IGCSE · Mathematics 0580 · Algebra & graphs

Proportion: IGCSE Mathematics questions with answers

Free Proportion questions for IGCSE Mathematics (0580), Extended tier (Supplement content), part of Algebra & graphs. Each question has the answer and the marking points an examiner would look for.

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Proportion practice questions

Question 1Structured · 6 marksA* challenge
(a)

y is inversely proportional to the square root of x.
When x = 16, y = 30.
Find y when x = 8.

[3]
(b)

x is increased by 44%.
Find the percentage change in y. State whether it is an increase or a decrease.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)42.4
y = k ÷ √x M1
k = 120 A1
42.4 (ft their k) A1
3
(b)16.7% decrease
multiplier 1.44 for x B1
1.44−0.5 = 0.8333 M1
16.7% decrease A1
3
Question 2Structured · 7 marksA* challenge

y is directly proportional to the square of x and inversely proportional to z.
When x = 6 and z = 4, y = 27.

(a)

Find a formula for y in terms of x and z.

[2]
(b)

Find the value of x when y = 12 and z = 9, given that x > 0.

[2]
(c)

x is increased by 50% and z is decreased by 20%. Find the percentage change in y.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)y = 3x2z
y = kx2z M1
k = 3 A1
2
(b)x = 6
12 = 3x29 M1
x = 6 A1
2
(c)181.3% increase
x multiplied by 1.5 M1
y multiplied by 1.520.8 = 2.8125 M1
181.3% increase A1
3
Question 3Structured · 3 marks
(a)

y is directly proportional to the square of x. When x = 2, y = 12. Find a formula for y in terms of x.

[2]
(b)

Find y when x = 6.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)y = 3x2
k = 3 M1
y = 3x2 A1
2
(b)108
108 B1
1
Question 4Structured · 3 marks

y is inversely proportional to the square root of x. When x = 9, y = 12.

Find y when x = 16.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
9
y = k√x M1
k = 36 A1
9 A1
3
Question 5Structured · 6 marksA* challenge
(a)

y is directly proportional to the square of x.
When x = 2, y = 7.
Find y when x = 1.

[3]
(b)

x is increased by 20%.
Find the percentage change in y. State whether it is an increase or a decrease.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)1.75
y = kx2 M1
k = 1.75 A1
1.75 (ft their k) A1
3
(b)44% increase
multiplier 1.20 for x B1
1.202 = 1.44 M1
44% increase A1
3
Question 6Structured · 7 marksA* challenge

y is directly proportional to the square of x and inversely proportional to z.
When x = 6 and z = 4, y = 27.

(a)

Find a formula for y in terms of x and z.

[2]
(b)

Find the value of x when y = 12 and z = 9, given that x > 0.

[2]
(c)

x is increased by 50% and z is decreased by 10%. Find the percentage change in y.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)y = 3x2z
y = kx2z M1
k = 3 A1
2
(b)x = 6
12 = 3x29 M1
x = 6 A1
2
(c)150% increase
x multiplied by 1.5 M1
y multiplied by 1.520.9 = 2.5 M1
150% increase A1
3

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in