Rotation: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

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gcse maths rotations worksheet

GCSE Rotations Worksheet HOT

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40 GCSE Foundation Maths Number Algebra Geometry Statistics Worksheets Bundle

40 GCSE Foundation Maths Number Algebra Geometry Statistics Worksheets Bundle

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Worksheet Whisperer

Last updated

10 February 2024

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gcse maths rotations worksheet

Overview This resource is a comprehensive set of 40 downloadable worksheets designed to reinforce and enhance students’ skills in GCSE Foundation Maths topics on number, algebra, geometry and statistics.

Worksheet Structure It includes 40 practice pyramid worksheets, each worksheet is split into practice and exam questions, one for each of the following topics: BIDMAS FDP Fractions Fractions and Recurring Decimals Percentages Powers and Roots Ratio Prime Factors, HCF & LCM Standard Form Rounding Forming and Solving Equations Simultaneous Equations Changing the Subject Collecting Like Terms Expanding and Factorising Indices Inequalities Sequences Solving Equations Substitution Area/Circumference of a Circle Equation of a Straight Line Bearings Interior and Exterior Angles Loci and Constructions Parallel Line Angle Rules Pythagoras’ Theorem Transformations Trigonometry Volume and Surface Area Speed, Distance, Time Density, Mass, Volume Estimate of the Mean Frequency Tables Mean, Mode, Median & Range Probability Tree Diagrams Questionnaires Relative Frequency Sets and Venn Diagrams Stratified Sampling

Answer Key Accompanying the 40 worksheets are answers to each one. This resource serves as a valuable tool for both self-assessment and facilitator guidance, allowing students to review their work independently or seek assistance when needed.

Printable Format The GCSE Foundation Maths Worksheet Bundle is available in a downloadable PDF format, making it easy for teachers, parents, or students to print the worksheets and answers for offline use. Clear instructions are provided to ensure a seamless learning experience.

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Transformations: Rotation

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gcse maths rotations worksheet

Visual maths worksheets, each maths worksheet is differentiated and visual.

Rotation Worksheet suitable for students in KS3

Rotation (A) worksheet

Total reviews: (0), rotation (a) worksheet description.

Give your students ample practice of rotating objects on individual square grids with this worksheet. There are 12 objects to rotate either clockwise or anticlockwise around a given point by multiples of 90 degrees. The polygons in each question are unique and have vertical, horizontal and diagonal sides. All centres of rotation are on a vertex of each polygon; the perfect place to introduce or discuss invariant points with your class or individual.

Other key questions include, why is no direction listed when rotating a shape 180 degrees and why have you not been asked to rotate a shape 360 degrees?

Ensure learners are equipped with a pencil and a ruler and they may require access to tracing paper.

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GCSE Maths

Transformations

Here we will learn about transformations, including similar shapes and congruent shapes and triangles, reflections, translations,  rotations and enlargements.

There are also transformations 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 transformations?

Transformations change the size and/or the position of a shape.

To do this we need a 2D shape (such as a polygon) and to follow the instructions given.  These instructions are sometimes known as a mapping.

There are four geometric types of transformations:

Reflections involve a mirror line, also known as a line of reflection. 

The shapes are congruent.

Step-by-step guide: Reflection

Rotations involve a centre of rotation , an angle of rotation and a direction of rotation (clockwise or anticlockwise).

Step-by-step guide: Rotations

Translation

Translations involve a move in a horizontal direction and a move in a vertical direction.

Step-by-step guide: Translation

Enlargement

Enlargements make a shape bigger or smaller. They must have a scale factor and they may involve a centre of enlargement . 

The shapes are similar.

Questions can involve a single transformation or at Higher, GCSE questions can combine transformations.

When we combine transformations we need to do the first transformation on the original shape, then carry out a second transformation on the new shape. 

Step by step guide: Enlargement

What are transformations?

What are scale factors?

Scale factors tell us how much bigger or smaller a shape will become when it is enlarged.

To enlarge a shape we multiply each side length of the shape by the scale factor.

They can be integers or fractions.

  • If the scale factor is greater than 1 , the shape gets larger . E.g. The scale factor of enlargement from shape A to shape B is 2
  • If the scale factor is between 0 and 1 , the shape gets smaller . E.g. The scale factor of enlargement from shape A to shape B is \frac{1}{2} or 0.5

At GCSE Higher, there may be a negative scale factor of enlargement.

Step-by-step guide: Scale factor

What are invariant points?

Invariant points are points which have stayed in the same place after a transformation.

Here is a reflection.  The invariant point is labelled.

Similar and congruent shapes

For geometrical transformations we need to understand the terms similar and congruent .

