IGCSE · Mathematics 0580 · P3

IGCSE Mathematics Paper 3 · Calculator practice papers

Core · 80 marks · 1h 30m. Each generated paper follows the 0580 Paper 3 · Calculator format, with the same number and style of questions as the real exam, and comes with a Cambridge-style mark scheme.

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Sample Paper 3 · Calculator questions

Question 1Structured · 9 marksA* challenge

A is the point (−2, 4) and B is the point (2, 8).

(a)

Find the equation of the perpendicular bisector of AB. Give your answer in the form y = mx + c.

[4]
(b)

The perpendicular bisector crosses the x-axis at P and the y-axis at Q. Find the area of triangle OPQ, where O is the origin.

[3]
(c)

Show that the point (4, 2) is equidistant from A and B.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)y = −x + 6
midpoint (0, 6) B1
gradient AB = 1 B1
perpendicular gradient −1 M1
y = −x + 6 A1
4
(b)18
Q = (0, 6) B1
P = (6, 0) B1
18 A1
3
(c)it lies on the perpendicular bisector / distances equal
substitutes into the equation or finds both distances M1
convincing conclusion A1
2
Question 2Structured · 3 marksA* challenge

The mean mass of 12 boys is 41 kg.
The mean mass of 7 girls is 48 kg.
One more student joins the group. The mean mass of all 20 students is now 44.5 kg.
Find the mass of the student who joined.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
62 kg
12 × 41 + 7 × 48 = 828 M1
20 × 44.5 = 890 M1
62 A1
3
Question 3Structured · 2 marks

A rectangle measures 5 cm by 12 cm. Find the length of its diagonal.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
13 cm
√(52 + 122) M1
13 A1
2
Question 4Structured · 3 marks

Solve 3x2 + 11x + 6 = 0.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = −23 or x = −3
(3x + 2)(x + 3) = 0 B2
B1 for factors giving two of the three terms correctly
−23 and −3 A1
3
Question 5Structured · 3 marks

A bag contains 6 red, 4 blue and 2 green counters. One counter is taken at random.

(a)

Find the probability that it is red.

[1]
(b)

Find the probability that it is not green.

[1]
(c)

Find the probability that it is yellow.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)12
12 B1
1
(b)56
56 B1
1
(c)0
0 B1
1
Question 6Structured · 3 marks
(a)

Solve 3x + 1 < 16.

[2]
(b)

List the positive integers that satisfy the inequality.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x < 5
3x < 15 M1
x < 5 A1
2
(b)1, 2, 3, 4
1, 2, 3, 4 B1
1

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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