0606.14.13: Evaluate definite integrals and apply Plane areas include — IGCSE Additional Mathematics 0606 past paper questions

Real questions on 0606.14.13: evaluate definite integrals and apply plane areas include

The newest 20 of 33 written questions. Open one to see it on the real paper.

0606/12 · May/June 2026 · Q12[11]
11-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/21 · May/June 2026 · Q11[10]
10-mark “Give” question — its maths and diagrams are best seen on the paper.
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0606/02 · Specimen 2025 · Q12[9]
9-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/11 · October/November 2025 · Q10[11]
11-mark question — its maths and diagrams are best seen on the paper.
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0606/13 · October/November 2025 · Q8[7]
7-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/11 · May/June 2025 · Q9[10]
10-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/13 · May/June 2025 · Q8b[7]
7-mark “Show” question — its maths and diagrams are best seen on the paper.
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0606/12 · February/March 2025 · Q7b[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/22 · February/March 2025 · Q9b[4]
In this question, all lengths are in metres and time is in seconds. A particle, $P$ , moves in a straight line such that $t$ seconds after passing through a fixed point $O$ its displacement, $s$ , is given by $s = 5 ln (2 t + 1) - 5 t$ . (b) Find the distance $P$ travels between $t = 0$ and $t = 2$ .See it on the paper →
0606/11 · October/November 2024 · Q11[9]
9-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/11 · May/June 2024 · Q6[4]
6 Find $\int_{2}^{4} (\frac{2}{2 x - 3} - \frac{3}{( 3 x - 5 ) ^{2}}) d x$ , giving your answer in exact form.See it on the paper →
0606/11 · May/June 2024 · Q10c[3]
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 $t ⩾ 0$ . (c) Find the distance travelled by $P$ for $0 ⩽ t ⩽ π$ .See it on the paper →
0606/22 · May/June 2024 · Q9[9]
9-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/21 · October/November 2023 · Q3b[3]
(b) Hence find the exact value of $\int_{1}^{3} (4 x + 5 - \frac{1}{2 x + 3}) d x$ , simplifying your answer.See it on the paper →
0606/22 · October/November 2023 · Q6[6]
6 Find the exact value of $\int_{2}^{3} \frac{( x + 2 ) ^{2}}{x} d x$ .See it on the paper →
0606/22 · October/November 2023 · Q8c[5]
A curve has equation $y = x sin 2 x$ . (c) Use your answer to part (a) to find the exact value of $\int_{0}^{\frac{π}{6}} 2 x cos 2 x d x$ .See it on the paper →
0606/21 · May/June 2023 · Q7a[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/23 · May/June 2023 · Q9b[8]
8-mark question — its maths and diagrams are best seen on the paper.
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0606/12 · February/March 2023 · Q8[11]
11-mark “Find” question — its maths and diagrams are best seen on the paper.
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0606/23 · October/November 2022 · Q9d[2]
The equation of a curve is $y = k x e^{- 2 x}$ , where $k$ is a constant. (d) Find the exact value of $\int_{0}^{1} 4 x e^{- 2 x} d x$ .See it on the paper →

What examiners said

Most candidates successfully identified y = 3, differentiated correctly, and formed a correct equation for the tangent. Those who obtained the correct equation were generally able to find the x-intercept. However, few candidates were successful in calculating the correct area of the triangle – whether by integration or by using 1 base height. Integration was generally well attempted, though some c...
— Examiner report, May/June 2025, 0606/11 Q9 (Cambridge)

The most straightforward method of solution was to find the area of the trapezium that could be formed and subtract the area under the curve. Some candidates made the problem more complex than necessary by finding the equation of the line AB first and then using subtraction and integration. Errors were more likely to occur using this method. Few completely correct solutions were seen due to errors...
— Examiner report, May/June 2025, 0606/13 Q8(b) (Cambridge)

This question part was probably one of the most demanding parts of the paper, with many candidates finding the value of s when t = 0 and the value of s when t = 2. Again, candidates were expected to consider the work done in part (a) which was meant to inform them that the particle was at rest in the time interval stated. Consideration of the value of s when t = 0.5 was also essential. Candidates...
— Examiner report, February/March 2025, 0606/22 Q9(b) (Cambridge)