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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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15 questions

SA-9709-P1-SR-0102 marksL1 FoundationCalculatorSum to infinity
Find the sum to infinity of the geometric progression 81, 54, 36, …81,\ 54,\ 36,\ \dots

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0041 markL1 FoundationCalculatorConvergence
Which of these geometric series has a sum to infinity?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-G012 marksL1 FoundationCalculatorSum to infinity
For the geometric series 12+6+3+…12+6+3+\dots, find the common ratio and the sum to infinity.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-Q011 markL1 FoundationCalculatorSum to infinity
1+12+14+18+…1+\tfrac12+\tfrac14+\tfrac18+\dots (forever) equals
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR-Q021 markL1 FoundationCalculatorConvergence
A geometric series has a sum to infinity when
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR-0113 marksL2 StandardCalculatorProblems
A geometric progression has first term 1616 and sum to infinity 6464. Find the common ratio and the third term.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR-0162 marksL2 StandardCalculatorSum to infinity
A geometric progression has first term 55 and second term 44. Find its sum to infinity.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0012 marksL2 StandardCalculatorProblems
By writing 0.3˙=0.3+0.03+0.003+…0.\dot{3}=0.3+0.03+0.003+\dots as a geometric series, write 0.3˙0.\dot3 as a fraction.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0032 marksL2 StandardCalculatorSum to infinity
Find the sum to infinity of the geometric series 9−3+1−…9-3+1-\dots

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0052 marksL2 StandardCalculatorProblems
The sum to infinity of a geometric series is three times its first term. Find the common ratio.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0022 marksL3 ExamCalculatorProblems
Write 0.2˙7˙=0.272727…0.\dot2\dot7=0.272727\dots as a fraction in its lowest terms.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0073 marksL3 ExamCalculatorProblems
A ball is dropped from a height of 1010 m and rises to 34\tfrac34 of its previous height after each bounce. Find the total distance it travels before coming to rest.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0082 marksL3 ExamCalculatorConvergence
The geometric series 1+2x+4x2+…1+2x+4x^2+\dots converges for −k<x<k-k<x<k. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR-0125 marksL4 ChallengingCalculatorProblems
A geometric progression has sum to infinity 1212 and second term 83\dfrac83. Find the two possible values of the common ratio.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR4-0064 marksL4 ChallengingCalculatorProblems
A geometric series with positive common ratio has sum to infinity 2020, and the sum of its first two terms is 1515. Find the common ratio and the first term.

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Salam Academy Original Practice · Proposed mark scheme