IB · Mathematics: Analysis & Approaches SL & HL · P2H

IB Mathematics: Analysis & Approaches Paper 2 · HL (calculator) · exams to Nov 2028 practice papers

HL · 110 marks · 2h · Section A short + Section B long. Each generated paper follows the SL & HL Paper 2 · HL (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 2 · HL (calculator) · exams to Nov 2028 questions

Question 1Structured · 6 marksA* challenge

The displacement s metres of a particle from a fixed point O, t seconds after it starts moving, is s(t) = 4te−0.4t − 1, t ≥ 0.

(a)

Find the times when the particle is at O.

[3]
(b)

Find the maximum distance of the particle from O, and the time at which this occurs.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)t = 0.280, t = 8.94
s(t) = 0 (M1)
t = 0.280 A1
t = 8.94 A1
3
(b)2.68 m at t = 2.50
s′(t) = 0 or graph (M1)
t = 2.50 A1
2.68 m A1
3
Question 2Structured · 7 marks

The plane Π has equation −3x − 2y + 2z = −13. The line L has equation r = 129−2 + λ32−1.

(a)

Find the coordinates of the point where L meets Π.

[4]
(b)

Find the acute angle between L and Π.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)(3, 3, 1)
substituting the parametric form of L into the equation of Π M1
−58 − 15λ = −13 A1
λ = −3 A1
(3, 3, 1) A1
4
(b)76.5°
sin θ = |b·n| ÷ (|b||n|), using the normal to the plane (M1)
sin θ = 15√238 (A1)
76.5° A1
3
Question 3Structured · 5 marks

The planes Π1 and Π2 have equations 3x − y + z = 2 and −x + 2y + z = −3.

(a)

Find the acute angle between the planes.

[3]
(b)

Find a vector in the direction of the line of intersection of the planes.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)60.5°
angle between the normals (M1)
cos θ = 4√66 (A1)
60.5° A1
3
(b)−3−45
n1 × n2 (M1)
−3−45 A1
2
Question 4Structured · 5 marks

A sector has radius 10 cm and perimeter 40 cm.

(a)

Find the angle of the sector in radians.

[2]
(b)

Find the area of the segment formed by the chord joining the ends of the arc.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)2.00
2(10) + 10θ = 40 (M1)
2.00 A1
2
(b)54.5 cm2
sector area (M1)
minus triangle area (M1)
54.5 A1
3
Question 5Structured · 5 marks

The number of bacteria in a culture is modelled by N(t) = 500e0.2t, where t is in hours.

(a)

Find the number of bacteria after 3 hours.

[2]
(b)

Find the time taken for the number of bacteria to double.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)911
substituting (M1)
911 A1
2
(b)3.47 hours
e0.2t = 2 (M1)
taking ln (M1)
3.47 hours A1
3
Question 6Structured · 6 marks

The masses of bottles filled by a machine are normally distributed with mean 50 g and standard deviation 8 g.

(a)

Find the probability that a randomly chosen bottle has mass less than 60.4 g.

[2]
(b)

Find the probability that a bottle has mass between 42 g and 66 g.

[2]
(c)

10% of bottles have mass greater than k g. Find k.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.903
normal CDF with correct parameters (M1)
0.903 A1
2
(b)0.819
normal CDF (M1)
0.819 A1
2
(c)60.3
P(X > k) = 0.1, inverse normal (M1)
60.3 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