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Rotations

Free Printable Rotations PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 3)

Download free rotations worksheets (PDF), GCSE maths past paper questions and worked solutions for Rotations (3S). This is a Grade 3 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Dr Austin, 1st Class Maths, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our rotations revision notes and worked examples with diagrams, try real GCSE past paper rotations questions with step-by-step solutions, or download a PDF of all rotations worksheet links.

Free Rotations PDF Worksheets & Answers

Grade 3 • Topic 3S
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
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Practice Questions & answers
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Textbook Exercise & answers
 Qs Ans
Practice grid / worksheet & answers
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Practice grid / worksheet & answers
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Edexcel exam questions & solutions
 Qs Ans
AQA exam questions & solutions
 Qs Ans
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Interactive online lesson & practice
 Page
Grade 3 topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables
GCSE Maths Grade 3 Revision Notes & Method

Guide to Rotations: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To describe a rotation fully (3 marks), you must state three things: (1) the word rotation, (2) the angle and direction (90° clockwise, 90° anticlockwise, or 180° — note that 180° does not need a direction), and (3) the coordinates of the centre of rotation.

In the exam, always ask for tracing paper: trace the shape and draw a small arrow pointing North at the centre of rotation, hold your pencil tip firmly on the centre, and turn the tracing paper through the required angle.

Example 1: Point A(1, 4) is rotated 90° clockwise about (0, 0). Find the coordinates of A'.

A(1,4) A'(4,−1) 90°
From (0,0): 1 right, 4 up.
90° CW → 4 right, 1 down.
Answer: (4, −1)

Example 2: Triangle P (2,2), (2,5), (4,2) maps to Q (2,0), (2,−3), (0,0). Describe the transformation.

P Q (2,1)
Turned upside down (180°).
Midpoint of (2,2) & (2,0) is (2, 1).
Rotation, 180°, centre (2, 1)
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Rotations Questions & Answers

Past Paper Example 1 GCSE Nov 2017 2F Q20 / 2H Q5 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
–7–6–5–4–3–2–11234567–7–6–5–4–3–2–11234567OxyT
(a) Rotate trapezium T 180° about the origin. Label A. (1) (b) Translate trapezium T by vector (–1, –3). Label B. (1)
(a) Rotate trapezium **T** 180° about the origin.
Label the new trapezium **A**. [1 mark]
(b) Translate trapezium **T** by the vector (-1-3)
Label the new trapezium **B**. [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
(x, y) → (–x, –y) B1
Answer (a): Trapezium A at (–2, 1), (–4, 1), (–5, 2), (–2, 2)
Part (b) Solution:
(x, y) → (x – 1, y – 3) B1
Answer (b): Trapezium B at (1, –4), (3, –4), (4, –5), (1, –5)
Past Paper Example 2 IGCSE Jun 2023 1F Q19 / 1H Q4 8 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a sketch of triangle **A** and triangle **B** on a coordinate grid.
xyOA(–7, 2)(–11, –5)(f, –3)B(6, 12)(2, d)(9, e)Diagram NOTaccurately drawn
(a) Given that triangle **A** has been translated to give triangle **B**, work out the value of d, the value of e and the value of f [3 marks]
(b) Describe fully the single transformation that maps shape **P** onto shape **Q** [3 marks]
112233445566778899101011111212OxyPQ
(c) On the grid above, rotate shape **P** 90° clockwise about (3, 5)
Label your shape **R** [2 marks]
Worked Solution & Mark Scheme (8 marks)
Part (a) Solution:
Translation vector = (6 – –7, 12 – 2) = (13, 10). d = –5 + 10 = 5, e = –3 + 10 = 7, f = 9 – 13 = –4 M2 A1
Answer (a): d = 5, e = 7, f = –4
Part (b) Solution:
Enlargement, scale factor 3, centre (0, 2) M2 C1
Answer (b): Enlargement, scale factor 3, centre (0, 2)
Part (c) Solution:
Shape R drawn at vertices (0, 5), (1, 5), (1, 6), (3, 6) M1 A1
Answer (c): Shape R drawn at vertices (0, 5), (1, 5), (1, 6), (3, 6)
Past Paper Example 3 IGCSE Jan 2023 1F Q14 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Rotate triangle A 90° anticlockwise about O (2) (b) Describe fully the single transformation that maps triangle B onto triangle C (2)
(a) On the grid, rotate triangle A 90° anticlockwise about centre O [2 marks]
xyO–6–5–4–3–2–1123456–6–5–4–3–2–1123456A
(b) Describe fully the single transformation that maps triangle B onto triangle C [2 marks]
xyO–2–112345678910–2–112345678910BC
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
(x, y) → (−y, x): (2, −1) → (1, 2), (2, −3) → (3, 2), (5, −3) → (3, 5) M1 A1
Answer (a): Triangle with vertices at (1, 2), (3, 2) and (3, 5)
Part (b) Solution:
Lengths multiplied by 3 and rays pass through origin O(0, 0) M1 C1
Answer (b): Enlargement, scale factor 3, centre (0, 0)

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