Enlargement: Worksheets with Answers

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GCSE Enlargements

GCSE Enlargements

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

keitheames

Last updated

22 February 2018

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Thank you for sharing. Will use the fractional enlargement with Y7 Set 1

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Great resources. Thanks for sharing.

londonteachsec

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Thank you - this is an excellent resource.

Nice split into different types of enlargement, useful powerpoint to explain. Used with Year 9 middle ability to go through the past lesson's teaching. Thank-you!

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Scale Factor

Here we will learn about scale factor, including enlarging a shape by a scale factor on a grid. We will extend this to learn about fractional scale factors and how to calculate scale factors.

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

What is a scale factor?

A scale factor describes how much a shape has been enlarged.

We multiply every side length of a shape by the scale factor to enlarge it. The sizes of the angles do not change.

  • Enlarging a shape by a scale factor greater than 1 will make the shape bigger.

Shape A has been enlarged by scale factor 2 to give shape B .

The corresponding angles are identical but each side in shape B is double the size of the original shape. The corresponding angles are identical.

The two shapes are similar shapes.

  • Enlarging a shape by a scale factor between 0 and 1 will make the shape smaller. This is often written as a fraction and is known as a fractional scale factor.

Shape A has been enlarged by scale factor \frac{1}{2} to shape B .

If you look at the corresponding sides, each side in shape B is half the size of the original shape. The corresponding angles are identical.

What is a scale factor?

How to use a scale factor

In order to use a scale factor to enlarge a shape:

Draw an enlargement of the first side.

Enlarge another side.

Complete the enlarged shape.

How to use a scale factor

Scale factor worksheet

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

Scale factor examples

Example 1: use a scale factor to enlarge a shape.

Enlarge this shape by scale factor 2 :

Let’s start with the base. The base in the original shape is 1 , so the base in the enlarged shape will be 2 .

You can draw it anywhere on the grid.

2 Enlarge another side.

Let’s choose a side that is attached to the first side. The height of the first shape is 3 , so the height of the enlarged shape will be 6 .

3 Complete the enlarged shape.

Now continue to draw the new shape.

The lengths of the sides of the second shape are double the lengths of the original shape.

Example 2: use a scale factor to enlarge a shape

Enlarge this shape by scale factor 3 :

The base in the original shape is 2 , so the base in the enlarged shape will be 6 .

The left vertical side of the first shape is 3 , so the corresponding side of the enlarged shape will be 9 .

Now continue to draw the new shape. It is easier to do the horizontal and vertical sides first.

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

Example 3: use a scale factor to enlarge a shape

Enlarge this shape by scale factor \frac{1}{2} :

 The base in the original shape is 4 , so the base in the enlarged shape will be 2 .

The left vertical side of the first shape is 2 , so the corresponding side of the enlarged shape will be 1 .

The lengths of the sides of the second shape are half the lengths of the original shape.

How to calculate a scale factor

In order to calculate a scale factor:

Choose a pair of corresponding sides.

Divide the length of the enlarged shape by the length of the original shape.

Write down the scale factor.

How to calculate a scale factor

Calculating a scale factor examples

Example 4: calculating a scale factor.

Calculate the scale factor for the enlargement of Triangle A to Triangle B :

The two triangles are similar triangles.

Choose a pair of sides, either horizontal or vertical. Here I am choosing the bases.

The base of shape A is 3 .

The base of shape B is 9 .

We need to divide the enlarged length by the original length.

The scale factor of enlargement for Triangle A to Triangle B is 3 .

Example 5: calculating a scale factor

Calculate the scale factor for the enlargement of Shape A to Shape B :

Choose a pair of corresponding sides .

Let’s choose the vertical sides on the left.

The length of shape A is 2 .

The length of shape B is 4 .

The scale factor of enlargement for shape A to shape B is 2 .

Example 6: calculating a scale factor

Let’s choose the bases.

The length of shape A is 9 .

The base of shape B is 3 .

The scale factor of enlargement for shape A to shape B is \frac{1}{3} .

Common misconceptions

  • Fractional scale factors and enlargement

When we are asked to enlarge a shape by a fractional scale factor such as \frac{1}{2} , the shape becomes smaller.

  • Diagonal lines

Diagonal lines can be tricky to enlarge, so it is best to use horizontal and vertical lines. In this kite a horizontal and a vertical line are added to make the enlargement by scale factor 2 easier.

  • Areas of enlarged shapes

For these squares the scale factor of enlargement is 2 . All the lengths have doubled.  The perimeter is doubled.

But the area of the second shape is 4 times larger than the area of the first shape.

For more information on this, check out our lesson on similar shapes.

Step-by-step guide : Similar shapes

Related lessons

Scale factor is part of our series of lessons to support revision on enlargement. You may find it helpful to start with the main enlargement 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:

  • Enlargement
  • Centre of enlargement

Practice scale factor questions

1. Enlarge this shape by scale factor 2

GCSE Quiz False

The original shape is a rectangle. The base of the original shape is 2 , so the base of the enlarged shape will be 4 .

