0606.14.10: Understand integration as the reverse process Solutions for indefinite integrals should… — IGCSE Additional Mathematics 0606 past paper questions

Real questions on 0606.14.10: understand integration as the reverse process solutions for indefinite integrals should…

The newest 20 of 42 written questions. Open one to see it on the real paper.

0606/11 · May/June 2026 · Q4[5]
4 Given that $\int_{0}^{a} \frac{1}{3 x + 2} d x = ln 4$ , find the value of the constant $a$ .See it on the paper →
0606/22 · May/June 2026 · Q3b[3]
(b) Find $\int sec^{2} \frac{x}{3} d x$ .See it on the paper →
0606/11 · October/November 2025 · Q7b[3]
(b) Find $\int (1 + tan^{2} 3 x) d x$ .See it on the paper →
0606/22 · October/November 2025 · Q7b[4]
(b) Hence find $\int x sin 2 x d x$ .See it on the paper →
0606/22 · October/November 2025 · Q10[10]
10-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/23 · October/November 2025 · Q10b(i)[2]
10 In this question the units are metres and seconds. A particle moves along a straight line through a point $A$ . Its displacement, $s$ , from $A$ at time $t$ is given by $s = \frac{10 t + 100}{2 t ^{2} + 100}$ . The diagram shows the displacement–time graph for the first 30 seconds of the motion. [Diagram: A graph wit...See it on the paper →
0606/21 · May/June 2025 · Q10a(ii)[3]
A particle $P$ moves in a straight line. $t$ seconds after passing a fixed point, $O$ , the acceleration of $P$ , $a ms^{- 2}$ , is given by $a = t^{2} - 2 for 0 \leq t \leq 4$ $a = 19 - 5 e^{8 - 2 t} for 4 \leq t \leq 10.$ When $t = 3$ , the velocity of $P$ is $-\frac{1}{3} \text{ ms}^{...See it on the paper →
0606/21 · May/June 2025 · Q10b[5]
A particle $P$ moves in a straight line. $t$ seconds after passing a fixed point, $O$ , the acceleration of $P$ , $a ms^{- 2}$ , is given by $a = t^{2} - 2 for 0 ⩽ t ⩽ 4$ $a = 19 - 5 e^{8 - 2 t} for 4 ⩽ t ⩽ 10.$ When $t = 3$ , the velocity of $P$ is $...See it on the paper →
0606/22 · May/June 2025 · Q8[11]
11-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/23 · May/June 2025 · Q8b[4]
(b) A curve is such that $\frac{d y}{d x} = sin (3 x + π)$ . The curve passes through the point $(\frac{π}{9}, \frac{4}{3})$ . Find the exact $y$ -coordinate of the point on the curve where $x = \frac{5 π}{12}$ .See it on the paper →
0606/11 · October/November 2024 · Q4[5]
Given that $\int_{0}^{2 a + 1} \frac{8}{4 x + 3} d x = ln 16$ , find the exact value of the constant $a$ .See it on the paper →
0606/23 · October/November 2024 · Q12b[8]
12 A particle moves in a straight line. Its velocity, $v ms^{- 1}$ , at time $t$ seconds is given by $v = cos t - sin t$ . (b) Find the displacement at the time when the particle first changes direction after passing through $O$ .See it on the paper →
0606/11 · May/June 2024 · Q10b[4]
In this question, all distances are in metres and time, $t$ , is in seconds. A particle $P$ is at a fixed point $O$ at time $t = 0$ . The velocity, $v$ , of $P$ is given by $v = 3 sin 2 t$ for $t ⩾ 0$ . (b) Find an expression, in terms of $t$ , for the displacement of $P$ from $O$ at time $t$ .See it on the paper →
0606/11 · May/June 2024 · Q12b[4]
(b) Hence find $\int \frac{l n 3 x}{x ^{3}} d x$ .See it on the paper →
0606/22 · May/June 2024 · Q2a[4]
(a) Evaluate $\int_{\frac{π}{3}}^{\frac{π}{2}} cos \frac{x}{4} d x$ . You must show all your working.See it on the paper →
0606/12 · February/March 2024 · Q6a(i)[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/12 · February/March 2024 · Q7a[4]
Find $\int_{2}^{4} (5 x - 2)^{- \frac{2}{3}} d x$ , giving your answer in exact form.See it on the paper →
0606/12 · February/March 2024 · Q7b[5]
(b) Find $\int_{0}^{\frac{1}{2}} (\frac{4}{2 x + 1} + \frac{8}{( 2 x + 1 ) ^{2}}) d x$ , giving your answer in the form $a + ln b$ , where $a$ and $b$ are integers.See it on the paper →
0606/22 · February/March 2024 · Q6[4]
6 Find the exact area of the region enclosed by the curve $y = e^{2 - 4 x}$ , the $x$ -axis, the line $x = - 0.25$ and the line $x = 0.5$ .See it on the paper →
0606/21 · October/November 2023 · Q7d[4]
A particle moves in a straight line. At time $t$ seconds after passing through a fixed point $O$ , its velocity, $v ms^{- 1}$ , is given by $v = 10 sin 2 t - 6 cos 2 t$ . (d) Find the displacement of the particle between $t = \frac{π}{4}$ and $t = \frac{π}{2}$ .See it on the paper →

What examiners said

Candidates were slightly less successful with this part although there were still a good number of correct responses. Most candidates realised they should integrate again but a number misapplied integration rules or again omitted the constant of integration.
— Examiner report, May/June 2025, 0606/21 Q10(a)(ii) (Cambridge)

In this part of the question candidates needed to work with the acceleration given for 4 t 10. Few fully correct answers were seen, although many candidates had a good plan, they often incorrectly integrated the exponential function – either making a sign error or differentiating instead. Again, the constant of integration proved problematic for some candidates who either omitted it altogether or...
— Examiner report, May/June 2025, 0606/21 Q10(b) (Cambridge)

Some fully correct responses were seen. In these responses, candidates produced clear and careful solutions, integrating and stating an exact constant of integration which they found by interpreting the information given in the question. A few candidates found the correct equation of the curve but were unable to state the required y-coordinate in exact, surd form. Other candidates integrated corre...
— Examiner report, May/June 2025, 0606/23 Q8(b) (Cambridge)