IGCSE · Mathematics 0580 · P1

IGCSE Mathematics Paper 1 · Non-calculator practice papers

Core · 80 marks · 1h 30m. Each generated paper follows the 0580 Paper 1 · Non-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 1 · Non-calculator questions

Question 1Structured · 4 marksA* challenge

Amir, Bella and Chen share some money.
The ratio Amir’s share : Bella’s share = 2 : 3.
The ratio Bella’s share : Chen’s share = 2 : 3.
Chen receives $175 more than Amir.
Calculate the total amount of money they share.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
$665
A : B : C = 4 : 6 : 9 M1
9 − 4 = 5 parts = $175 M1
1 part = $35 M1
665 A1
4
Question 2Structured · 4 marksA* challenge

The probability that it rains on any day is 0.4. The weather on different days is independent.

(a)

Find the probability that it rains on exactly one of two days.

[2]
(b)

Find the probability that it rains on at least one of three days.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.48
2 × 0.4 × 0.6 M1
0.48 A1
2
(b)0.784
1 − 0.63 M1
0.784 A1
2
Question 3Structured · 4 marks
(a)

A train travels 135 km in 2 hours 30 minutes. Calculate its average speed in km/h.

[2]
(b)

Change this speed into metres per second.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)54 km/h
2 h 30 min = 2.5 h M1
54 A1
2
(b)15 m/s
× 1000 ÷ 3600 M1
15 A1
2
Question 4Structured · 6 marks

f(x) = 5x − 1 g(x) = x2 − 5

(a)

Find f(g(−3)).

[2]
(b)

Find f−1(x).

[2]
(c)

Find gf(x), giving your answer in the form px2 + qx + r.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)19
g(−3) = 4 M1
19 A1
2
(b)x + 15
x = 5y − 1 seen M1
x + 15 A1
2
(c)25x2 − 10x − 4
(5x − 1)2 − 5 M1
25x2 − 10x − 4 A1
2
Question 5Structured · 4 marks

The equation of a line is 2x + 4y = 8.

(a)

Find the gradient of the line.

[2]
(b)

Find the coordinates of the points where the line crosses the x-axis and the y-axis.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)−12
rearranges to y = … M1
−12 A1
2
(b)(4, 0) and (0, 2)
(4, 0) B1
(0, 2) B1
2
Question 6Structured · 4 marks
(a)

Change 2.5 m² into cm².

[1]
(b)

Change 2750 cm³ into litres.

[1]
(c)

Change 54 km/h into m/s.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)25000 cm²
25000 B1
1
(b)2.75 litres
2.75 B1
1
(c)15 m/s
× 1000 ÷ 3600 M1
15 A1
2

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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