# AU Maths Methods Help & Practice!

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##### 1Solving Linear Equations

##### 2Introduction to Relations and Functions

##### 3Linear Functions

- 3.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 3.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 3.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 3.4Gradient intercept form: y = mx + b
- 3.5General form: Ax + By + C = 0
- 3.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 3.7Rate of change
- 3.8Graphing linear functions using table of values
- 3.9Graphing linear functions using x- and y-intercepts
- 3.10Graphing from slope-intercept form y=mx+b
- 3.11Graphing linear functions using a single point and gradient
- 3.12Word problems of graphing linear functions
- 3.13Parallel and perpendicular lines in linear functions
- 3.14Applications of linear relations

- 3.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 4Linear Equations

- 4.1Introduction to linear equations
- 4.2Introduction to nonlinear equations
- 4.3Special case of linear equations: Horizontal lines
- 4.4Special case of linear equations: Vertical lines
- 4.5Parallel line equation
- 4.6Perpendicular line equation
- 4.7Combination of both parallel and perpendicular line equations
- 4.8Applications of linear equations

- 4.1Introduction to linear equations
##### 5Quadratic Functions

- 5.1Introduction to 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 quadratic functions: General form VS. Vertex form
- 5.9Finding the quadratic functions for given parabolas
- 5.10Applications of quadratic functions

- 5.1Introduction to quadratic functions
##### 6Solving Quadratic Equations

##### 7Functions

##### 8Transformations of Functions

- 8.1Transformations of functions: Horizontal translations
- 8.2Transformations of functions: Vertical translations
- 8.3Reflection across the y-axis:
*y = f(-x)* - 8.4Reflection across the x-axis:
*y = -f(x)* - 8.5Transformations of functions: Horizontal stretches
- 8.6Transformations of functions: Vertical stretches
- 8.7Combining transformations of functions
- 8.8Even and odd functions

- 8.1Transformations of functions: Horizontal translations
##### 9Factorisation

##### 10Conics

##### 11Trigonometric Ratios and Angle Measure

- 11.1Angle in standard position
- 11.2Coterminal angles
- 11.3Reference angle
- 11.4Find the exact value of trigonometric ratios
- 11.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 11.6Unit circle
- 11.7Converting between degrees and radians
- 11.8Trigonometric ratios of angles in radians
- 11.9Radian measure and arc length

- 11.1Angle in standard position
##### 12Sine Rule and Cosine Rule

##### 13Bearings

##### 14Graphing Trigonometric Functions

##### 15Applications of Trigonometric Functions

##### 16Trigonometric Identities

##### 17Solving Trigonometric Equations

- 17.1Solving first degree trigonometric equations
- 17.2Determining non-permissible values for trig expressions
- 17.3Solving second degree trigonometric equations
- 17.4Solving trigonometric equations involving multiple angles
- 17.5Solving trigonometric equations using pythagorean identities
- 17.6Solving trigonometric equations using sum and difference identities
- 17.7Solving trigonometric equations using double-angle identities

- 17.1Solving first degree trigonometric equations
##### 18Permutations and Combinations

##### 19Probability

##### 20Indices

- 20.1Indices: Product rule
*(a^x)(a^y) = a^(x+y)* - 20.2Indices: Division rule (a^x / a^y) = a^(x-y)
- 20.3Indices: Power rule
*(a^x)^y = a^(x * y)* - 20.4Indices: Negative exponents
- 20.5Indices: Zero exponent:
*a^0 = 1* - 20.6Indices: Rational exponents
- 20.7Combining laws of indices
- 20.8Scientific notation
- 20.9Convert between radicals and rational exponents
- 20.10Solving for indices

- 20.1Indices: Product rule
##### 21Exponential Functions

##### 22Applications of Exponential Functions

##### 23Logarithmic Functions

- 23.1What is a logarithm?
- 23.2Converting from logarithmic form to exponential form
- 23.3Evaluating logarithms without a calculator
- 23.4Common logarithms
- 23.5Natural log: ln
- 23.6Evaluating logarithms using change-of-base formula
- 23.7Converting from exponential form to logarithmic form
- 23.8Solving exponential equations with logarithms
- 23.9Product rule of logarithms
- 23.10Quotient rule of logarithms
- 23.11Combining product rule and quotient rule in logarithms
- 23.12Evaluating logarithms using logarithm rules
- 23.13Solving logarithmic equations
- 23.14Graphing logarithmic functions
- 23.15Finding a logarithmic function given its graph

- 23.1What is a logarithm?
##### 24Applications of Logarithmic Functions

##### 25Sequences and Series

##### 26Limits and Derivatives

- 26.1Finding limits from graphs
- 26.2Definition of derivative
- 26.3Power rule
- 26.4Slope and equation of tangent line
- 26.5Chain rule
- 26.6Derivative of trigonometric functions
- 26.7Derivative of exponential functions
- 26.8Product rule
- 26.9Quotient rule
- 26.10Implicit differentiation
- 26.11Derivative of inverse trigonometric functions
- 26.12Derivative of logarithmic functions
- 26.13Higher order derivatives

- 26.1Finding limits from graphs
##### 27Derivative Applications

##### 28Integrals

##### 29Integration Applications

##### 30Normal Distribution and Z-score

##### 31Discrete Probabilities

##### 32Confidence Intervals