SL · 80 marks · 1h 30m · Section A short + Section B long. Each generated paper follows the SL & HL Paper 2 · SL (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.
Generate Paper 2 · SL (calculator) · exams to Nov 2028 →In triangle ABC, BC = 7.4 cm, AC = 9 cm and BÂC = 35°.
Find the two possible values of AB̂C.
Find the difference between the areas of the two possible triangles.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 44.2° or 136° sin AB̂C9 = sin 35°7.4 (M1)(A1) 44.2° A1 180° − 44.2° = 136° A1 | 4 |
| (b) | 27.4 cm2 AĈB = 101° or 9.23° (A1) 12(7.4)(9)sin C for each (M1) 27.4 cm2 A1 | 3 |
Let f(x) = ln(x + 2) and g(x) = x2 − 1. The graphs of f and g intersect at x = p and x = q, where p < q are the two smallest solutions of f(x) = g(x).
Find the value of p and the value of q.
Find the area of the region enclosed by the graphs of f and g between x = p and x = q.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | p = −1.85, q = 6.21 p = −1.85 A1 q = 6.21 A1 | 2 |
| (b) | 8.78 integral of the difference of the functions (M1) correct limits (A1) 8.78 A1 | 3 |
A right pyramid VABCD has a square base ABCD with sides of length 12 cm. The vertex V is 7 cm vertically above the centre M of the base.
Find the length of the edge VA.
Find the angle between the edge VA and the base ABCD.
Find the volume of the pyramid.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 11.0 cm AM = 12√122 + 122 = 8.49 (M1)(A1) VA = √72 + AM2 = 11.0 cm A1 | 3 |
| (b) | 39.5° tan VÂM = 78.49 (M1) 39.5° A1 | 2 |
| (c) | 336 cm3 13 × 122 × 7 (M1) 336 cm3 A1 | 2 |
The number of bacteria in a culture is modelled by N(t) = 1200ekt, where t is in hours. After 5 hours there are 2880 bacteria.
Find the value of k.
Find the time taken for the number of bacteria to reach 9600.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.175 2880 = 1200e5k (M1) k = 15ln28801200 (A1) k = 0.175 A1 | 3 |
| (b) | 11.9 hours 1200ekt = 9600 (M1) t = ln(9600/1200)k (A1) 11.9 hours A1 | 3 |
A disease affects 1% of a population. A test gives a positive result for 95% of people with the disease and for 10% of people without it.
Find the probability that a randomly chosen person tests positive.
Given that a person tests positive, find the probability that they have the disease.
Comment on the usefulness of the test.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 217/2000 (= 0.1085) tree or total probability (M1) 0.1085 = 217/2000 A1 | 2 |
| (b) | 19/217 (≈ 0.0876) conditional probability (M1) 0.00950.1085 (A1) 19/217 (≈ 0.0876) A1 | 3 |
| (c) | many false positives most positive results are false positives, so a positive result alone is not reliable R1 | 1 |
The plane Π has equation −3x + 2y − z = −4. The line L has equation r = 140 + λ−312.
Find the coordinates of the point where L meets Π.
Find the acute angle between L and Π.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (4, 3, −2) substituting the parametric form of L into the equation of Π M1 5 + 9λ = −4 A1 λ = −1 A1 (4, 3, −2) A1 | 4 |
| (b) | 40.0° sin θ = |b·n| ÷ (|b||n|), using the normal to the plane (M1) sin θ = 914 (A1) 40.0° A1 | 3 |
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Meet Riyaz →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