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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-P3-T33-0011 markL1 FoundationCalculatorIdentities
To solve cos⁡2x+sin⁡x=0\cos2x+\sin x=0, the best form of cos⁡2x\cos2x to use is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T33-0021 markL1 FoundationCalculatorDouble angles
Find the exact value of 2sin⁡15∘cos⁡15∘2\sin15^\circ\cos15^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T33-G013 marksL1 FoundationCalculatorDouble angles
Given that sin⁡θ=35\sin\theta=\tfrac35 and θ\theta is acute, find the exact values of sin⁡2θ\sin2\theta and cos⁡2θ\cos2\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T33-Q011 markL1 FoundationCalculatorDouble angles
sin⁡2A\sin2A is identical to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0152 marksL1 FoundationCalculatorDouble angles
Given that tan⁡θ=12\tan\theta=\tfrac12, find the exact value of tan⁡2θ\tan2\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-Q031 markL1 FoundationCalculatorDouble angles
Which of these equals cos⁡2A\cos2A?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T33-0031 markL2 StandardCalculatorDouble angles
Find the exact value of cos⁡222.5∘−sin⁡222.5∘\cos^222.5^\circ-\sin^222.5^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T33-0052 marksL2 StandardCalculatorIdentities
Express sin⁡2x\sin^2x in the form a+bcos⁡2xa+b\cos2x. Find aa and bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0074 marksL2 StandardCalculatorEquations
Solve cos⁡2x=3sin⁡x−1\cos2x=3\sin x-1 for 0∘≤x≤360∘0^\circ\le x\le360^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T33-0044 marksL3 ExamCalculatorEquations
Solve cos⁡2x=cos⁡x\cos2x=\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-0064 marksL3 ExamCalculatorDouble angles
Given that cos⁡θ=−13\cos\theta=-\tfrac13 and 90∘<θ<180∘90^\circ<\theta<180^\circ, find the exact values of sin⁡2θ\sin2\theta and cos⁡2θ\cos2\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0084 marksL3 ExamCalculatorEquations
Solve sin⁡2θ=sin⁡θ\sin2\theta=\sin\theta for 0∘≤θ≤360∘0^\circ\le\theta\le360^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T33-0065 marksL4 ChallengingCalculatorEquations
Solve tan⁡2θ=3tan⁡θ\tan2\theta=3\tan\theta for 0∘≤θ≤180∘0^\circ\le\theta\le180^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0134 marksL4 ChallengingCalculatorIdentities
Express cos⁡4θ\cos4\theta as a polynomial in cos⁡θ\cos\theta. Enter your answer in terms of xx, where x=cos⁡θx=\cos\theta.

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Salam Academy Original Practice · Proposed mark scheme