How many Integration questions are there for 9709?

This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Integration. Each links straight to instant marking against the official 9709 scheme.

How are Integration answers marked?

Type or photograph your working and MarkScheme scores it against the real 9709 mark scheme for this topic — method, accuracy and any band descriptors — so you see exactly where the marks are.

Where can I learn Integration first?

Start with the free Mathematics lesson on Integration, then come back and drill past-paper questions under timed conditions.

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9709 · topic questions

Integration

Mathematics12 questions

12 past-paper questions on Integration

9709/11 · May/June 20246 marks
The diagram shows part of the curve with equation y = 1/(5x-4)³ and the lines x = 2.4 and y = 1. The curve intersects the line y…
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9709/11 · May/June 20255 marks
The diagram shows the curve with equation y = 5x² – 20x and the line with equation y = x-16. The x-coordinates of the points of…
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9709/12 · October/November 20245 marks
The diagram shows part of the curve with equation y=-2x² +8x+11 and the line with equation y = 8x+9. Find the area of the shaded…
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9709/22 · May/June 20245 marks
Show that the x-coordinate of B is In2 and hence find the area of the shaded region.
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9709/41 · May/June 20245 marks
(ii) Find the distance travelled by the particle in the first 16s.
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9709/21 · May/June 20254 marks
(b) Find the area of the shaded region. Give your answer in the form, where p and q are integers. [4]
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9709/11 · October/November 20244 marks
Find the area of the region bounded by the curve and the lines x = 0, x = 7/2 and y = 0.
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9709/13 · May/June 20254 marks
Given that ∫(from 1 to a) ((4x-3)⁻² + 2) dx = 12, find the value of the constant a.
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9709/11 · May/June 20254 marks
(b) Find the equation of the curve.
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9709/13 · May/June 20244 marks
A curve passes through the point (3/5, -3) and is such that dy/dx = -20/(5x-3)². Find the equation of the curve.
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9709/13 · October/November 20244 marks
Find the area of the shaded region.
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9709/11 · October/November 20244 marks
Given that the curve passes through the point (4, 11), find the equation of the curve.
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Question stems are shortened previews. Open a question to attempt the full version and have it marked.

Worked example

What a lost mark actually looks like

This answer reaches the right coordinates and still drops a mark — the conclusion is stated, but never justified. Examiners pay for the reasoning, not the answer.

MARKED

80%

Strong

M1dy/dx = 3x^2 - 12x + 9M1 earned
M1(x - 1) $(x - 3) = 0$ M1 earned
A1 $x = 1$ or $x = 3$ A1 earned
B1(1, 5) is a maximum and (3, 1) is a minimumB1 not earned

B1 — withheld
You stated the nature of each point correctly, but stated it without justification. This mark needs the reasoning shown — either evaluate the second derivative (d²y/dx² = 6x − 12, giving −6 at $x = 1$ and +6 at $x = 3$ ) or show a sign change of dy/dx either side of each point. An unsupported assertion earns nothing here even when the conclusion is right.

Integration (9709) past-paper questions — marked instantly

These are real Cambridge Mathematics past-paper questions on Integration. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.

Mark your answer →Learn Integration 9709 grade boundaries

Frequently asked questions

How many Integration questions are there for 9709?: This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Integration. Each links straight to instant marking against the official 9709 scheme.
How are Integration answers marked?: Type or photograph your working and MarkScheme scores it against the real 9709 mark scheme for this topic — method, accuracy and any band descriptors — so you see exactly where the marks are.
Where can I learn Integration first?: Start with the free Mathematics lesson on Integration, then come back and drill past-paper questions under timed conditions.