# GCSE Maths Help & Practice!

Get better marks with our complete help for GCSE Maths! Our maths tutors have you all covered - whether it's for Edexcel (Pearson), AQA, OCR or WJEC.

Aligning with the new GCSE maths 9 - 1 specifications of all exam boards, our comprehensive lessons cover content in all six topic areas including Number; Algebra; Ratio, proportion and rates of change; Geometry and measures; Probability; and Statistics. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest gcse maths questions. Then, strengthen your understanding with tons of GCSE maths practice questions.

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##### 1Numbers and Relations

##### 2Adding and Subtracting Integers

##### 3Multiplying and Dividing Integers

##### 4Operations with decimals

##### 5Adding and Subtracting Fractions

##### 6Multiplying and Dividing Fractions

##### 7Percents

##### 8Ratios, Rates, and Proportions

##### 9Pythagorean Theorem

##### 10Scale Factors and Similarity

##### 11Solving Linear Equations

##### 12Measuring Systems

##### 13Number System

##### 14Surds

##### 15Algebraic Expressions

##### 16Linear Functions

- 16.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 16.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 16.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 16.4Gradient intercept form: y = mx + b
- 16.5General form: Ax + By + C = 0
- 16.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 16.7Rate of change
- 16.8Graphing linear functions using table of values
- 16.9Graphing linear functions using x- and y-intercepts
- 16.10Graphing linear functions using various forms
- 16.11Graphing linear functions using a single point and gradient
- 16.12Word problems of graphing linear functions
- 16.13Parallel and perpendicular lines in linear functions
- 16.14Applications of linear relations
- 16.15Perpendicular line equation

- 16.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 17Simultaneous Equations

- 17.1Determining number of solutions to linear equations
- 17.2Solving simultaneous linear equations by graphing
- 17.3Solving simultaneous linear equations by elimination
- 17.4Solving simultaneous linear equations by substitution
- 17.5Money related questions in linear equations
- 17.6Unknown number related questions in linear equations
- 17.7Distance and time related questions in linear equations
- 17.8Rectangular shape related questions in linear equations
- 17.9Simultaneous linear-quadratic equations
- 17.10Simultaneous quadratic-quadratic equations
- 17.11Solving 3 variable simultaneous equations by substitution
- 17.12Solving 3 variable simultaneous equations by elimination
- 17.13Solving 3 variable simultaneous equations with no solution, infinite solutions
- 17.14Word problems relating 3 variable simultaneous equations

- 17.1Determining number of solutions to linear equations
##### 18Factorising Quadratic Functions

##### 19Quadratic Functions

- 19.1Introduction to quadratic functions
- 19.2Transformations of quadratic functions
- 19.3Quadratic function in general form:
*y = ax^2 + bx + c* - 19.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 19.5Completing the square
- 19.6Converting from general to vertex form by completing the square
- 19.7Shortcut: Vertex formula
- 19.8Graphing quadratic functions: General form VS. Vertex form
- 19.9Finding the quadratic functions for given parabolas
- 19.10Applications of quadratic functions

- 19.1Introduction to quadratic functions
##### 20Solving Quadratic Equations

- 20.1Solving quadratic equations by factorising
- 20.2Solving quadratic equations by completing the square
- 20.3Using quadratic formula to solve quadratic equations
- 20.4Nature of roots of quadratic equations: The discriminant
- 20.5Solving polynomial equations by iteration
- 20.6Applications of quadratic equations

- 20.1Solving quadratic equations by factorising
##### 21Inequalities

##### 22Algebraic Fractions

- 22.1Simplifying algebraic fractions and restrictions
- 22.2Adding and subtracting algebraic fractions
- 22.3Multiplying algebraic fractions
- 22.4Dividing algebraic fractions
- 22.5Solving equations with algebraic fractions
- 22.6Applications of equations with algebraic fractions
- 22.7Simplifying complex fractions
- 22.8Partial fraction decomposition

- 22.1Simplifying algebraic fractions and restrictions
##### 23Reciprocal Functions

##### 24Functions

- 24.1Function notation
- 24.2Operations with functions
- 24.3Adding functions
- 24.4Subtracting functions
- 24.5Multiplying functions
- 24.6Dividing functions
- 24.7Composite functions
- 24.8Inequalities of combined functions
- 24.9Inverse functions
- 24.10One to one functions
- 24.11Difference quotient: applications of functions

- 24.1Function notation
##### 25Transformations

- 25.1Transformations of functions: Horizontal translations
- 25.2Transformations of functions: Vertical translations
- 25.3Reflection across the y-axis:
*y = f(-x)* - 25.4Reflection across the x-axis:
*y = -f(x)* - 25.5Transformations of functions: Horizontal stretches
- 25.6Transformations of functions: Vertical stretches
- 25.7Combining transformations of functions
- 25.8Even and odd functions

- 25.1Transformations of functions: Horizontal translations
##### 26Sequences

##### 27Indices and Exponential Functions

- 27.1Indices: Product rule
*(a^x)(a^y) = a^(x+y)* - 27.2Indices: Division rule (a^x / a^y) = a^(x-y)
- 27.3Indices: Power rule
*(a^x)^y = a^(x * y)* - 27.4Indices: Negative exponents
- 27.5Indices: Zero exponent:
*a^0 = 1* - 27.6Indices: Rational exponents
- 27.7Combining laws of indices
- 27.8Standard form
- 27.9Convert between radicals and rational exponents
- 27.10Solving for indices
- 27.11Graphing exponential functions

- 27.1Indices: Product rule
##### 28Growth and Decay

##### 29Congruent Triangles

##### 30Circle Theorems

##### 31Surface Area and Volume

##### 32Trigonometry

- 32.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 32.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 32.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 32.4Combination of SohCahToa questions
- 32.5Solving expressions using 45-45-90 special right triangles
- 32.6Solving expressions using 30-60-90 special right triangles
- 32.7Word problems relating ladder in trigonometry
- 32.8Word problems relating guy wire in trigonometry
- 32.9Other word problems relating angles in trigonometry

- 32.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 33Sine Rule and Cosine Rule

##### 34Graphing Trigonometric Functions

##### 35Bearings

##### 36Vectors

##### 37Set Theory

##### 38Probability

##### 39Statistics

##### 40Data and Graphs

- 40.1Reading and drawing bar graphs
- 40.2Reading and drawing histograms
- 40.3Reading and drawing line graphs
- 40.4Box-and-whisker plots and scatter plots
- 40.5Scatter plots and correlation
- 40.6Frequency distribution and histograms
- 40.7Frequency polygons
- 40.8Reading and drawing Venn diagrams
- 40.9Stem-and-leaf plots
- 40.10Shapes of distributions

- 40.1Reading and drawing bar graphs