Where can I download free proportion (harder) PDF worksheets with answers?

On this MathsLinks page you can download free printable proportion (harder) PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Corbett Practice, Corbett Textbook, Dr Frost, plus a printable one-page proportion (harder) revision guide.

What GCSE grade is proportion (harder) (7C)?

Proportion (harder) (topic code 7C) is a Grade 7 ratio & proportion topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Proportion (harder) Worksheets (PDF) with Answers — GCSE Maths

Free Proportion (harder) PDF Worksheets & Answers

Grade 7 • Topic 7C

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Maths4EveryOne GCSE 9–1 practice booklet & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Maths Takeaway GCSE Maths Takeaway exam questions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Maths DIY Exam-style booklet & 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

Grade 7 topics
7A - Surds	7B - Bounds
7C - Proportion (harder)	7D - Algebraic fractions
7E - The quadratic formula	7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs	7H - Rearranging (harder)
7J - Functions (harder)	7K - Iteration
7L - Area of any triangle	7M - The sine rule
7N - The cosine rule	7P - Congruent triangles
7Q - 3D pythagoras / trig.	7R - Histograms
7S - Conditional probability	7T - Exact trig. values (harder)
7U - Area of a segment

Explanation:

Translate the proportion statement into an algebraic equation using a constant of proportionality k: if y is directly proportional to xⁿ, write y = kxⁿ; if y is inversely proportional to xⁿ, write y = kxⁿ. Substitute the given pair of values to find k and write the full formula before finding any unknown values.

For compound three-variable problems (where y depends on x and x depends on z), substitute the second formula directly into the first and simplify the powers and constants carefully. Remember to take both roots or the positive physical root when solving for x² or √x.

Example 1: y is inversely proportional to x². Given y = 5 when x = 6, find x when y = 20 (x > 0).

Solution:

y = kx² ⇒ 5 = k6²

k = 5 × 36 = 180, so y = 180x²

When y = 20: 20 = 180x² ⇒ x² = 18020 = 9

Since x > 0, x = √9 = 3

Answer: x = 3

Example 2: P = 3Q² and Q is inversely proportional to √R. Given Q = 4 when R = 9, write P in terms of R.

Solution:

Q = k√R ⇒ 4 = k√9 ⇒ k = 4 × 3 = 12

Substitute Q = 12√R into P = 3Q²:

P = 3 × (12√R)² = 3 × 144R

Answer: P = 432R

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Proportion (harder) Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Nov 2021 3H Q8 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

Work out
(a) Sketch graph for y is directly proportional to x (1) (b) Sketch graph for y is inversely proportional to x (1)

(a) Using the axes below, sketch a graph to represent the statement
y is directly proportional to x [1 mark]

(b) Using the axes below, sketch a graph to represent the statement
y is inversely proportional to x [1 mark]

Worked Solution & Mark Scheme (2 marks)

Part (a) Solution:

y = kx is a straight line through (0, 0) B1

Answer (a): Straight line with positive gradient passing through the origin O

Part (b) Solution:

y = k/x is a decreasing hyperbola in quadrant 1 B1

Answer (b): Reciprocal curve y = k/x in the first quadrant asymptotic to both axes

Past Paper Example 2 OCR Jun 2023 1F Q22 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Hiro and Taylor are both electricians.
Hiro **does not** charge to visit a house but charges a fixed rate per hour for the work needed.
This graph shows the relationship between the hours worked and the total charge made by Hiro.

(a) Explain how this graph shows that Hiro’s total charge is directly proportional to the hours worked. [2 marks]

(b) Taylor **does** charge to visit a house and charges the same fixed rate per hour as Hiro for the work needed.
On the axes above, draw a graph to show the relationship between the hours worked and the total charge made by Taylor. [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

A graph showing direct proportion must be a straight line through the origin. M1 C1

Answer (a): It is a straight line that passes through the origin (0, 0).

Part (b) Solution:

Same hourly rate ⇒ same gradient (parallel line) M1
call-out charge ⇒ positive y-intercept. A1

Answer (b): Straight line parallel to Hiro’s line with a positive vertical intercept.

Past Paper Example 3 OCR Nov 2023 4H Q8 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here are sketches of six graphs, labelled **A** to **F**.

(a) y is directly proportional to x. [1 mark]

(b) y is inversely proportional to x. [1 mark]

Worked Solution & Mark Scheme (2 marks)

Part (a) Solution:

Direct proportion y = kx is a straight line through the origin ⇒ Graph C. B1

Answer (a): C

Part (b) Solution:

Inverse proportion y = k/x is a reciprocal curve in the first quadrant ⇒ Graph E. B1

Answer (b): E

← 7B Bounds

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Proportion (harder)

Free Proportion (harder) PDF Worksheets & Answers

Guide to Proportion (harder): Explanation, Diagrams & Worked Examples

GCSE Past Paper Proportion (harder) Questions & Answers