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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-LE-0082 marksL1 FoundationCalculatorDefinition
Find the exact value of log⁡381+log⁡319\log_3 81+\log_3\tfrac19.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0011 markL1 FoundationCalculatorDefinition
Find the value of log⁡5125\log_5\dfrac{1}{25}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0031 markL1 FoundationCalculatorLog laws
lg⁡12=lg⁡3+klg⁡2\lg12=\lg3+k\lg2. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0041 markL1 FoundationCalculatorLog laws
Which of these equals ln⁡6\ln6?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-G012 marksL1 FoundationCalculatorDefinition
Find the values of log⁡232\log_2 32 and log⁡101000\log_{10}1000.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-Q011 markL1 FoundationCalculatorDefinition
For any valid base aa, log⁡a1\log_a1 equals
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE-G012 marksL1 FoundationCalculatorLog laws
Express 2ln⁡3+ln⁡4−ln⁡62\ln3+\ln4-\ln6 as a single logarithm ln⁡k\ln k. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE-Q011 markL1 FoundationCalculatorLog laws
Which of these is always true for a,b>0a,b>0?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0021 markL2 StandardCalculatorDefinition
Find the value of log⁡93\log_9 3.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0052 marksL2 StandardCalculatorCombining
Write 2lg⁡5+lg⁡42\lg5+\lg4 as a single logarithm and hence find its value.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0062 marksL2 StandardCalculatorCombining
Express 3ln⁡2−ln⁡4+ln⁡53\ln2-\ln4+\ln5 in the form ln⁡k\ln k. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0082 marksL2 StandardCalculatorCombining
Find the exact values of ln⁡(e5)\ln\left(e^5\right) and e2ln⁡3e^{2\ln3}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0072 marksL3 ExamCalculatorDefinition
Solve log⁡x64=3\log_x64=3.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-LE1-0093 marksL4 ChallengingCalculatorLog laws
Given that log⁡a2=p\log_a2=p and log⁡a3=q\log_a3=q, log⁡a18\log_a18 can be written as mp+nqmp+nq, and log⁡a(a212)\log_a\left(\dfrac{a^2}{12}\right) as r−2p−qr-2p-q. Find mm, nn and rr.

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Salam Academy Original Practice · Proposed mark scheme