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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-T31-0012 marksL1 FoundationCalculatorReciprocal functions
Find the exact values of cot⁡45∘\cot45^\circ and sec⁡180∘\sec180^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T31-0021 markL1 FoundationCalculatorIdentities
Simplify tan⁡2θ−sec⁡2θ\tan^2\theta-\sec^2\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T31-G012 marksL1 FoundationCalculatorReciprocal functions
Find the exact values of sec⁡60∘\sec60^\circ and cosec⁡30∘\operatorname{cosec}30^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T31-Q011 markL1 FoundationCalculatorReciprocal functions
The graph of y=sec⁡xy=\sec x has vertical asymptotes where
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0012 marksL1 FoundationCalculatorReciprocal functions
Given that tan⁡θ=34\tan\theta=\tfrac34 and θ\theta is acute, find the exact values of sec⁡θ\sec\theta and csc⁡θ\csc\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-Q011 markL1 FoundationCalculatorReciprocal functions
sec⁡θ\sec\theta is defined as
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-Q021 markL1 FoundationCalculatorIdentities
1+tan⁡2θ1+\tan^2\theta is identical to
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T31-0032 marksL2 StandardCalculatorIdentities
Given that sec⁡θ=3\sec\theta=3 and θ\theta is acute, find the exact value of tan⁡θ\tan\theta.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T31-0042 marksL2 StandardCalculatorEquations
Solve cosec⁡x=2\operatorname{cosec}x=2 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-0024 marksL2 StandardCalculatorEquations
Solve sec⁡2θ=3+tan⁡θ\sec^2\theta=3+\tan\theta for 0∘≤θ≤180∘0^\circ\le\theta\le180^\circ. Give answers correct to 1 decimal place where necessary.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-TR-0163 marksL2 StandardCalculatorEquations
Solve sec⁡x=2\sec x=2 for 0≤x≤2π0\le x\le2\pi, giving exact answers in radians.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-T31-0054 marksL3 ExamCalculatorEquations
Solve tan⁡2x=2sec⁡x−1\tan^2x=2\sec 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-TR-0036 marksL4 ChallengingCalculatorEquations
Solve 3csc⁡2x−5cot⁡x−5=03\csc^2x-5\cot x-5=0 for 0∘<x<360∘0^\circ<x<360^\circ, giving answers correct to 1 decimal place.

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Salam Academy Original Practice · Proposed mark scheme