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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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14 questions

SA-9709-P2-IN-Q031 markL1 FoundationCalculatorOver or under
For a curve that bends upwards (is convex) over the whole interval, the trapezium rule gives
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I34-0041 markL1 FoundationCalculatorTrapezium rule
How many ordinates (yy-values) are needed to apply the trapezium rule with 44 strips?

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I34-G013 marksL1 FoundationCalculatorTrapezium rule
Use the trapezium rule with 22 strips to estimate ∫02x2 dx\displaystyle\int_0^2x^2\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I34-Q011 markL1 FoundationCalculatorTrapezium rule
In the trapezium rule, which ordinates are multiplied by 22?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0154 marksL2 StandardCalculatorOver or under
Use the trapezium rule with 2 intervals to estimate ∫13ln⁡x dx\displaystyle\int_1^3\ln x\,dx, giving your answer to 2 decimal places. State whether this is an overestimate or an underestimate.
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0164 marksL2 StandardCalculatorTrapezium rule
Use the trapezium rule with 4 intervals to estimate ∫022x dx\displaystyle\int_0^2 2^x\,dx, giving your answer to 2 decimal places. State whether this is an overestimate or an underestimate.
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I34-0013 marksL2 StandardCalculatorTrapezium rule
Use the trapezium rule with 44 strips to estimate ∫121x dx\displaystyle\int_1^2\frac1x\,dx, giving your answer to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I34-0023 marksL2 StandardCalculatorTrapezium rule
Use the trapezium rule with 22 strips to estimate ∫011+x dx\displaystyle\int_0^1\sqrt{1+x}\,dx, giving your answer to 2 decimal places.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I34-0031 markL2 StandardCalculatorOver or under
The curve y=1+xy=\sqrt{1+x} bends downwards (is concave) for 0≤x≤10\le x\le1. The trapezium rule estimate of ∫011+x dx\displaystyle\int_0^1\sqrt{1+x}\,dx is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0174 marksL2 StandardCalculatorTrapezium rule
Use the trapezium rule with 2 intervals to estimate ∫021+x3 dx\displaystyle\int_0^2\sqrt{1+x^3}\,dx, giving your answer to 2 decimal places. State whether this is an overestimate or an underestimate.
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0174 marksL3 ExamCalculatorTrapezium rule
Use the trapezium rule with 3 intervals to estimate ∫01.2sec⁡x dx\displaystyle\int_0^{1.2}\sec x\,dx, giving your answer to 2 decimal places.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0183 marksL3 ExamCalculatorTrapezium rule
Use the trapezium rule with 4 intervals to estimate ∫01ex2 dx\displaystyle\int_0^1e^{x^2}\,dx, giving your answer to 2 decimal places.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-IN-0186 marksL4 ChallengingCalculatorAccuracy
(i) Use the trapezium rule with 2 intervals to estimate ∫01e2x dx\displaystyle\int_0^1e^{2x}\,dx, to 3 significant figures. (ii) Find the exact value of the integral. (iii) Find the percentage error in the estimate, to 2 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I34-0054 marksL4 ChallengingCalculatorAccuracy
(a) Use the trapezium rule with 22 strips to find an exact estimate of ∫0πsin⁡x dx\displaystyle\int_0^{\pi}\sin x\,dx. (b) The exact value is 22. Find the percentage error of the estimate, to 1 decimal place.

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Salam Academy Original Practice · Proposed mark scheme