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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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13 questions

SA-9709-P3-T32-0032 marksL1 FoundationCalculatorCompound angles
Use the compound-angle formula to simplify cos⁡(x+π2)\cos\left(x+\dfrac{\pi}{2}\right).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T32-Q011 markL1 FoundationCalculatorCompound angles
cos⁡(A−B)\cos(A-B) is identical to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-G013 marksL1 FoundationCalculatorExact values
Use sin⁡(45∘+30∘)\sin(45^\circ+30^\circ) to find the exact value of sin⁡75∘\sin75^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T32-0012 marksL2 StandardCalculatorExact values
Find the exact value of cos⁡75∘\cos75^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T32-0023 marksL2 StandardCalculatorCompound angles
Angles AA and BB are acute, with sin⁡A=45\sin A=\tfrac45 and cos⁡B=513\cos B=\tfrac5{13}. Find the exact value of sin⁡(A−B)\sin(A-B).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T32-0052 marksL2 StandardCalculatorCompound angles
Given that tan⁡A=12\tan A=\tfrac12 and tan⁡B=13\tan B=\tfrac13, find the exact value of tan⁡(A+B)\tan(A+B).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T32-0061 markL2 StandardCalculatorCompound angles
sin⁡(A+B)+sin⁡(A−B)\sin(A+B)+\sin(A-B) simplifies to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0044 marksL2 StandardCalculatorCompound angles
Angles AA and BB are acute, with sin⁡A=35\sin A=\tfrac35 and cos⁡B=1213\cos B=\tfrac{12}{13}. Find the exact values of sin⁡(A+B)\sin(A+B) and cos⁡(A−B)\cos(A-B).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0052 marksL2 StandardCalculatorCompound angles
Given that tan⁡A=2\tan A=2 and tan⁡B=13\tan B=\tfrac13, find the exact value of tan⁡(A+B)\tan(A+B).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0143 marksL2 StandardCalculatorExact values
Use tan⁡(45∘−30∘)\tan(45^\circ-30^\circ) to find the exact value of tan⁡15∘\tan15^\circ, in the form a+b3a+b\sqrt3.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T32-0044 marksL3 ExamCalculatorEquations
Solve sin⁡(x+30∘)=2cos⁡x\sin(x+30^\circ)=2\cos x for 0∘≤x≤360∘0^\circ\le x\le360^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0124 marksL3 ExamCalculatorEquations
Solve sin⁡(θ+45∘)=2cos⁡(θ−45∘)\sin(\theta+45^\circ)=2\cos(\theta-45^\circ) for 0∘≤θ≤360∘0^\circ\le\theta\le360^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T32-0073 marksL4 ChallengingCalculatorEquations
Given that cos⁡(x−30∘)=2sin⁡x\cos(x-30^\circ)=2\sin x, find the exact value of tan⁡x\tan x.

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Salam Academy Original Practice · Proposed mark scheme