2029 syllabus · HL · 100 marks · 2h · Section A short + Section B long. Each generated paper follows the SL & HL Paper 2 · HL (calculator) · 2029 syllabus format, with the same number and style of questions as the real exam, and comes with an IB-style mark scheme.
Generate Paper 2 · HL (calculator) · 2029 syllabus →In an arithmetic sequence, u3 = 12 and u9 = 48.
Find the common difference and the first term.
Find the smallest value of n for which Sn > 1875.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | d = 6, u1 = 0 u1 + 2d = 12, u1 + 8d = 48 (M1) d = 6 A1 u1 = 0 A1 | 3 |
| (b) | n = 26 n2(2(0) + (n − 1)(6)) > 1875 (M1) attempt to solve, e.g. graph or table: S25 = 1800, S26 = 1950 (M1) n = 26 A1 | 3 |
A ladder of length 5 m leans against a vertical wall. The bottom of the ladder slides away from the wall at a constant 0.3 m s−1.
Find the rate at which the top of the ladder is sliding down the wall when the bottom is 3 m from the wall.
| Part | Answer and marking points | Marks |
|---|---|---|
| 0.225 m s−1 x2 + y2 = 25 (A1) 2xdxdt + 2ydydt = 0 M1A1 y = 4 when x = 3 (A1) dydt = −0.225, so sliding down at 0.225 m s−1 A1 | 5 |
Let f(x) = 4cos x and g(x) = x2 − 2, for −4 ≤ x ≤ 4.
Find the x-coordinates of the points where the graphs of f and g intersect.
Hence solve the inequality f(x) < g(x).
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | x = −1.50, x = 1.50 attempt to solve f(x) = g(x), e.g. graph or solver (M1) x = −1.50, x = 1.50 A2 award A1 if one value is missing or incorrect | 3 |
| (b) | −4 ≤ x < −1.50 or 1.50 < x ≤ 4 using the graph to choose the correct regions (M1) correct critical values used as endpoints (A1) −4 ≤ x < −1.50 or 1.50 < x ≤ 4 A1 | 3 |
A continuous random variable X has probability density function f(x) = kx2 for 0 ≤ x ≤ 3, and 0 otherwise.
Find k.
Find E(X).
Find the median of X.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 19 ∫ f(x) dx = 1 (M1) 19 A1 | 2 |
| (b) | 94 ∫ x f(x) dx (M1) 94 A1 | 2 |
| (c) | 2.38 ∫ from 0 to m = 0.5 (M1) m3 = 272 (A1) 2.38 A1 | 3 |
The number of bacteria in a culture is modelled by N(t) = 500ekt, where t is in hours. After 5 hours there are 800 bacteria.
Find the value of k.
Find the time taken for the number of bacteria to reach 4000.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.0940 800 = 500e5k (M1) k = 15ln800500 (A1) k = 0.0940 A1 | 3 |
| (b) | 22.1 hours 500ekt = 4000 (M1) t = ln(4000/500)k (A1) 22.1 hours A1 | 3 |
A right circular cone has base radius 6 cm and height 10 cm.
Find the volume of the cone.
Find the total surface area of the cone.
Find the angle between the slant edge and the base.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 377 cm3 13πr2h (M1) 377 cm3 A1 | 2 |
| (b) | 333 cm2 slant height 11.7 (A1) πrl + πr2 (M1) 333 cm2 A1 | 3 |
| (c) | 59.0° tan θ = 106 (M1) 59.0° A1 | 2 |
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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