrix row operations
- 32.5The inverse of 3 x 3 matrix with determinants and adjugate
- 32.62 x 2 invertible matrix
- 32.7Solving linear systems using Cramer's Rule
- 32.8Solving linear systems using 2 x 2 inverse matrices

- 32.1The determinant of a 2 x 2 matrix
##### 33Transformations with Matrices