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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-AL-0083 marksL1 FoundationCalculatorLinear factors
Express 5x+1(x−1)(x+2)\dfrac{5x+1}{(x-1)(x+2)} in the form Ax−1+Bx+2\dfrac{A}{x-1}+\dfrac{B}{x+2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-G012 marksL1 FoundationCalculatorLinear factors
Express 3(x+1)(x−2)\dfrac{3}{(x+1)(x-2)} in the form Ax+1+Bx−2\dfrac{A}{x+1}+\dfrac{B}{x-2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-Q011 markL1 FoundationCalculatorLinear factors
In 5x+1(x−1)(x+2)≡Ax−1+Bx+2\dfrac{5x+1}{(x-1)(x+2)}\equiv\dfrac{A}{x-1}+\dfrac{B}{x+2}, which substitution finds AA directly?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-Q031 markL1 FoundationCalculatorRepeated factors
The correct partial-fraction form of 1(x+1)(x−2)2\dfrac{1}{(x+1)(x-2)^2} is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-0013 marksL2 StandardCalculatorLinear factors
Express 7x−1(x+1)(2x−1)\dfrac{7x-1}{(x+1)(2x-1)} in the form Ax+1+B2x−1\dfrac{A}{x+1}+\dfrac{B}{2x-1}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-0024 marksL2 StandardCalculatorLinear factors
Express 2x2−x+3x(x−1)(x+1)\dfrac{2x^2-x+3}{x(x-1)(x+1)} in the form Ax+Bx−1+Cx+1\dfrac{A}{x}+\dfrac{B}{x-1}+\dfrac{C}{x+1}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-0032 marksL2 StandardCalculatorRepeated factors
Express 2x+1(x−1)2\dfrac{2x+1}{(x-1)^2} in the form Ax−1+B(x−1)2\dfrac{A}{x-1}+\dfrac{B}{(x-1)^2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-0071 markL2 StandardCalculatorQuadratic factors
The correct form of partial fractions for x(x+3)(x2+4)\dfrac{x}{(x+3)(x^2+4)} is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-0095 marksL3 ExamCalculatorRepeated factors
Express x+5(x+1)(x−1)2\dfrac{x+5}{(x+1)(x-1)^2} in the form Ax+1+Bx−1+C(x−1)2\dfrac{A}{x+1}+\dfrac{B}{x-1}+\dfrac{C}{(x-1)^2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-0105 marksL3 ExamCalculatorQuadratic factors
Express 3x2+4x+7(x+1)(x2+2)\dfrac{3x^2+4x+7}{(x+1)(x^2+2)} in the form Ax+1+Bx+Cx2+2\dfrac{A}{x+1}+\dfrac{Bx+C}{x^2+2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-0044 marksL3 ExamCalculatorRepeated factors
Express 4x2(x+2)\dfrac{4}{x^2(x+2)} in the form Ax+Bx2+Cx+2\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{C}{x+2}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-0054 marksL3 ExamCalculatorQuadratic factors
Express 3x+1(x−1)(x2+1)\dfrac{3x+1}{(x-1)(x^2+1)} in the form Ax−1+Bx+Cx2+1\dfrac{A}{x-1}+\dfrac{Bx+C}{x^2+1}.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL4-0064 marksL4 ChallengingCalculatorQuadratic factors
Express x2+2(x+1)(x−1)\dfrac{x^2+2}{(x+1)(x-1)} in the form P+Ax+1+Bx−1P+\dfrac{A}{x+1}+\dfrac{B}{x-1}, where PP is a constant.

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Salam Academy Original Practice · Proposed mark scheme