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GCSE Maths Revision Worksheets

Here are the Metatutor Foundation & Higher maths revision worksheets. These are really useful tools in your revision, as they allow you to focus on weak areas. Solutions to each maths worksheet are also provided in case you get stuck and need to know how to solve the questions. The worksheets have been written in such a way to replicate real GCSE maths past papers, starting each topic off with easier questions, which become harder as you progress through the worksheet. The search function below allows you to find the specific topic you are looking for. You can also sort by Foundation and Higher or by topic name. Click on the Worksheet or Answers buttons to view the document in PDF form. If you want someone to work through some of these with you in person, book a free taster session . We also have a set of GCSE mini maths exams to test out your knowledge in realistic exam conditions. If you’ve already completed our maths worksheets and want more practice, here are some more excellent websites where you can find further free resources: CorbettMaths , MathsMadeEasy , TES

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GCSE Maths Revision Worksheets

Maths Worksheets / GCSE Maths Revision Worksheets

New resources from Cazoom Maths – An excellent range of GCSE Maths Revision resources. Our range of GCSE Maths Revision worksheets include 1000s of GCSE maths questions and cover all key topics in the GCSE curriculum. These revision questions are divided by topic and by target grade , so there is something to suit students of all abilities. These maths revision worksheets in PDF are suitable for all exam boards, including AQA, Edexcel and OCR. The worksheets include answers  and so are perfect for classroom learning or homeschooling.  

The full collection of over 170 GCSE Maths Revision worksheets are now available below. Get a Cazoom Maths Free Trial  and access our GCSE revision materials right now, along with 1000’s of KS1 to KS4 maths worksheets. 

NUMBER GCSE REVISION WORKSHEETS

Target grade, number of questions, estimated time to complete, geometry gcse revision worksheets, algebra gcse revision worksheets, statistics and probability gcse revision worksheets, list of topics.

Our printable maths worksheets cover the full range of topics. See below the list of topics covered. All our maths worksheets can be accessed here .

  • Expanding Brackets
  • Factorising
  • Inequalities
  • Linear Functions
  • Real Life Graphs
  • Rearranging Equations
  • Simplification
  • Solving Equations
  • Substitution
  • Calculator Methods
  • Fractions Decimals Percentages
  • Mental Methods
  • Negative Numbers
  • Percentages
  • Place Value
  • Types of Number
  • Written Methods
  • Area and Perimeter
  • Bearings Scale and Loci
  • Compound Measures
  • Constructions
  • Coordinates
  • Lines and Angles
  • Similarity and Congruence
  • Transformations
  • Volume and Surface Area
  • Histograms and Frequency Polygons
  • Mean Median Mode
  • Pie Charts and Bar Charts
  • Probability
  • Scatter Graphs
  • Stem-and-Leaf Diagrams
  • Two-Way Tables and Pictograms

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Gcse maths revision.

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Revision Notes

Key Topics

Revision notes and tutorials covering key GCSE maths topics you need to learn.

Maths Workouts

Practise your skills and collect StudyPoints with these interactive maths workouts.

Maths Games

Coffee Break Maths Games

A collection of maths games and puzzles. Earn bonus StudyPoints for your high scores!

Question Bank

Question Bank

A bank of GCSE exam style questions to aid your revision. Try to answer them all!

Formulae

Formulae you will need for your maths exam with interactive examples of how to use them.

Glossary

A glossary of key mathematical words and their meanings.

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GCSE Maths

Alternate Angles

Here we will learn about alternate angles including how to recognise when angles are alternate and apply this understanding to solve problems.

There are also angles in parallel lines worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are alternate angles?

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size . 

Alternate angles are equal :

We can often spot interior alternate angles by drawing a Z shape:

There are two different types of alternate angles, alternate interior angles and alternate exterior angles . 

Below are diagrams showing these two variations. 

Alternate interior angles :

Here, the two angles of a and b are in between the parallel lines and therefore are pairs of alternate interior angles.

Alternate exterior angles :

Here, the two angles of c and d are outside of the parallel lines and so these are two examples of pairs of alternate exterior angles.

It is important to notice that the transversal on each diagram is at a different angle but the two angles in each diagram are the same size. As is the case with all diagrams for angles in parallel lines, never use a protractor to find an angle as all the diagrams, unless stated otherwise, are not to scale.

