# AS-Level Maths (Legacy) Help & Practice

Get better marks with our comprehensive AS level Maths help ? whether it's for Edexcel (Pearson), AQA, OCR or WJEC. Our AS Maths tutors have you all covered!

Keeping with the specifications of all the exam boards, our thorough help for the exam includes topics such as Trigonometry, Factorisation, Quadratic functions, Exponential functions, Logarithms, Calculus, Statistics, and a lot more. Learn the concepts with our online video tutorials that show you step-by-step solutions to even the hardest maths problems. Then, strengthen your understanding with tons of as maths practice.

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##### 1Surds

##### 2Factorisation

##### 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 linear functions using various forms
- 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: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 4Quadratic Functions

- 4.1Introduction to quadratic functions
- 4.2Transformations of quadratic functions
- 4.3Quadratic function in general form:
*y = ax^2 + bx + c* - 4.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 4.5Completing the square
- 4.6Converting from general to vertex form by completing the square
- 4.7Shortcut: Vertex formula
- 4.8Graphing quadratic functions: General form VS. Vertex form
- 4.9Finding the quadratic functions for given parabolas
- 4.10Applications of quadratic functions

- 4.1Introduction to quadratic functions
##### 5Quadratic Equations

##### 6Inequalities

##### 7Simultaneous Equations

- 7.1Simultaneous linear equations
- 7.2Simultaneous linear-quadratic equations
- 7.3Simultaneous quadratic-quadratic equations
- 7.4Solving 3 variable simultaneous equations by substitution
- 7.5Solving 3 variable simultaneous equations by elimination
- 7.6Solving 3 variable simultaneous equations (no solution, infinite solutions)
- 7.7Word problems relating 3 variable simultaneous equations

- 7.1Simultaneous linear equations
##### 8Operations with Algebraic Fractions

- 8.1Simplifying algebraic fractions and restrictions
- 8.2Adding and subtracting algebraic fractions
- 8.3Multiplying algebraic fractions
- 8.4Dividing algebraic fractions
- 8.5Solving equations with algebraic fractions
- 8.6Applications of equations with algebraic fractions
- 8.7Simplifying complex fractions
- 8.8Partial fraction decomposition

- 8.1Simplifying algebraic fractions and restrictions
##### 9Algebraic Division

##### 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

- 11.1Transformations of functions: Horizontal translations
##### 12Reciprocal Functions

##### 13Rational Functions

##### 14Circle Theorems

##### 15Trigonometry

- 15.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 15.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 15.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 15.4Combination of SohCahToa questions
- 15.5Solving expressions using 45-45-90 special right triangles
- 15.6Solving expressions using 30-60-90 special right triangles
- 15.7Word problems relating ladder in trigonometry
- 15.8Word problems relating guy wire in trigonometry
- 15.9Other word problems relating angles in trigonometry

- 15.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 16Trigonometric Ratios and Angle Measure

##### 17Sine Rule and Cosine Rule

##### 18Bearings

##### 19Trigonometric Identities and Equations

##### 20Graphing Trigonometric Functions

##### 21Laws of Indices

##### 22Exponentials Functions

##### 23Logarithms

- 23.1What is a logarithm?
- 23.2Converting from logarithmic form to exponential form
- 23.3Evaluating logarithms without a calculator
- 23.4Common logarithms
- 23.5Natural log: ln
- 23.6Evaluating logarithms using change-of-base formula
- 23.7Converting from exponential form to logarithmic form
- 23.8Solving exponential equations with logarithms
- 23.9Product rule of logarithms
- 23.10Quotient rule of logarithms
- 23.11Combining product rule and quotient rule in logarithms
- 23.12Evaluating logarithms using logarithm rules
- 23.13Solving logarithmic equations
- 23.14Graphing logarithmic functions
- 23.15Finding a logarithmic function given its graph

- 23.1What is a logarithm?
##### 24Sequences and Series

##### 25Binomial Expansion

##### 26Differentiation

##### 27Integration

##### 28Statistics

##### 29Data and Graphs

##### 30Probability

##### 31Discrete Probabilities

##### 32Normal Distribution and Confidence Intervals

##### 33Correlation and Regression