Where can I download free changing the subject PDF worksheets with answers?

On this MathsLinks page you can download free printable changing the subject PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, IGCSE MT, Maths Genie, Maths4Everyone, Corbett Practice, plus a printable one-page changing the subject revision guide.

What GCSE grade is changing the subject (5F)?

Changing the subject (topic code 5F) is a Grade 5 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Changing the subject Worksheets (PDF) with Answers — GCSE Maths

Free Changing the subject PDF Worksheets & Answers

Grade 5 • Topic 5F

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
IGCSE MT IGCSE (9–1) past paper booklet	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom 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
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page

Grade 5 topics
5A - Combining ratios	5B - Direct and inverse proportion
5C - Reverse percentages	5D - Standard form
5E - Speed	5F - Changing the subject
5G - Quadratic expressions	5H - Solving quadratic equations
5J - Drawing quadratic graphs	5K - Cubic/reciprocal graphs
5L - Simultaneous equations	5M - Sector areas and arc lengths
5N - Sim. equ. graphically	5P - Midpoint of a line segment
5Q - Gradient of a line	5R - Equation of a line
5S - Spheres and cones	5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)	5V - Exact trig. values
5W - Probability trees	5X - Vectors
5Y - Venn diagrams	5Z - Density
5AA - Pressure

Explanation:

To change the subject of a formula, use inverse operations step by step to isolate the target letter on one side of the equals sign (multiply out fractions first, expand brackets, and undo powers with roots or vice versa).

If the letter you want appears twice in the formula, expand any brackets, collect all terms containing the target letter on one side and all other terms on the opposite side, then factorise out the target letter before dividing.

Example 1: Make v the subject of E = 12mv².

Solution:

Multiply both sides by 2: 2E = mv²

Divide both sides by m: 2Em = v²

Square root both sides to isolate v:

Answer: v = ±√(2Em)

Example 2: Make x the subject of y = 3x + 2x − 4.

Solution:

Multiply by (x − 4): y(x − 4) = 3x + 2 → xy − 4y = 3x + 2

Collect x terms on left: xy − 3x = 4y + 2

Factorise out x: x(y − 3) = 4y + 2

Answer: x = 4y + 2y − 3

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Changing the subject Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Jan 2023 1F Q13 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

p = t - ac
t = 18 a = -3 c = 5

(a) Work out the value of p [2 marks]

(b) Make x the subject of the formula d = 3x + 10 [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

p = 18 − (−3)(5) = 18 − (−15) = 33 M1 A1

Answer (a): p = 33

Part (b) Solution:

d − 10 = 3x M1
⇒ x = (d − 10)/3 A1

Answer (b): x = x = d - 103

Past Paper Example 2 IGCSE Jun 2025 2F Q12 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Make y the subject of w = 3y – d. (2) (b) Diego buys b boxes (12 crayons each) and p packets (3 crayons each) for a total of T crayons. Write down a formula for T in terms of b and p. (3)

(a) Make y the subject of w = 3y - d [2 marks]

(b) Write down a formula for T in terms of b and p [3 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

w + d = 3y M1
⇒ y = (w + d)/3 A1

Answer (a): y = y = w + d3

Part (b) Solution:

Use + for more/older, - for less/fewer/younger, and multiply/divide for rates. M1
e.g. 4 less than m is m - 4 M1
3 times m is 3m
Answer: T = 12b + 3p A1

Answer (b): T = T = 12b + 3p

Past Paper Example 3 IGCSE Nov 2020 2F Q14 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Factorise 25f − 10 (1) (b) Make y subject of c = 5y − h (2) (c) Solve 4x + 7 > 2 (2)

(a) Factorise 25f - 10 [1 mark]

(b) Make y the subject of the formula c = 5y - h [2 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

5(5f − 2)

Answer (a): 5(5f - 2)

Part (b) Solution:

c + h = 5y M1
⇒ y = (c + h) / 5 A1

Answer (b): y = y = c + h5

Part (c) Solution:

4x > −5 M1
⇒ x > −1.25 A1

Answer (c): x > -1.25

← 5E Speed

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Changing the subject

Free Changing the subject PDF Worksheets & Answers

Guide to Changing the subject: Explanation, Diagrams & Worked Examples

GCSE Past Paper Changing the subject Questions & Answers