GCSE Maths

Please Note: These are just some of the topics that may be covered for GCSE maths which may help with revision

Contents

Number
Standard Form

Algebra
Identity or Equation?
Expanding Brackets
Solving Linear Equations
Indices
Surds
Working with Functions
Factorising
Completing the Square
Simultaneous Equations
Quadratic Equations
Gradient
Lines
Intersection of Graphs
Quadratic Graphs
Inequalities
Graph Transformations
Circles
Rational Expressions
Sequences and Series
Iteration
Ratio, proportion and rates of change
Percentages

Geometry and Measures
Sectors: Area and Arc Length
Pythagoras’ Theorem
Trigonometry: Right-Angled Triangles
Trigonometric Ratios
Trigonometry: Non Right-Angled Triangles
Trigonometry: Graphs
Vectors

Probability
Possibility Space (Sample Space)
Tree Diagrams
Venn Diagrams

Statistics
Mean
Median and Quartiles
Statistical Diagrams

About Maths GCSE

Number

Standard Form (Scientific Notation)

  1. Expressing a number in standard form or scientific form

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Algebra

Identity or Equation?

  1. Identity or equation - what is the difference?

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Expanding Brackets

  1. Expanding a single bracket
  2. Expanding two or more brackets
  3. Squaring a bracket

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Solving Linear Equations

  1. Terms in expressions and equations
  2. Linear Equations with a positive x term
  3. Linear equations with a negative x-term
  4. Linear equations with two x-terms
  5. Linear equations with brackets
  6. Fractional linear equations

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Indices

  1. Introduction to indices (exponents)
  2. Multiplication rules for indices
  3. Division rule for indices
  4. Negative indices
  5. Fractions raised to a negative index
  6. Rational (fractional) indices
  7. Simplifying terms with negative powers
  8. Expressing terms in the form axn
  9. Equations in which the power has to be found
  10. Summary of indices

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Surds

  1. Surds - introduction & simplifying
  2. Addition and subtraction of surds
  3. Multiplying surds
  4. Dividing surds
  5. Rationalising surds
  6. Exam Questions - Surds

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Working with Functions

  1. f(x) notation
  2. Combination of functions
  3. The inverse of a function

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Factorising

  1. Introduction to factorising
  2. Highest common factor (HCF)
  3. Factorising by grouping
  4. Factorising quadratic expressions
  5. Mixed Exercise - Factorising

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Completing the Square

  1. Completing the square
  2. Applications of completing the square
  3. Exam Questions - Completing the square

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Simultaneous Equations

  1. Elimination method for linear equations
  2. Substitution method for linear and non-linear equations
  3. Exam Questions - Simultaneous equations

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Quadratic Equations

  1. Solve by factorising
  2. Solve by completing the square
  3. Solve by the quadratic formula
  4. Exam Questions - Solved by the quadratic formula

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Gradient

  1. Line segment
  2. Parallel lines
  3. Perpendicular lines

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Lines

  1. Equation of a straight line: y=mx+c
  2. Equation of a line given the gradient and point
  3. Distance between two points
  4. Mid-point of a line segment
  5. Equation of a parallel line
  6. Equation of a perpendicular bisector

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Intersection of Graphs

  1. Intersection of two straight lines
  2. Intersection of a straight line and a parabola
  3. Intersection of a straight line and a hyperbola

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Quadratic Graphs

  1. Sketching quadratic graphs

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Inequalities

  1. Rules for reversing the inequality sign
  2. Solving a linear type
  3. Quadratic inequalities

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Graph Transformations

  1. Basic graphs used in transformations
  2. Translations of graphs
  3. Reflections of graphs

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Circles

  1. Equation of a circle
  2. Finding the centre and radius

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Rational Expressions

  1. Simplifying algebraic fractions
  2. Exam Questions - Simplifying a rational expression
  3. Addition and subtraction of algebraic fractions
  4. Exam Questions - Addition & subtraction
  5. Multiplication of algebraic fractions
  6. Further simplifying of 'stacked fractions'

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Sequences and Series

  1. Definition and finding the nth term
  2. Recurrence relationships
  3. Exam Questions - Recurrence relationships

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Iteration

  1. Iteration

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Ratio, proportion and rates of change

Percentages

  1. What is a percentage?
  2. Finding a percentage of a quantity
  3. Converting a fraction to a percentage
  4. Calculating a percentage change
  5. Increasing / decreasing a quantity by a percentage

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Geometry and measures

Sectors: area and arc length

  1. Area and arc length

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Pythagoras’ Theorem

  1. Pythagoras' theorem

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Trigonometry: Right-Angled Triangles

  1. Introduction to trigonometry
  2. Finding the length of a side
  3. Finding an angle

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Trigonometric Ratios

  1. Trigonometric ratios for 30°, 45° and 60°
  2. Trig ratios for multiples of 30°, 45° and 60°

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Trigonometry: Non Right-Angled Triangles

  1. Area of a triangle - Given two sides and an included angle
  2. Sine rule
  3. Cosine rule
  4. Bearings - Applications of the sine and cosine rules

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Trigonometry: Graphs

  1. Trigonometric graphs
  2. Translations of trig graphs
  3. Reflections of trig graphs

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Vectors

  1. What is a vector and a scalar quantity?
  2. Vector notation 2d
  3. Position vectors 2d
  4. Equal and negative vectors
  5. Multiplying a vector by a scalar 2d
  6. Addition and subtraction of vectors 2d
  7. Magnitude of a 2 dimensional vector

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Probability

Possibility Space (Sample Space)

  1. Possibility space diagrams

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Tree Diagrams

  1. Tree Diagrams
  2. Probability Tree Diagrams for Independent Events
  3. And Rule (multiplication) / Or Rule (addition for mutually exclusive events)
  4. Probability Tree Diagrams for Dependent Events

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Venn Diagrams

  1. Algebra of sets
  2. Venn diagrams
  3. Notation and defining regions

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Statistics

Mean

  1. Mean for discrete data
  2. Calculating the mean from a frequency table
  3. Exam Questions - Discrete data / mean

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Median and Quartiles

  1. Cumulative frequency curves

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Statistical diagrams

  1. Box and whisker plots

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About GCSE Maths

GCSE maths has a grading system that uses numbers 1-9 to identify levels of performance with 9 being the top level. A student will either enter for the Higher tier covering grades 4-9 or for the Foundation tier covering grades 1-5.

There will be three papers at each tier, two papers where candidates can use a calculator and a third paper where calculators are not to be used.

The syllabus is divided into six sections that test

1. Number

2. Algebra

3. Ratio, proportion and rates of change

4. Geometry and measure

5. Probability

6. Statistics

  • The main examination boards for GCSE maths are Edexcel, AQA and OCR.
  • On this site you will find plenty of video tutorials which hopefully will give you the confidence and support you need to tackle your GCSE maths course.
  • Don’t forget to take a look at the GCSE math exam tips page.

Check out the official GCSE maths specifications here: Edexcel | OCR | AQA

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