IB Mathematics: Applications & Interpretation Paper 1 · SL (short questions) · 2029 syllabus practice papers
2029 syllabus · SL · 75 marks · 1h 30m · calculator. Each generated paper follows the SL & HL Paper 1 · SL (short questions) · 2029 syllabus format, with the same number and style of questions as the real exam, and comes with an IB-style mark scheme.
The temperature is modelled by f(t) = a cos(b(t − c)) + d, where t is in hours. The maximum value 18 occurs at t = 14, the minimum value is 8, and the period is 24.
(a)
Find a, b, c and d.
[4]
(b)
Find the length of time in one period for which f(t) > 15.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
a = 5, b = 0.262, c = 14, d = 13
a = 5 A1 b = 2π24 = 0.262 A1 c = 14 A1 d = 13 A1
4
(b)
8.86
f(t) = 15 (M1) t = 9.57, 18.4 A1 8.86 A1
3
Question 2Structured · 6 marksA* challenge
On any day the probability that it rains is 0.25. If it rains, the probability that Ana is late is 0.55. If it does not rain, the probability that she is late is 0.1.
(a)
Find the probability that Ana is late on a given day.
[2]
(b)
Given that Ana is late, find the probability that it rained.
[2]
(c)
Find the probability that Ana is late on exactly one of two days.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.213
0.25 × 0.55 + 0.75 × 0.1 (M1) 0.213 A1
2
(b)
0.647
0.138/0.213 (M1) 0.647 A1
2
(c)
0.335
2 × 0.213 × 0.787 (M1) 0.335 A1
2
Question 3Structured · 4 marks
The table shows the age x (months) of a car and its value y (% of new price).
x
13
48
18
44
46
39
31
y
82
40
80
51
45
59
66
Table 3.1
(a)
Find Pearson’s correlation coefficient r.
[2]
(b)
Describe the correlation and explain whether it implies causation.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
−0.982
GDC (M1) −0.982 A1
2
(b)
strong negative; not necessarily causal
strong negative A1 correlation does not imply causation R1
2
Question 4Structured · 4 marks
The number of cars passing a checkpoint per minute follows a Poisson distribution with mean 4.
(a)
Find the probability that exactly 2 cars pass in one minute.
[2]
(b)
Find the probability that at least 10 cars pass in 3 minutes.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.147
Po(4) (M1) 0.147 A1
2
(b)
0.758
Po(12.0): 1 − P(X ≤ 9) (M1) 0.758 A1
2
Question 5Structured · 5 marks
A ship sails 15 km on a bearing of 040° and then 8 km on a bearing of 150°.
(a)
Find the distance of the ship from its starting point.
[3]
(b)
Find the bearing of the ship from its starting point.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
14.4 km
angle between legs (A1) cosine rule (M1) 14.4 km A1
3
(b)
71.5°
sine rule or coordinates (M1) 71.5° A1
2
Question 6Structured · 6 marks
Let f(x) = 3x3 + 4x2, x ≠ 0.
(a)
Find f′(x).
[2]
(b)
Find the equation of the tangent to the graph of f at the point where x = 1.
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
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