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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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12 questions

SA-FP-SUM-0012 marksL1 FoundationCalculatorStandard sums
Find ∑r=120r2\displaystyle\sum_{r=1}^{20}r^2.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-G012 marksL1 FoundationNon-calculatorStandard sums
Find ∑r=110(2r+1)\displaystyle\sum_{r=1}^{10}(2r+1).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-Q011 markL1 FoundationNon-calculatorStandard sums
∑r=1nr3\displaystyle\sum_{r=1}^{n}r^3 equals
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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-X011 markL1 FoundationNon-calculatorStandard sums
Find ∑r=120r\sum_{r=1}^{20}r.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-X021 markL1 FoundationNon-calculatorStandard sums
Find ∑r=110r2\sum_{r=1}^{10}r^2.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-X031 markL1 FoundationNon-calculatorStandard sums
Find ∑r=15r3\sum_{r=1}^{5}r^3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-0022 marksL2 StandardNon-calculatorStandard sums
Find ∑r=1120r\displaystyle\sum_{r=11}^{20}r.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-0032 marksL2 StandardNon-calculatorDifferences
Using 1r(r+1)=1r−1r+1\dfrac1{r(r+1)}=\dfrac1r-\dfrac1{r+1}, find ∑r=191r(r+1)\displaystyle\sum_{r=1}^{9}\dfrac1{r(r+1)}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-0041 markL2 StandardNon-calculatorDifferences
State the sum to infinity of ∑r=1∞1r(r+1)\displaystyle\sum_{r=1}^{\infty}\dfrac1{r(r+1)}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-X042 marksL2 StandardNon-calculatorDifferences
Using 1r(r+1)=1r−1r+1\frac1{r(r+1)}=\frac1r-\frac1{r+1}, find ∑r=191r(r+1)\sum_{r=1}^{9}\frac1{r(r+1)}.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-X052 marksL2 StandardNon-calculatorStandard sums
Find ∑r=1120r\sum_{r=11}^{20}r.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-SUM-0054 marksL4 ChallengingNon-calculatorDifferences
Using 2r(r+2)=1r−1r+2\dfrac2{r(r+2)}=\dfrac1r-\dfrac1{r+2}, find ∑r=1∞2r(r+2)\displaystyle\sum_{r=1}^{\infty}\dfrac2{r(r+2)}.

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Salam Academy Original Practice · Proposed mark scheme