IB Mathematics: Applications & Interpretation Paper 1 · HL (short questions) · 2029 syllabus practice papers
2029 syllabus · HL · 100 marks · 2h · calculator. Each generated paper follows the SL & HL Paper 1 · HL (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.
A coin is tossed 20 times and lands heads 13 times. A test is carried out at the 5% significance level to decide whether the coin is biased towards heads.
(a)
State the hypotheses.
[1]
(b)
Find the p-value.
[2]
(c)
State the conclusion of the test.
[1]
(d)
State what is meant by a Type I error in this context.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
H0: p = 0.5, H1: p > 0.5
H0: p = 0.5; H1: p > 0.5 A1
1
(b)
0.132
P(X ≥ 13), X ~ B(20, 0.5) (M1) 0.132 A1
2
(c)
do not reject H0
0.132 > 0.05, do not reject H0: insufficient evidence of bias R1
1
(d)
conclude biased when fair
concluding the coin is biased when it is actually fair R1
1
Question 2Structured · 7 marksA* challenge
For events A and B, P(A) = 0.3, P(B) = 0.4 and P(A | B) = 0.2.
(a)
Find P(A ∩ B).
[2]
(b)
Find P(A ∪ B).
[2]
(c)
Find P(B | A′).
[2]
(d)
Determine whether A and B are independent, giving a reason.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.0800
P(A | B) × P(B) (M1) 0.0800 A1
2
(b)
0.620
P(A) + P(B) − P(A ∩ B) (M1) 0.620 A1
2
(c)
0.457
P(B ∩ A′)P(A′) = 0.3200.700(M1) 0.457 A1
2
(d)
not independent
P(A | B) = 0.2 ≠ P(A) = 0.3, so not independent R1
1
Question 3Structured · 5 marks
The mean distance from the Earth to the Sun is 1.50 × 108 km. Light travels at 3.00 × 105 km s−1.
(a)
Find the time taken for light to travel this distance, in seconds. Give your answer in the form a × 10k, where 1 ≤ a < 10 and k ∈ ℤ.
[3]
(b)
Sam estimates the time to be 540 s. Find the percentage error in Sam’s estimate.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
4.99 × 102 s
1.50 × 1083.00 × 105(M1) 499 (A1) 4.99 × 102 s A1
3
(b)
8.29%
540 − 499499 × 100% (M1) 8.29% A1
2
Question 4Structured · 6 marks
A particle moves in a straight line with velocity v(t) = t2 − 7t + 10 m s−1, for 0 ≤ t ≤ 7.
(a)
Find the times when the particle changes direction.
[2]
(b)
Find the total distance travelled.
[2]
(c)
Find the displacement at t = 7.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
t = 2, t = 5
v(t) = 0 with a sign change (M1) t = 2, t = 5 A1
2
(b)
21.8 m
∫07|v|dt (M1) 21.8 m A1
2
(c)
12.8 m
∫07v dt (M1) 12.8 m A1
2
Question 5Structured · 5 marks
A ball is thrown upwards. Its height h metres after t seconds is modelled by h(t) = −4.9t2 + 15t + 1.2.
(a)
Find the maximum height of the ball.
[2]
(b)
Find the time at which the ball hits the ground.
[2]
(c)
State a reason why the model might not be appropriate for large values of t.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
12.7 m
vertex, e.g. GDC or t = −b2a(M1) 12.7 m A1
2
(b)
3.14 s
h(t) = 0 (M1) 3.14 s A1
2
(c)
h becomes negative
h(t) < 0 after the ball lands, which is not physically possible R1
1
Question 6Structured · 5 marks
A ship sails 12 km on a bearing of 075° and then 8 km on a bearing of 185°.
(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)
11.9 km
angle between legs (A1) cosine rule (M1) 11.9 km A1
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