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Mixed transformations

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

Download free mixed transformations worksheets (PDF), GCSE maths past paper questions and worked solutions for Mixed transformations (3W). 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 Maths4Everyone, Dr Austin, Metatutor, E Classroom and PMT, along with past paper question booklets.

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

Free Mixed transformations PDF Worksheets & Answers

Grade 3 • Topic 3W
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
GCSE 9–1 practice booklet & solutions
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Topic worksheet & worked solutions
 Qs Ans
Practice grid / worksheet & answers
 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
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 Mixed transformations: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

When a question asks for the single transformation that maps shape A onto shape B, you must name only one of the four transformations: Translation (with column vector), Reflection (with mirror line equation), Rotation (with angle, direction, and centre), or Enlargement (with scale factor and centre).

Never combine two transformations in your description (e.g. “reflected and then translated” scores 0 marks). Check the size first (changed size = Enlargement), then orientation (same way up = Translation; flipped = Reflection; turned = Rotation).

Example 1: Triangle A is reflected in the x-axis to B, then in the y-axis to C. Describe the single transformation from A to C.

A B C
(2,3) → (2,−3) → (−2,−3).
Half-turn around origin:
Rotation, 180°, about (0, 0)

Example 2: Shape P is translated by 3
−2 then −1
6 to Q. Describe the single transformation.

P Q
Add vectors:
3 + (−1) = 2;  −2 + 6 = 4
Translation 2
4
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Mixed transformations Questions & Answers

Past Paper Example 1 AQA Nov 2018 3F Q15 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
xyO–4–22442–2–4AB
Describe fully the single transformation that maps shape A to shape B.
Describe fully the single transformation that maps shape A to shape B.
Worked Solution & Mark Scheme (3 marks)
The orientation of the shape is reversed, so it is a reflection M1
Connecting corresponding vertices: midpoint of (-4, 4) and (-4, -4) is (-4, 0) M1
midpoint of (-4, 1) and (-1, -4) is (-2.5, -1.5)
The line through these midpoints has gradient -1 and equation y = -x - 4. C1
xyO–4–22442–2–4ABy = -x - 4
Answer: Transformation Reflection in the line y = -x - 4
Past Paper Example 2 Practice Set 3 2H Q12 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
xyAB–2–112345678910–2–112345678910O
Describe fully the single transformation that maps triangle A onto triangle B.
Describe fully the single transformation that maps triangle A onto triangle B.
Worked Solution & Mark Scheme (3 marks)
Rotation of 90° clockwise about (1, 4) M2 C1
Answer: Rotation, 90° clockwise, centre (1, 4)
Past Paper Example 3 Eduqas Nov 2023 2F Q18 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The grid below shows triangle A and triangle B.
–6–5–4–3–2–1123456–4–3–2–112345678xyAB
(a) Describe fully the single transformation that maps triangle A onto triangle B. [2 marks]
(b) Translate triangle A using the vector (-32), label it C. [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Triangle A is rotated 90° clockwise M1
Perpendicular bisectors of corresponding vertices intersect at (0.5, -0.5). C1
Answer (a): Rotation of 90° clockwise about center (0.5, -0.5) (or 270° anticlockwise)
Part (b) Solution:
(2,1)+(-3,2)=(-1,3) M1
(6,1)+(-3,2)=(3,3)
(5,4)+(-3,2)=(2,6). A1
Answer (b): Triangle C drawn with vertices (-1, 3), (3, 3), (2, 6)

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