# Maths Extension 1 Help & Practice

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##### 1Adding and Subtracting Fractions

##### 2Multiplying and Dividing Fractions

##### 3Pythagorean Theorem

##### 4Percents

##### 5Surds

##### 6Algebraic Expressions

##### 7Introduction to Relations and Functions

##### 8Linear Functions

- 8.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 8.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 8.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 8.4Gradient intercept form: y = mx + b
- 8.5General form: Ax + By + C = 0
- 8.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 8.7Rate of change
- 8.8Graphing linear functions using table of values
- 8.9Graphing linear functions using x- and y-intercepts
- 8.10Graphing from slope-intercept form y=mx+b
- 8.11Graphing linear functions using a single point and gradient
- 8.12Word problems of graphing linear functions
- 8.13Parallel and perpendicular lines in linear functions
- 8.14Applications of linear relations
- 8.15Perpendicular line equation

- 8.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 9Simultaneous Equations

- 9.1Determining number of solutions to linear equations
- 9.2Solving simultaneous linear equations by graphing
- 9.3Solving simultaneous linear equations by elimination
- 9.4Solving simultaneous linear equations by substitution
- 9.5Money related questions in linear equations
- 9.6Unknown number related questions in linear equations
- 9.7Distance and time related questions in linear equations
- 9.8Rectangular shape related questions in linear equations
- 9.9Simultaneous linear-quadratic equations
- 9.10Simultaneous quadratic-quadratic equations
- 9.11Solving 3 variable simultaneous equations by substitution
- 9.12Solving 3 variable simultaneous equations by elimination
- 9.13Solving 3 variable simultaneous equations with no or infinite solutions
- 9.14Word problems relating 3 variable simultaneous equations

- 9.1Determining number of solutions to linear equations
##### 10Factorisation

##### 11Quadratic Functions

- 11.1Introduction to quadratic functions
- 11.2Transformations of quadratic functions
- 11.3Quadratic function in general form:
*y = ax^2 + bx + c* - 11.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 11.5Completing the square
- 11.6Converting from general to vertex form by completing the square
- 11.7Shortcut: Vertex formula
- 11.8Graphing quadratic functions: General form VS. Vertex form
- 11.9Finding the quadratic functions for given parabolas
- 11.10Applications of quadratic functions

- 11.1Introduction to quadratic functions
##### 12Solving Quadratic Equations

##### 13Inequalities

- 13.1Express linear inequalities graphically and algebraically
- 13.2Solving one-step linear inequalities
- 13.3Solving multi-step linear inequalities
- 13.4Compound inequalities
- 13.5Solving absolute value inequalities
- 13.6Graphing linear inequalities in two variables
- 13.7Graphing simultaneous inequalities
- 13.8Solving quadratic inequalities in one variable

- 13.1Express linear inequalities graphically and algebraically
##### 14Algebraic Fractions

- 14.1Simplifying algebraic fractions and restrictions
- 14.2Adding and subtracting algebraic fractions
- 14.3Multiplying algebraic fractions
- 14.4Dividing algebraic fractions
- 14.5Solving equations with algebraic fractions
- 14.6Applications of equations with algebraic fractions
- 14.7Simplifying complex fractions
- 14.8Partial fraction decomposition

- 14.1Simplifying algebraic fractions and restrictions
##### 15Reciprocal Functions

##### 16Angles, Lines, and Transversals

##### 17Scale Factors and Similarity

##### 18Properties of Triangles

##### 19Congruent Triangles

##### 20Circles

##### 21Functions

##### 22Polynomial Functions

- 22.1What is a polynomial function?
- 22.2Polynomial long division
- 22.3Polynomial synthetic division
- 22.4Remainder theorem
- 22.5Factor theorem
- 22.6Rational zero theorem
- 22.7Characteristics of polynomial graphs
- 22.8Multiplicities of polynomials
- 22.9Imaginary zeros of polynomials
- 22.10Determining the equation of a polynomial function
- 22.11Applications of polynomial functions
- 22.12Solving polynomial inequalities
- 22.13Fundamental theorem of algebra
- 22.14Descartes' rule of signs

- 22.1What is a polynomial function?
##### 23Rational Functions

##### 24Indices

- 24.1Indices: Product rule
*(a^x)(a^y) = a^(x+y)* - 24.2Indices: Division rule (a^x / a^y) = a^(x-y)
- 24.3Indices: Power rule
*(a^x)^y = a^(x * y)* - 24.4Indices: Negative exponents
- 24.5Indices: Zero exponent:
*a^0 = 1* - 24.6Indices: Rational exponents
- 24.7Combining laws of indices
- 24.8Scientific notation
- 24.9Convert between radicals and rational exponents
- 24.10Solving for indices

- 24.1Indices: Product rule
##### 25Exponential Functions

##### 26Logarithmic Functions

- 26.1What is a logarithm?
- 26.2Converting from logarithmic form to exponential form
- 26.3Evaluating logarithms without a calculator
- 26.4Common logarithms
- 26.5Natural log: ln
- 26.6Evaluating logarithms using change-of-base formula
- 26.7Converting from exponential form to logarithmic form
- 26.8Solving exponential equations with logarithms
- 26.9Product rule of logarithms
- 26.10Quotient rule of logarithms
- 26.11Combining product rule and quotient rule in logarithms
- 26.12Evaluating logarithms using logarithm rules
- 26.13Solving logarithmic equations
- 26.14Graphing logarithmic functions
- 26.15Finding a logarithmic function given its graph

- 26.1What is a logarithm?
##### 27Trigonometric Ratios and Angle Measure

- 27.1Angle in standard position
- 27.2Coterminal angles
- 27.3Reference angle
- 27.4Find the exact value of trigonometric ratios
- 27.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 27.6Unit circle
- 27.7Converting between degrees and radians
- 27.8Trigonometric ratios of angles in radians
- 27.9Radian measure and arc length

- 27.1Angle in standard position
##### 28Sine Rule and Cosine Rule

##### 29Trigonometric Graphs

##### 30Trigonometric Identities

##### 31Solving Trigonometric Equations

- 31.1Solving first degree trigonometric equations
- 31.2Determining non-permissible values for trig expressions
- 31.3Solving second degree trigonometric equations
- 31.4Solving trigonometric equations involving multiple angles
- 31.5Solving trigonometric equations using pythagorean identities
- 31.6Solving trigonometric equations using sum and difference identities
- 31.7Solving trigonometric equations using double-angle identities

- 31.1Solving first degree trigonometric equations
##### 32Inverse Trigonometric Functions

##### 33Bearings

##### 34Series

##### 35Growth and Decay

##### 36Conics

##### 37Permutations and Combinations

##### 38Discrete Probabilities

##### 39Probability

##### 40Limits

##### 41Derivatives

- 41.1Definition of derivative
- 41.2Power rule
- 41.3Slope and equation of tangent line
- 41.4Chain rule
- 41.5Derivative of trigonometric functions
- 41.6Derivative of exponential functions
- 41.7Product rule
- 41.8Quotient rule
- 41.9Derivative of inverse trigonometric functions
- 41.10Derivative of logarithmic functions
- 41.11Higher order derivatives

- 41.1Definition of derivative
##### 42Derivative Applications

##### 43Integrals

##### 44Integral Applications

##### 45Parametric Equations