What are alternate angles?

How to calculate with alternate angles

In order to calculate with alternate angles:

  • Highlight the angle(s) that you already know.
  • Use alternate angles to find a missing angle.

Use a basic angle fact to calculate the missing angle.

How to calculate with alternate angles.

How to calculate with alternate angles.

Alternate angles worksheet

Get your free alternate angles worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Alternate angles examples

Example 1: alternate angles.

Calculate the size of the missing angle θ. Justify your answer.

Highlight the angle(s) that you already know .

2 State the alternate angle, co-interior angle or corresponding angle fact to find a missing angle in the diagram.

Here we can label the alternate angle on the diagram as 50 °.

3 Use a basic angle fact to calculate the missing angle.

Here as θ is on a straight line with 50 °.

Example 2:  alternate angles

State the alternate angle, co-interior angle or corresponding angle fact to find a missing angle in the diagram.

Here we can state the angle 62 ° as it is corresponding to the original angle.

The angle θ is the alternate angle to the sum of 56 ° and 62 ° as shown in the diagram below.

Example 3: alternate angles with algebra

By working out the value for x , calculate the size of the missing angle θ. Justify your answer.

Here we know most of the angles so highlight the angles that are going to help you find the value of x .

Here, 3x and 30 ° are alternate to each other. We can therefore find the value for x :

Here we can use the sum of angles in a triangle to help us calculate the value for θ. The value for 10x=100 ° as x=10 °. We therefore can calculate θ:

Common misconceptions

  • Mixing up angle facts

There are a lot of angle facts and it is easy to mistake alternate angles with corresponding angles. To prevent this from occurring, think about the alternate angles being on the alternate sides of the line.

  • Using a protractor to measure an angle.

Using a protractor to measure an angle. Most diagrams are not to scale and so using a protractor will not result in a correct answer unless it is a coincidence.

Related lessons

Alternate angles is part of our series of lessons to support revision on angles in parallel lines. You may find it helpful to start with the main angles in parallel lines lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

  • Angles in parallel lines
  • Corresponding angles
  • Co-interior angles

Practice alternate angles questions

1. Calculate the size of angle \theta .

GCSE Quiz False

104^{\circ} and \theta are alternate angles so \theta = 104^{\circ}.

2. Calculate the size of angle \theta.

Using alternate angles and angles on a straight line: \theta=180-103=77^{\circ}

3. Find the value of \theta

Using alternate angles, we can see that the angle in the bottom right vertex of the triangle is 38^{\circ} . We can then use angles in a triangle: \theta = 180-(79+38)=63^{\circ}

4. Work of the value of \theta

Using alternate angles, we can see the angle \theta=22^{\circ} . We can then use the fact that this is an isosceles triangle and the other two angles in the triangle are the same.

180-22=158 \begin{aligned} 158 \div 2 &= 79^{\circ}\\ \theta &= 79^{\circ} \end{aligned}

5. Calculate the size of angle \theta

Using alternate angles, we can see the angle 110^{\circ} . Then \theta=110-42=68^{\circ}

6. By calculating the value for x , work out the value of each angle labelled.

Alternate angles are equal so 7x-20=4x+10

When x=10 : 7x-20=710-20=50^{\circ} 4x+10=410+10=50^{\circ}

Alternate Angles GCSE questions

1. Find the size of angle a . Give reasons for your answer.

180 – 70 = 110 since angles in a triangle add up to 180^{\circ}.

Isosceles triangle so two angles equal 110 \div 2 = 55.

Alternate angles are equal so a=55^{\circ}.

2. Find the size of angle y .

Angle ACD = 72^{\circ}

Angle ACB = 180 - \left (90+48 \right ) = 42^{\circ}

72-42=30^{\circ}

3. Show that the lines AB and CD are parallel.

5x+3+4x-12=180

\begin{aligned} 9x-9&=180\\ 9x&=189\\ x&=21 \end{aligned}, \begin{aligned} 5 \times 21+3&=108\\ 6 \times 21 - 18&=108 \end{aligned}.

Alternate angles are equal therefore the lines are parallel.

Learning checklist

You have now learned how to:

  • Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
  • Understand and use the relationship between parallel lines and alternate and corresponding angles

The next lessons are

  • Angles in polygons
  • How to calculate volume

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