A-Level Maths (Legacy) Help & Practice
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1Surds
2Factorisation
3Quadratic Functions
- 3.1Introduction to quadratic functions
- 3.2Transformations of quadratic functions
- 3.3Quadratic function in general form: y = ax^2 + bx + c
- 3.4Quadratic function in vertex form: y = a(x-p)^2 + q
- 3.5Completing the square
- 3.6Converting from general to vertex form by completing the square
- 3.7Shortcut: Vertex formula
- 3.8Graphing quadratic functions: General form VS. Vertex form
- 3.9Finding the quadratic functions for given parabolas
- 3.10Applications of quadratic functions
- 3.1Introduction to quadratic functions
4Quadratic Equations
5Inequalities
6Simultaneous Equations
- 6.1Simultaneous linear equations
- 6.2Simultaneous linear-quadratic equations
- 6.3Simultaneous quadratic-quadratic equations
- 6.4Solving 3 variable simultaneous equations by substitution
- 6.5Solving 3 variable simultaneous equations by elimination
- 6.6Solving 3 variable simultaneous equations with no or infinite solutions
- 6.7Word problems relating 3 variable simultaneous equations
- 6.1Simultaneous linear equations
7Operations with Algebraic Fractions
- 7.1Simplifying algebraic fractions and restrictions
- 7.2Adding and subtracting algebraic fractions
- 7.3Multiplying algebraic fractions
- 7.4Dividing algebraic fractions
- 7.5Solving equations with algebraic fractions
- 7.6Applications of equations with algebraic fractions
- 7.7Simplifying complex fractions
- 7.8Partial fraction decomposition
- 7.1Simplifying algebraic fractions and restrictions
8Algebraic Division
9Linear Functions
- 9.1Distance formula:
- 9.2Midpoint formula:
- 9.3Gradient equation:
- 9.4Gradient intercept form: y = mx + b
- 9.5General form: Ax + By + C = 0
- 9.6Gradient-point form:
- 9.7Rate of change
- 9.8Graphing linear functions using table of values
- 9.9Graphing linear functions using x- and y-intercepts
- 9.10Graphing from slope-intercept form y=mx+b
- 9.11Graphing linear functions using a single point and gradient
- 9.12Word problems of graphing linear functions
- 9.13Parallel and perpendicular lines in linear functions
- 9.14Applications of linear relations
- 9.1Distance formula:
10Functions
11Transformations of Functions
- 11.1Transformations of functions: Horizontal translations
- 11.2Transformations of functions: Vertical translations
- 11.3Reflection across the y-axis: y = f(-x)
- 11.4Reflection across the x-axis: y = -f(x)
- 11.5Transformations of functions: Horizontal stretches
- 11.6Transformations of functions: Vertical stretches
- 11.7Combining transformations of functions
- 11.1Transformations of functions: Horizontal translations
12Reciprocal Functions
13Rational Functions
14Absolute Value Functions
15Laws of Indices
16Exponentials Functions
17Logarithms
- 17.1What is a logarithm?
- 17.2Converting from logarithmic form to exponential form
- 17.3Evaluating logarithms without a calculator
- 17.4Common logarithms
- 17.5Natural log: ln
- 17.6Evaluating logarithms using change-of-base formula
- 17.7Converting from exponential form to logarithmic form
- 17.8Solving exponential equations with logarithms
- 17.9Product rule of logarithms
- 17.10Quotient rule of logarithms
- 17.11Combining product rule and quotient rule in logarithms
- 17.12Evaluating logarithms using logarithm rules
- 17.13Solving logarithmic equations
- 17.14Graphing logarithmic functions
- 17.15Finding a logarithmic function given its graph
- 17.1What is a logarithm?
18Trigonometry
- 18.1Use sine ratio to calculate angles and sides (Sin = )
- 18.2Use cosine ratio to calculate angles and sides (Cos = )
- 18.3Use tangent ratio to calculate angles and sides (Tan = )
- 18.4Combination of SohCahToa questions
- 18.5Solving expressions using 45-45-90 special right triangles
- 18.6Solving expressions using 30-60-90 special right triangles
- 18.7Word problems relating ladder in trigonometry
- 18.8Word problems relating guy wire in trigonometry
- 18.9Other word problems relating angles in trigonometry
- 18.1Use sine ratio to calculate angles and sides (Sin = )
19Trigonometric Ratios and Angle Measure
20Sine Rule and Cosine Rule
21Bearings
22Graphing Trigonometric Functions
23Trigonometric Identities
24Solving Trigonometric Equations
- 24.1Solving first degree trigonometric equations
- 24.2Determining non-permissible values for trig expressions
- 24.3Solving second degree trigonometric equations
- 24.4Solving trigonometric equations involving multiple angles
- 24.5Solving trigonometric equations using pythagorean identities
- 24.6Solving trigonometric equations using sum and difference identities
- 24.7Solving trigonometric equations using double-angle identities
- 24.1Solving first degree trigonometric equations
25Inverse Trigonometric Functions
26Circle Theorems
27Sequences and Series
28Binomial Expansion
29Differentiation
- 29.1Power rule
- 29.2Gradient and equation of tangent line
- 29.3Chain rule
- 29.4Derivative of trigonometric functions
- 29.5Derivative of exponential functions
- 29.6Product rule
- 29.7Quotient rule
- 29.8Derivative of inverse trigonometric functions
- 29.9Derivative of logarithmic functions
- 29.10Higher order derivatives
- 29.11Critical number & maximum and minimum values
- 29.12Curve sketching
- 29.1Power rule
30Integration
31Parametric Equations
32Differential Equations
33Vectors
34Statistics
35Data and Graphs
36Probability
37Discrete Probabilities
38Normal Distribution and Confidence Intervals
- 38.1Introduction to normal distribution
- 38.2Normal distribution and continuous random variable
- 38.3Z-scores and random continuous variables
- 38.4Sampling distributions
- 38.5Central limit theorem
- 38.6Confidence levels and critical values
- 38.7Confidence intervals to estimate population mean
- 38.8Student's t-distribution
- 38.1Introduction to normal distribution
39Correlation and Regression
40Hypothesis Testing
