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:
- 8.2Midpoint formula:
- 8.3Gradient equation:
- 8.4Gradient intercept form: y = mx + b
- 8.5General form: Ax + By + C = 0
- 8.6Gradient-point form:
- 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:
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 (a^x)(a^y) = a^(x+y)
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 (All Students Take Calculus)
- 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
