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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-P1-TR4-0011 markL1 FoundationCalculatorIdentities
tan⁡xcos⁡x\tan x\cos x simplifies to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-G012 marksL1 FoundationCalculatorIdentities
Simplify 1−cos⁡2xsin⁡x\dfrac{1-\cos^2x}{\sin x}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-Q011 markL1 FoundationCalculatorIdentities
sin⁡2θ\sin^2\theta is identical to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR-Q011 markL1 FoundationCalculatorIdentities
tan⁡θ\tan\theta is identical to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR-0172 marksL2 StandardCalculatorIdentities
Which expression is identical to (sin⁡x+cos⁡x)2(\sin x+\cos x)^2?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-0033 marksL2 StandardCalculatorExact ratios
Given that sin⁡θ=13\sin\theta=\dfrac13 and θ\theta is acute, find the exact values of cos⁡θ\cos\theta and tan⁡θ\tan\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-0042 marksL2 StandardCalculatorIdentities
Express 3sin⁡2x+2cos⁡2x3\sin^2x+2\cos^2x in the form a+bcos⁡2xa+b\cos^2x. Find aa and bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-0052 marksL2 StandardCalculatorIdentities
Simplify (sin⁡x+cos⁡x)2+(sin⁡x−cos⁡x)2(\sin x+\cos x)^2+(\sin x-\cos x)^2.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR-0092 marksL3 ExamCalculatorIdentities
Simplify sin⁡2x1−cos⁡x\dfrac{\sin^2x}{1-\cos x}.
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR-0103 marksL3 ExamCalculatorIdentities
Given that sin⁡θ=35\sin\theta=\dfrac35 and θ\theta is obtuse, find the exact values of cos⁡θ\cos\theta and tan⁡θ\tan\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-0023 marksL3 ExamCalculatorProof
Show that sin⁡4x−cos⁡4x\sin^4x-\cos^4x can be written in the form asin⁡2x+ba\sin^2x+b. Find aa and bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-0061 markL3 ExamCalculatorProof
1cos⁡x−cos⁡x\dfrac{1}{\cos x}-\cos x is identical to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-0073 marksL3 ExamCalculatorExact ratios
Given that tan⁡θ=2\tan\theta=2 and 180∘<θ<270∘180^\circ<\theta<270^\circ, find the exact values of sin⁡θ\sin\theta and cos⁡θ\cos\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-TR4-0084 marksL5 ExtensionCalculatorProof
Show that 1+sin⁡xcos⁡x+cos⁡x1+sin⁡x\dfrac{1+\sin x}{\cos x}+\dfrac{\cos x}{1+\sin x} can be written as kcos⁡x\dfrac{k}{\cos x}, and find kk.

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Salam Academy Original Practice · Proposed mark scheme