  • Similar shapes

Similar shapes are two or more shapes which are the same shape, but different sizes. One shape is an enlargement of the other.

These two triangles are similar.

Step-by-step guide: Similar shapes

  • Congruent shapes

Congruent shapes are shapes that are exactly the same.

These two triangles are congruent.

Step-by-step guide: Congruent shapes

  • Congruent triangles

Congruent triangles also have special conditions of congruence. These involve looking at their sides and angles. 

The four conditions are known by abbreviations:

SSS (three sides the same),

RHS (right-angled triangle, hypotenuse and a side the same),

ASA or AAS (two angles and one side the same),

SAS (side-angle-side, two sides and the included angle the same).

Step-by-step guide: Congruent triangles

How to use transformations

  • Use a pencil, additional construction lines and tracing paper to help.
  • Remember: Reflections have a mirror line. Rotations have an angle of rotation, a direction and a centre of rotation. Enlargements have a scale factor (and sometimes a centre of enlargement). Translations have a distance across and a distance up or down.
  • Similar shapes are linked to enlargements.
  • Congruent shapes are linked to reflection, rotations and translations.

Transformations worksheet

Transformations worksheet

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

Transformations examples

Example 1: similar shapes.

These shapes are similar. Find the value of x.

  • Match up the corresponding sides and consider the ratio. 4:x=7:14
  • Find a scale factor. 14\div 7 =2
  • Use the scale factor to find the missing side. x=4\times 2=8 The missing side is 8 cm .

Example 2: congruent shapes

Which shape is congruent to shape A?

  • Look at the shapes and see if any are the same type of shape.
  • Then look carefully and check the corresponding angles and sides. Congruent shapes can be rotated or reflected or both.
  • Shape Y is congruent to shape A.

Example 3: congruent triangles

Are these triangles congruent?

  • Check the corresponding sides and angles. \begin{aligned} &\text{side} \ AC = \text{side} \ DE \\ &\text{angle} \ BAC = \text{angle} \ EDF\\ &\text{angle} \ BCA = \text{angle} \ FED \end{aligned}
  • Triangle ABC is congruent to triangle DEF. This is because they have two equal corresponding angles and the included side in both triangles is also equal. This is known as angle-side-angle (ASA).

Example 4: reflection

Reflect the shape in the mirror line.

  • Consider each point (the vertices of the original shape) and reflect it in the mirror line. The new points will be the same distance from the mirror line as the original points.
  • Then join up the new points.

Example 5: rotations

Rotate the shape 90^{\circ} clockwise about the centre of rotation.

  • Use tracing paper.  Trace the original shape and check where the centre of rotation is.

Transformations Example 5

  • Put the tip of your pencil on the centre of rotation.  Rotate the correct angle and in the right direction.

Transformations Example 5-1

  • Then draw your new shape onto the paper.

Example 6: translation

Translate the shape using the vector

  • Choose a point (vertex) of the original shape and move it using the column vector.
  • The column vector gives instructions on how to move the original point. \begin{pmatrix} 3\\ -1 \end{pmatrix} \text{is} \begin{pmatrix} 3 \ \text{right}\\ 1 \ \text{down}\\ \end{pmatrix} ​
  • Repeat for the other points (vertices). Or you can just draw in the rest of the polygon. You may use tracing paper to check.

Example 7: enlargements – scale factor

Enlarge the shape by scale factor 3

  • Choose a side to enlarge first.  The left-side in the original shape is 1 , so the left-side in the new shape will be 9 .  This can be drawn anywhere on the grid. 3\times3=9
  • Enlarge the other sides using the same scale factor.

The lengths of the sides of the second shape are three times the lengths of the original shape.

Example 8: enlargements – centre of enlargement

Enlarge the shape by scale factor 2 , using the centre of enlargement.

  • Draw ray lines through the centre of enlargement and each of the vertices of the original shape.
  • Measure the distance from the centre of enlargement to a point (vertex) and then use the scale factor of 2 and mark the position of the new point.
  • Repeat for the other points (vertices).

Example 9: combined transformations (Higher)

Reflect triangle A in the line x =1 to give triangle B . Reflect triangle B in the line y =0 to give triangle C .

Carry out the first transformation on the original shape (triangle A ).

Then carry out the second transformation on the new shape (triangle B ).The line y=0 is the x-axis.

Transformations Example 9 (Higher)-1

You may be asked to describe the single transformation that maps triangle A onto triangle C .  

For this example the single transformation would be:Rotate triangle A   180° about (1,0) to give triangle C .

Common misconceptions

  • Use the grid to help put the vertices of the shape in the correct position

Geometric transformations of shapes are often on grid paper.  Use the lines and squares on the grid to help you be accurate about the position of the new shape.

