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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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12 questions

SA-FP-TF-0012 marksL1 FoundationNon-calculatorIdentities
If t=12t=\frac12, find cos⁡x\cos x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-0021 markL1 FoundationNon-calculatorIntegrals
With t=tan⁡x2t=\tan\frac x2, dxdt=k1+t2\frac{dx}{dt}=\frac{k}{1+t^2}. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-G011 markL1 FoundationNon-calculatorIdentities
If t=tan⁡x2=1t=\tan\frac x2=1, find sin⁡x\sin x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-Q011 markL1 FoundationNon-calculatorIdentities
With t=tan⁡x2t=\tan\frac x2, tan⁡x=\tan x=
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-X011 markL1 FoundationNon-calculatorIdentities
If t=tan⁡x2=12t=\tan\frac x2=\frac12, find sin⁡x\sin x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-X021 markL1 FoundationNon-calculatorIdentities
If t=tan⁡x2=12t=\tan\frac x2=\frac12, find cos⁡x\cos x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-X031 markL1 FoundationNon-calculatorIdentities
If t=tan⁡x2=12t=\tan\frac x2=\frac12, find tan⁡x\tan x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-X041 markL1 FoundationNon-calculatorIntegrals
With t=tan⁡x2t=\tan\frac x2, dxdx becomes
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-0034 marksL3 ExamCalculatorEquations
Solve 3sin⁡x+4cos⁡x=43\sin x+4\cos x=4 for 0<x<π0<x<\pi (radians, 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-0044 marksL3 ExamNon-calculatorIntegrals
Evaluate ∫0π/2dx1+sin⁡x\displaystyle\int_0^{\pi/2}\frac{dx}{1+\sin x}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-X053 marksL3 ExamNon-calculatorIntegrals
Use t=tan⁡x2t=\tan\frac x2 to find ∫0π/211+cos⁡x dx\int_0^{\pi/2}\frac1{1+\cos x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-TF-0055 marksL4 ChallengingCalculatorIntegrals
Evaluate ∫0π/2dx2+cos⁡x\displaystyle\int_0^{\pi/2}\frac{dx}{2+\cos x} (to 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme