It can be so important to get a good grade in the maths GCSE, no matter whether you want to take maths on to A-Level or not, it can be a fundamental pre-requisite to many jobs, even the non-maths related ones! Maths can be one of the harder subjects to master however, and there are many topics to cover.

We have developed a special GCSE revision course with great maths tutors to give you the boost you need in the subject. We can help you identify areas you need to work on, support you through those trickier problems and give you some great tips and guidance on exam technique. Look at the revision guide below to see areas we can cover in our tailored maths tuition.

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1. Structure and calculation

In this section you should show competency with different types of numbers, such as

Structure and calculation
  • Positive integers
  • Negative integers
  • Fractions
  • Decimals
  • Prime numbers
  • Indices
  • Surds

Ability to add, subtract, multiply and divide these numbers. This includes simplifying and cancelling, understanding the use of brackets, powers and roots.

Recognise relationships between these numbers.

Order these numbers from highest to lowest, using the symbols =, ≠, <, >, ≤, ≥

Use and solve calculations with positive powers 2, 3, 4 and 5 and their accompanying roots.

Calculate and interpret standard index form, A x 〖10〗^n where n is any number.

You should be familiar with the following vocabulary

  • Factors/divisors
  • Multiples
  • Common factors
  • Common multiples
  • Highest common factor
  • Lowest common multiple
  • Prime factorisation

2. Fractions decimals and percentage

You should be able to understand, convert and solve calculations between

  • Fractions and terminating decimals
  • Fractions and ratios
  • Fractions and percentages

3. Measures and accuracy

In this section, you should be familiar with measures and their corresponding units of the following,

  • Mass
  • Length
  • Time
  • Money

You should be able to estimate, approximate, check answers with estimations and approximations and round numbers.


1. Notation, vocabulary and manipulation

You should be able to use and interpret algebraic notations

Algebra - Expanding and Factorizing

You should be able to

  • Substitute in numbers
  • Simplify and manipulate expressions
  • Collect like terms
  • Multiply out brackets
  • Factorising quadratic equations

2. Graphs

You should be able to work with co-ordinates in all four quadrants of the x,y axis
You should be able to

  • plot graphs of straight lines with their perpendiculars
  • calculate gradients and intercepts of linear functions
  • calculate roots and turning points of quadratic functions
  • sketch translations
  • calculate areas under graphs
  • understand the equation of a circle and calculate its tangent

3. Solving equations and inequalities

In this section you should show competency in the following areas

  • Linear equations
  • Quadratic equations
  • Simultaneous equations
  • Linear inequalities

You should be able to find unknown values, solutions using graphs, completing the square by factorisation and the quadratic formula, solve equations with more than one variable, find approximate solutions by iteration, and solve equations for more than one variable.

4. Sequences

You should be familiar with many types of sequence,

  • Triangular, square and cube sequences
  • Arithmetic , geometric and quadratic progressions
  • Fibonacci sequences

You should be able to find the next terms of a sequence and calculate the n^th term

Ratio, proportion and rates of change

Show competency switching between various units of measure and attributing the correct units, for time, length, area, volume, mass, speed, money and density.

Express quantities as fractions and ratios, compare and relate different quantities. Link percentages to quantities, fractions, ratios and decimals, and solve problems relating to percentage change.

You should be comfortable with direct proportion and inverse proportion, their graphical representations and their equations; how X is inversely proportionate to Y and X is proportional to 1/Y.

Calculate the rate of change by solving for the gradient of a line.

Geometry and measures

1. Properties and constructions

You should be familiar with the following vocabulary and use it correctly in labelling and drawing

hypotenuse, adjacent, opposite
  • Points
  • Vertices
  • Edges
  • Planes
  • Parallel
  • Perpendicular
  • Polygon
  • Reflection
  • Rotation

Have competency with a ruler and compass to bisect lines and angles, form perpendiculars and construct figures.

Understand polygon and angle properties, such as opposite, alternate and corresponding angles and summation of angles in polygons.

You should be familiar with the co-ordinate axes and use to solve geometrical problems.

You should be able familiar with circle properties, to solve and prove theorems.

Identify between congruency and similarity, apply rotation, reflection, translation and enlargement to polygons and construct these on co-ordinate axes.

Apply Pythagoras theorem to obtain results on angles and lengths of triangles and quadrilaterals.

2. Mensuration and calculation

Understand standard measure units for, length, area, volume, mass, time and money.

You should be able to measure lines and angles in shapes, graphs and bearings

Know and apply the formulae for

  • Area of a triangle, parallelogram and a trapezium
  • Volume of a cuboid and various prisms
  • Circumference of a circle
  • Area of a circle
  • Surface areas for spheres, pyramids and cones
  • Volumes for spheres, pyramids and cones
  • Pythagoras’ theorem
  • Trigonometric ratios
  • Sine and cosine rule

Understand congruence and similarity and their relationships between lengths, areas and volumes of shapes.

Know the exact values of sin, cos and tan, with the angles 0°, 30°, 45°, 60° and 90°.

3. Vectors

You should be able to define translations as a 2D vector.

Apply addition, subtraction and scalar multiplication to a vector.

Use vectors for arguments and proofs.



Record the frequency of outcomes in frequency tables and analyse results.

Understand the concept of a random event and fair events and predict future outcomes.

Convert frequencies into probabilities on the 0-1 scale, understanding that all probabilities sum to one.

Understand the relationship between increased sample size and reduced bias.

Represent probabilities through Venn diagrams and tree diagrams.

Understand the difference between dependant and independent events, and calculate their probabilities.

Interpret conditional probabilities and expected frequencies.


Interpret and build tables, charts and diagrams, including

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  • Bar charts
  • Pie charts
  • Pictograms
  • Line graphs
  • Scatter graphs
  • Box plots
  • Histograms
  • Cumulative frequency graphs

Analyse data distributions with box plots and apply mean, median and mode, range and quartiles.

Analyse scatter graphs and their degree of correlation

Interpret and understand the use of cumulative frequency graphs, and histograms with their class intervals.

Do you have problems grasping any of these topics?

There is so much to cover in GCSE maths. If you are struggling in any of these topics, or need an extra push to get that grade you need, the Maths Doctor revision course is just what you need.

Fill out the form on the right with your parent’s details, and you are only a few steps away from getting maths help.