# A-Level Maths Help & Practice

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##### 1Surds

##### 2Laws of Indices

##### 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: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 4Factorisation

##### 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
##### 6Quadratic Equations

##### 7Inequalities

##### 8Simultaneous Equations

##### 9Operations with Algebraic Fractions

- 9.1Simplifying algebraic fractions and restrictions
- 9.2Adding and subtracting algebraic fractions
- 9.3Multiplying algebraic fractions
- 9.4Dividing algebraic fractions
- 9.5Solving algebraic fraction equations
- 9.6Applications of algebraic fraction equations
- 9.7Simplifying complex fractions
- 9.8Partial fraction decomposition

- 9.1Simplifying algebraic fractions and restrictions
##### 10Absolute Value Functions

##### 11Algebraic Division

##### 12Functions

##### 13Transformations of Functions

- 13.1Transformations of functions: Horizontal translations
- 13.2Transformations of functions: Vertical translations
- 13.3Reflection across the y-axis:
*y = f(-x)* - 13.4Reflection across the x-axis:
*y = -f(x)* - 13.5Transformations of functions: Horizontal stretches
- 13.6Transformations of functions: Vertical stretches
- 13.7Combining transformations of functions

- 13.1Transformations of functions: Horizontal translations
##### 14Reciprocal Functions

##### 15Rational Functions

##### 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?
##### 18Applications of Exponential and Logarithmic Functions

- 18.1Exponential growth and decay by a factor
- 18.2Exponential decay: Half-life
- 18.3Exponential growth and decay by percentage
- 18.4Finance: Compound interest
- 18.5Continuous growth and decay
- 18.6Logarithmic scale: Richter scale (earthquake)
- 18.7Logarithmic scale: pH scale
- 18.8Logarithmic scale: dB scale
- 18.9Finance: Future value and present value

- 18.1Exponential growth and decay by a factor
##### 19Trigonometry

- 19.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 19.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 19.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 19.4Combination of SohCahToa questions
- 19.5Solving expressions using 45-45-90 special right triangles
- 19.6Solving expressions using 30-60-90 special right triangles
- 19.7Word problems relating ladder in trigonometry
- 19.8Word problems relating guy wire in trigonometry
- 19.9Other word problems relating angles in trigonometry

- 19.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 20Trigonometric Ratios and Angle Measure

##### 21Sine Rule and Cosine Rule

##### 22Graphing Trigonometric Functions

##### 23Applications of Trigonometric Functions

##### 24Trigonometric Identities

##### 25Solving Trigonometric Equations

- 25.1Solving first degree trigonometric equations
- 25.2Determining non-permissible values for trig expressions
- 25.3Solving second degree trigonometric equations
- 25.4Solving trigonometric equations involving multiple angles
- 25.5Solving trigonometric equations using pythagorean identities
- 25.6Solving trigonometric equations using sum and difference identities
- 25.7Solving trigonometric equations using double-angle identities

- 25.1Solving first degree trigonometric equations
##### 26Circle Theorems

##### 27Sequences and Series

##### 28Binomial Expansion

##### 29Vectors

##### 30Differentiation

- 30.1Power rule
- 30.2Gradient and equation of tangent line
- 30.3Chain rule
- 30.4Derivative of trigonometric functions
- 30.5Derivative of exponential functions
- 30.6Product rule
- 30.7Quotient rule
- 30.8Derivative of inverse trigonometric functions
- 30.9Derivative of logarithmic functions
- 30.10Higher order derivatives
- 30.11Critical number & maximum and minimum values
- 30.12Curve sketching

- 30.1Power rule
##### 31Integration

- 31.1Antiderivatives
- 31.2Fundamental theorem of calculus
- 31.3Definite integral
- 31.4Numerical integration
- 31.5U-Substitution
- 31.6Integration by parts
- 31.7Trigonometric substitution
- 31.8Integration of rational functions by partial fractions
- 31.9Volumes of solids of revolution - Disc method
- 31.10Volumes of solids of revolution - Shell method

- 31.1Antiderivatives
##### 32Parametric Equations

##### 33Differential Equations

##### 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

##### 41Scalars, Vectors, and Motion

##### 42Kinematics

##### 43Forces

##### 44Momentum

##### 45Equilibrium