The height of the original shape is 1 , so the height of the enlarged shape will be 2 .

The enlargement will be a rectangle with base 4 and height 2 .

2. Enlarge this shape by scale factor 4

The original shape is a square, so will the enlarged shape. The side of the original square is 1 , so the side of the enlarged square will be 4 .

The enlargement will be a square with side length 4 .

3. Enlarge this shape by scale factor \frac{1}{2}

The original shape has a base of 6 , so the base of the enlarged shape will be 3 .

The other sides need to be halved too.

4. Calculate the scale factor of the enlargement from shape A to shape B .

Scale factor \frac{1}{4}

Scale factor \frac{1}{2}

Scale factor 4

Scale factor 2

The original shape has a base of 2 .

The base of the enlarged shape is 4 .

5. Calculate the scale factor of the enlargement from shape A to shape B .

Scale factor \frac{1}{3}

Scale factor 3

The original shape has a base of 6 .

The base of the enlarged shape is 2 .

6. Calculate the scale factor of the enlargement from shape A to shape B .

The two triangles need to be similar triangles.

The original shape has a vertical height of 6 .

The vertical height of the enlarged shape is 3 .

Scale factor GCSE questions

1. On the grid, draw an enlargement of the rectangle with scale factor 3 .

For 2 sides correctly enlarged

For all 4 sides correctly enlarged

2. On the grid, draw an enlargement of the rectangle with scale factor 2 .

3. The shaded shape has been enlarged by scale factor \frac{1}{2} ? Which is the correct enlargement?

Circle your answer A B C D

(Correct answer only)

Learning checklist

You have now learned how to:

  • Enlarge a shape using a scale factor on a grid
  • Enlarge a shape using a fractional scale factor on a grid
  • Calculate the scale factor of an enlargement

The next lessons are

  • Pythagoras’ theorem
  • Trigonometry
  • Loci and construction
  • Standard form

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

Enlargement Worksheet fit for students in year 8 and year 9

Enlargement (A) worksheet

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

Enlargement (A) allows pupils to practice enlarging basic shapes by positive integer scale factors, with and without a centre of enlargement.

In section A, students will enlarge a cuboid, a triangle and an ‘L’ shaped hexagon by two different scale factors each. Giving learners a chance to see variations of scale factors with the same polygons and practice enlargement of shapes with vertical and horizontal edges before progressing.

Next, in section B, the same shapes are enlarged by the same scale factors but this time from a given centre of enlargement; opening up a chance for discussion of “What’s the same? What’s different?”. We have included centres of enlargement that are on and off the objects so students can again notice the difference between the two and teachers/parents can introduce and discuss invariance in enlargement.

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Enlargement - fractional and negative scale factors

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IMAGES

  1. Enlargement

    gcse maths enlargement worksheet

  2. Enlargement

    gcse maths enlargement worksheet

  3. Enlargement

    gcse maths enlargement worksheet

  4. GCSE Enlargements

    gcse maths enlargement worksheet

  5. Centre of Enlargement

    gcse maths enlargement worksheet

  6. Enlargement

    gcse maths enlargement worksheet

VIDEO

  1. SIMILARITY AND ENLARGEMENT MATHS

  2. Class 8 Exercise 4.6 SNC Maths PTB Maths Ex 4.6 Enlargement

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  4. Math 9 Similarity lesson 2 Enlargements and Reductions

  5. Fractional Enlargement

  6. How To EASILY Enlarge A Shape

COMMENTS

  1. Enlargement

    Enlargement is a type of transformation that changes the size of a shape by making it bigger or smaller by multiplying its side lengths by a scale factor. Enlargements have real life functions, such as changing the size of photographic prints or pictures in documents. Enlarging a shape by a scale factor greater than 1 will make the shape bigger.

  2. Enlargements Practice Questions

    Click here for Questions . Click here for Answers . enlarging, transformations Practice Questions Previous: Multiply and Dividing by 10, 100, 1000 etc Practice Questions Next: Enlargements Negative Scale Factor Practice Questions The Corbettmaths Practice Questions on Enlargements

  3. Enlargement: Worksheets with Answers

    Enlargement: 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

  4. PDF Mathematics (Linear) 1MA0 ENLARGEMENT

    Edexcel GCSE Mathematics (Linear) - 1MA0 ENLARGEMENT 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.

  5. PDF Name: GCSE (1

    Enlargements Instructions Use black ink or ball-point pen. Answer all Questions. Answer the Questions in the spaces provided there may be more space than you need. Diagrams are NOT accurately drawn, unless otherwise indicated. You must show all your working out. Information The marks for each Question are shown in brackets

  6. Centre of Enlargement

    An enlargement is a type of transformation where we change the size of the original shape to make it bigger or smaller by multiplying it by a scale factor. To use a centre of enlargement we need to draw lines from the centre of enlargement through the vertices of the original shape. These are called ray lines. E.g.

