IB · Mathematics: Analysis & Approaches SL & HL · P1S

IB Mathematics: Analysis & Approaches Paper 1 · SL (no calculator) · exams to Nov 2028 practice papers

SL · 80 marks · 1h 30m · Section A short + Section B long. Each generated paper follows the SL & HL Paper 1 · SL (no calculator) · exams to Nov 2028 format, with the same number and style of questions as the real exam, and comes with an IB-style mark scheme.

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Sample Paper 1 · SL (no calculator) · exams to Nov 2028 questions

Question 1Structured · 6 marksA* challenge

A committee of 4 people is chosen from 6 men and 7 women.

(a)

Find the number of committees that contain at least two women.

[3]
(b)

Two particular people refuse to serve on the committee together. Find the number of possible committees.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)560
total 13C4 = 715 (A1)
subtract committees with 0 or 1 woman: 15 + 140 (M1)
560 A1
3
(b)660
committees containing both: 11C2 = 55 (A1)
715 − 55 (M1)
660 A1
3
Question 2Structured · 6 marks

Machines A, B and C produce 60%, 25% and 15% of the items made in a factory. The percentages of defective items they produce are 1%, 4% and 6% respectively. An item is chosen at random.

(a)

Find the probability that the item is defective.

[3]
(b)

Given that the item is defective, find the probability that it was made by machine C.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)140
(0.6)(0.01) + (0.25)(0.04) + (0.15)(0.06) (M1)(A1)
0.025 = 140 A1
3
(b)925
P(C ∩ D)P(D) (M1)
0.0090.025 (A1)
925 A1
3
Question 3Structured · 6 marks

Consider the 8 letters of the word SYMMETRY.

(a)

Find the number of different arrangements of these 8 letters.

[2]
(b)

Find the number of these arrangements in which all the vowels are together.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)10080
8!2! 2! (M1)
10080 A1
2
(b)10080
treat the vowels as a single block (M1)
arrangements of the block and 7 consonants: 10080 (A1)
arrangements within the block: 1 (A1)
10080 A1
4
Question 4Structured · 6 marks

Use the substitution u = x + 1 to find the exact value of ∫03x√x + 1dx.

[6]
Show answers and mark scheme
PartAnswer and marking pointsMarks
83
x = u − 1, dx = du (A1)
∫14u − 1√udu A1
= ∫(u1/2 − u−1/2)du (M1)
[23u3/2 − 2u1/2] A1
substituting limits (M1)
83 A1
6
Question 5Structured · 5 marks

Air is pumped into a spherical balloon at a constant rate of 20 cm3 s−1.

Find the rate at which the radius is increasing when the radius is 5 cm.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
15π cm s−1
V = 43πr3 (A1)
dVdr = 4πr2 A1
dVdt = dVdr × drdt M1
20 = 4π(5)2drdt A1
drdt = 15π A1
5
Question 6Structured · 5 marks

The angles A and B are acute, with tan A = 13 and tan B = 111.

(a)

Find the exact value of tan(A + B).

[3]
(b)

Find the exact value of cos A.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)716
tan A + tan B1 − tan A tan B (M1)
14/3332/33 (A1)
716 A1
3
(b)3√10
right-angled triangle with opposite 1, adjacent 3 (M1)
cos A = 3√10 A1
2

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in