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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-INEQ-Q011 markL1 FoundationNon-calculatorRational inequalities
Why multiply both sides by (x−a)2(x-a)^2 rather than (x−a)(x-a)?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-X041 markL1 FoundationNon-calculatorRational inequalities
To clear the fraction in 1x−1>2\frac{1}{x-1}>2, you should multiply both sides by
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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-0013 marksL2 StandardNon-calculatorRational inequalities
1x−1>1\dfrac1{x-1}>1 has solution a<x<ba<x<b. Find bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-0032 marksL2 StandardNon-calculatorRational inequalities
Find the smallest positive integer satisfying 3x+2≤1\dfrac3{x+2}\le1.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-0042 marksL2 StandardNon-calculatorRational inequalities
How many integers xx with −5≤x≤5-5\le x\le5 satisfy x−3x+1>0\dfrac{x-3}{x+1}>0?

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-G012 marksL2 StandardNon-calculatorRational inequalities
Find the critical values when solving x+1x−2<2\dfrac{x+1}{x-2}<2.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-X012 marksL2 StandardNon-calculatorRational inequalities
The solution of xx−1<2\frac x{x-1}<2 is x<ax<a or x>bx>b. Find aa.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-X021 markL2 StandardNon-calculatorRational inequalities
For the same inequality, find bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-0023 marksL3 ExamNon-calculatorRational inequalities
Find the smallest value of xx satisfying xx+1≥2\dfrac{x}{x+1}\ge2.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-X033 marksL3 ExamNon-calculatorRational inequalities
How many integers xx with −5≤x≤5-5\le x\le5 satisfy x−3x+2≥0\frac{x-3}{x+2}\ge0?

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-X053 marksL3 ExamNon-calculatorRational inequalities
The solution of ∣x−3∣<2x|x-3|<2x is x>cx>c. Find cc.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-INEQ-0054 marksL4 ChallengingNon-calculatorRational inequalities
Find the critical values for 2xx−1>x\dfrac{2x}{x-1}>x.

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Salam Academy Original Practice · Proposed mark scheme