  • You can add extra details onto your diagram to help you

Try not to do transformation work in your head.  Make use of your pencil and ruler to add marks to help you.  You may also use tracing paper.

  • Describe transformations fully

When you are asked to describe a transformation make sure you state which kind of transformation it is and all other details.

  • Make sure you have the object and the image the right way around

The original shape is the object and the translated shape is the image.  Make sure you know which shape is the original shape and start there when describing transformations such as translations.

Practice transformations questions

1. These two shapes are similar. Find the missing value of x .

GCSE Quiz False

Sides BC and CE are a pair of corresponding sides. Sides AC and CD are also a pair of corresponding sides.

The scale factor is

2. Reflect the shape in the mirror line.

Reflect each point in the mirror line. The new points will be the same distance from the mirror line as the original points.

3. Rotate the shape 90^{\circ} anti-clockwise about the point O.

Use tracing paper to help with the rotation.

Transformations Practice Question 3 Explanation Image

4. Translate the shape using the vector

 The column vector gives the instructions on how to move each of the points.

5. Enlarge the shape using the scale factor \frac{1}{2}

The scale factor is \frac{1}{2} . The side lengths of the original shape need to be halved (or divided by 2 ). The height of the original shape is 4 , so the height of the new shape will be 2 .

The base of the original shape is 2 , so the base of the new shape will be 1.

6. Enlarge the shape by scale factor 3 , using the centre of enlargement O.

The distances between the points of the original shape and the centre of enlargement need to be multiplied by three.

Transformations GCSE questions

1. Give a reason why the two triangles are congruent.

Side-side-side (SSS)

2. Triangles ABC and DEF are similar.

Work out the value of x

For the scale factor

For the correct value of x

3.  (a)       Translate shape A using the vector

(b) Describe the single transformation that maps shape A onto shape P.

In the line x=4

4 (higher). Triangle A is rotated 90^{\circ} clockwise about the point (0, 0) to give triangle B.

Triangle B is translated by the vector \begin{pmatrix} 3\\ 2 \end{pmatrix} to give triangle C.

Describe fully the single transformation that maps triangle A onto triangle C.

About (1.5,2)

Learning checklist

You have now learned how to:

  • Recognise congruent shapes and triangles
  • Find missing lengths of similar shapes using a scale factor
  • Reflect shapes in a mirror line
  • Rotate shapes about a point
  • Translate shapes using a column vector
  • Enlarge shapes using a scale factor
  • Enlarge shapes with a centre of enlargement

The next lessons are

  • Trigonometry
  • Pythagoras’ theorem
  • Constructions

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COMMENTS

  1. Rotations Practice Questions

    The Corbettmaths Practice Questions on Rotations. GCSE Revision Cards. 5-a-day Workbooks

  2. Rotations

    Rotations worksheet Get your free rotations worksheet of 20+ questions and answers. Includes reasoning and applied questions. DOWNLOAD FREE Rotations examples Example 1: rotate a shape about a fixed point Rotate the shaded shape 90^o 90o clockwise about the fixed point: Trace the shape.

  3. PDF Mathematics (Linear) 1MA0 ROTATION

    Edexcel GCSE Mathematics (Linear) - 1MA0 ROTATION Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Instructions Items included with question papers Nil Use black ink or ball-point pen.

  4. PDF Name: GCSE (1

    Information The marks for each Question are shown in brackets use this as a guide as to how much time to spend on each Question. Advice Read each Question carefully before you start to answer it. Keep an eye on the time. Try to answer every Question. Check your answers if you have time at the end mathsgenie.co.uk 1 y

  5. Rotations. GCSE Maths Past Paper Questions.

    This resource contains all of the Rotations questions that have come up in the Edexcel GCSE maths papers to date (Autumn 2021), arranged as a printable worksheet. There is also reference to which paper each question came up on. The full solutions are also included (please let me know if you spot any mistakes).

  6. PDF Exam Style Questions

    Rotations Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance Read each question carefully before you begin answering it. Donʼt spend too long on one question. Attempt every question. Check your answers seem right. Always show your workings

  7. Rotations Textbook Exercise

    The Corbettmaths Textbook Exercise on Rotations. ... Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. Further Maths; ... Previous: Reflections Textbook Exercise. Next: Rounding to the Nearest Whole Number Textbook Exercise. GCSE Revision Cards. 5-a-day Workbooks. Primary Study Cards ...

