IGCSE · Additional Mathematics 0606 · P1

IGCSE Additional Mathematics Paper 1 · Non-calculator practice papers

80 marks · 2h. Each generated paper follows the 0606 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

The second term of a geometric progression is 18 and the fifth term is 163. Find the first term, the common ratio and the sum to infinity.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
a = 27, r = ⅔, S∞ = 81
r3 = 163 ÷ 18 = 827 M1
r = ⅔ A1
a = 27 A1
S∞ = 81 A1
4
Question 2Structured · 4 marksA* challenge

A boat travels at 8 m/s in still water. It heads due north across a river flowing at 6 m/s due east.

Find the resultant speed and the angle between the boat’s path and the bank.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
10 m/s; 53.1°
Pythagoras M1
10 m/s A1
tan θ = 8/6 M1
53.1° A1
4
Question 3Structured · 3 marks

The first term of an arithmetic progression is 7 and the common difference is 6.

(a)

Find the 20th term.

[1]
(b)

Find the sum of the first 20 terms.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)121
121 B1
1
(b)1280
S = n2(2a + (n − 1)d) M1
1280 A1
2
Question 4Structured · 4 marks
(a)

A sector has radius 10 cm and angle π3 radians. Find the arc length, in terms of π.

[2]
(b)

Find the area of the sector, in terms of π.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)103π cm
s = rθ M1
103π A1
2
(b)503π cm²
A = ½r2θ M1
503π A1
2
Question 5Structured · 4 marks
(a)

Show that sin x1 − cos x − sin x1 + cos x = 2tan x.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)shown
common denominator 1 − cos2x M1
sin x(1 + cos x) − sin x(1 − cos x) M1
2 sin x cos xsin2x A1
= 2 cos xsin x = 2tan x AG A1
4
Question 6Structured · 6 marks

f(x) = 4x + 6 for x ∈ ℝ g(x) = 4x − 1 for x > 1

(a)

Find f−1(x).

[2]
(b)

Find the range of g.

[1]
(c)

Solve fg(x) = 22.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x − 64
correct method M1
x − 64 A1
2
(b)g(x) > 0
g > 0 B1
1
(c)x = 2
f(g(x)) = 16x − 1 + 6 M1
16x − 1 = 16 M1
x = 2 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