  7. Enlargements Textbook Exercise

    The Corbettmaths Textbook Exercise on Enlargements. ... 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; Enlargements Textbook Exercise. Click here for Questions . Textbook Exercise. Previous: Enlargements (Centre of Enlargement ...

  8. PDF Exam Style Questions

    ......................... On the grid, enlarge the shape using a scale factor of 3. (2) On the grid, draw an enlargement of shape A with a scale factor of 2. (2) (a) Work out the area of rectangle A. Rectangle B is an enlargement of rectangle A. (b) What is the scale factor of the enlargement? .........................cm2 (1)

  9. Enlargement Worksheets

    Help your students prepare for their Maths GCSE with this free enlargement worksheet of 25 questions and answers Section 1 of the enlargement worksheet contains 18 skills-based enlargement questions, in 3 groups to support differentiation

  10. Enlargement GCSE Questions

    Enlargement GCSE Revision Description. This set of questions will give plenty of practice in constructing enlargements of shapes from a given point and scale factor and describing enlargements. The scale factors in this set of questions are all positive.

  11. Enlargement. GCSE Maths Past Paper Questions

    This resource contains all of the Enlargement 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).

  12. Enlargements (Centre of Enlargement) Textbook Exercise

    The Corbettmaths Textbook Exercise on Enlargements involving Centres of Enlargements. Welcome; 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; ... Enlarging with Fractional Scale Factors Textbook Exercise. Next: Enlargements Textbook Exercise ...

  13. GCSE Maths Enlargement Information Sheet

    This GCSE maths enlargement information sheet helps students understand enlargements and gives worked examples to consolidate students' understanding. This information sheet would be the perfect thing to use at the beginning of this maths topic, or it could work well as a revision sheet. It may be particularly useful for your lower-ability GCSE students who need to recap on the topic ...

  14. Similar Shapes and Enlargements

    Similar Shapes and Enlargements Example Questions. Question 1: Shapes P and Q are mathematically similar. The area of shape P is 6\text {cm}^2. a) Calculate the size of missing side-length x. b) (HIGHER ONLY) Calculate the area of shape Q. [3 marks] Level 6-7 GCSE AQA Edexcel OCR WJEC Cambridge iGCSE Edexcel iGCSE.

  15. Transformations Worksheets, Questions and Revision

    Topic Specification Transformations Revision The Four Transformations There are 4 types of transformation: translation, rotation, reflection, and enlargement. You need to be able to perform each transformation as well as identify which transformations have been performed. Level 1-3 GCSE KS3 AQA Edexcel OCR WJEC Cambridge iGCSE Edexcel iGCSE

  16. GCSE Maths Revision Worksheets. Foundation & Higher

    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.

  17. GCSE Enlargements

    GCSE Enlargements Subject: Mathematics Age range: 14-16 Resource type: Worksheet/Activity File previews pptx, 67.07 KB docx, 77.67 KB pptx, 67.46 KB docx, 105.65 KB docx, 124.11 KB pptx, 60.15 KB docx, 124.64 KB Powerpoints and accompanying work sheets. Grade E: Enlargement anywhere on a grid. Grade D: Enlargement with centre.

  18. GCSE Enlargements Worksheet

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

  19. Scale Factor

    Example 1: use a scale factor to enlarge a shape. Enlarge this shape by scale factor 2 2: Draw an enlargement of the first side. Let's start with the base. The base in the original shape is 1 1, so the base in the enlarged shape will be 2 2. 1\times2=2 1× 2 = 2. You can draw it anywhere on the grid.

  20. Enlargement (A) Worksheet

    Enlargement (A) worksheet description. Enlargement (A) allows pupils to practice enlarging basic shapes by positive integer scale factors, with and without a centre of enlargement. In section A, students will enlarge a cuboid, a triangle and an 'L' shaped hexagon by two different scale factors each. Giving learners a chance to see ...

  21. GCSE Maths Worksheets

    GCSE Maths Worksheets Practice for your GCSE Maths using the MME GCSE Maths worksheets by topic. Each topic of the GCSE Maths specification has its own worksheet, along with corresponding mark schemes. Gold Standard Education Learn an entire GCSE course for maths, English and science on the most comprehensive online learning platform.

  22. Enlargements Negative Scale Factor 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; Enlargements Negative Scale Factor Practice Questions. ... enlarging, negative sf. Practice Questions. Previous: Enlargements Practice Questions. Next: Ray Method Practice Questions. GCSE ...

  23. Enlargement

    Worksheet. Student activity. A draw-on GCSE worksheet with plenty of practice of completing and describing enlargements from a centre with fractional and negative scale factors. A challenging resource for higher tier students. 450.74 KB.

  24. Maths Genie • Learn GCSE Maths for Free

    Grade 8/9. Free online GCSE video tutorials, notes, exam style questions, worksheets, answers for all topics in Foundation and Higher GCSE. The content is suitable for the Edexcel, OCR and AQA exam boards.