  8. PDF Rotation

    1) On the grid, rotate the triangle 180 clockwise about the point . ................ (2 marks) 2) Rotate the rectangle 90 anticlockwise about (0, 0) 3) Describe fully the single transformation which maps shape A onto shape B. ................ (2 marks) ................ (3 marks) Rotations - Answers 5) 6) 4) 5) 6) Rotate these shapes

  9. Rotation GCSE Questions

    Rotation GCSE Revision Description. This collection covers a wide range of questions, from stating the order of rotational symmetry to describing a rotation on coordinate axes. Learners should experience all of the different rotation-style questions from this worksheet.

  10. Rotation Worksheet

    Help your students prepare for their Maths GCSE with this free rotation worksheet of 24 questions and answers Section 1 of the rotation worksheet contains 18 skills-based rotation questions, in 3 groups to support differentiation Section 2 contains 3 applied rotation questions with a mix of worded problems and deeper problem solving questions

  11. PDF GCSE Maths

    This worksheet will show you how to work through rotations, reflections, translations, and enlargements. Each section contains a worked example, a question with hints and then questions for you to work through on your own. This work by PMT https://bit.ly/pmt-edu-cc Education is licensed under https://bit.ly/pmt-cc CC BY-NC-ND 4.0

  12. PDF Rotations (F)

    Rotations (F) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. 3. Rotate the triangle 90° clockwise so that point C moves to point D. 4. Draw patterns like the given ones in each of the other 2 sections, so that the completed pattern has rotational symmetry of order 4 about O. [2] [2] 5.

  13. Rotation: Worksheets with Answers

    Rotation: Worksheets with Answers Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers. Contents Mathster Corbett Maths Mathster keyboard_arrow_up

  14. Rotation

    Rotation turns a shape around a fixed point called the centre of rotation. Rotation is an example of a transformation. A transformation is a way of changing the size or position of a shape. The ...

  15. GCSE maths rotations worksheet

    pdf, 142.02 KB A GCSE Maths Worksheet covering translation: rotations Suitable for GCSE Students sitting the 9 - 1, A-Level Maths students revision and some Key Stage 3 students. Suitable for all the big examination boards including AQA, Edexcel, OCR and WJEC. This was taken from my 150 Page workbook which covers many more maths topics.

  16. GCSE Rotations Worksheet

    Free Online Alevel, GCSE, Secondary, 11+ Maths Resources, Past Exam Papers, Worksheets, Specimen, Solution Videos, Online Test, Online Self-Assessment GCSE Rotations Worksheet 01245 261144 / 07533966636

  17. 40 GCSE Foundation Maths Number Algebra Geometry Statistics Worksheets

    The GCSE Foundation Maths Worksheet Bundle is available in a downloadable PDF format, making it easy for teachers, parents, or students to print the worksheets and answers for offline use. Clear instructions are provided to ensure a seamless learning experience.

  18. Transformations: Rotation

    Transformations: Rotation Presentations Demonstration PPT Worksheets Worksheet 2 Types PPT A4 PDF A5 PDF A6 PDF Worksheet With Vectors; 2 Levels PPT A4 PDF A5 PDF Activities Blank Grids PPT Standard PDF Small PDF Card Match PPT Quick Cut PDF Standard PDF Small PDF Teacher-Led Activities Bingo Method: With Vectors

  19. Rotational Symmetry Practice Questions

    Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. Further Maths; GCSE Revision; Revision Cards; Books; Rotational Symmetry Practice Questions ... here for Answers. Practice Questions. Previous: Line Symmetry Practice Questions. Next: Distance Charts Practice Questions. GCSE Revision Cards ...

  20. Rotational Symmetry Worksheet

    Help your students prepare for their Maths GCSE with this free rotational symmetry worksheet of 34 questions and answers Section 1 of the rotational symmetry worksheet contains 27 skills-based rotational symmetry questions, in 3 groups to support differentiation

  21. Rotation (A) Worksheet

    Rotation (A) worksheet description. Give your students ample practice of rotating objects on individual square grids with this worksheet. There are 12 objects to rotate either clockwise or anticlockwise around a given point by multiples of 90 degrees. The polygons in each question are unique and have vertical, horizontal and diagonal sides.

  22. Rotational Symmetry

    Rotational symmetry is the number of times a shape can "fit into itself" when it is rotated 360 360 degrees about its centre. E.g. A rectangle has a rotational symmetry of order 2 2 shown below where one vertex is highlighted with a circle and the centre of the shape is indicated with an 'x'. 'x'.

  23. GCSE Maths Revision Worksheets. Foundation & Higher

    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.

  24. Transformations

    Rotations have an angle of rotation, a direction and a centre of rotation. Enlargements have a scale factor (and sometimes a centre of enlargement). Translations have a distance across and a distance up or down. Similar shapes are linked to enlargements. Congruent shapes are linked to reflection, rotations and translations.