# 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: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 9.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 9.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 9.4Gradient intercept form: y = mx + b
- 9.5General form: Ax + By + C = 0
- 9.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 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: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 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 = $\frac{o}{h}$ )
- 18.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 18.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 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 = $\frac{o}{h}$ )
##### 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