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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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16 questions

SA-9709-P2-AL-0092 marksL1 FoundationCalculatorRemainder theorem
Find the remainder when x3+2x2−5x+1x^3+2x^2-5x+1 is divided by (x−2)(x-2).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-Q011 markL1 FoundationCalculatorRemainder theorem
The remainder when p(x)p(x) is divided by (x+3)(x+3) is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-0042 marksL1 FoundationCalculatorRemainder theorem
Find the remainder when x3−4x2+2x+5x^3-4x^2+2x+5 is divided by (x−3)(x-3).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-0102 marksL2 StandardCalculatorRemainder theorem
Find the remainder when 4x3−2x2+x−34x^3-2x^2+x-3 is divided by (2x+1)(2x+1).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-0125 marksL2 StandardCalculatorFactor theorem
Show that (x−2)(x-2) is a factor of p(x)=2x3+x2−13x+6p(x)=2x^3+x^2-13x+6. Hence solve p(x)=0p(x)=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-0064 marksL2 StandardCalculatorDivision
Find the quotient and the remainder when x3+2x2−5x+1x^3+2x^2-5x+1 is divided by x2+x−3x^2+x-3.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-0074 marksL2 StandardCalculatorFactor theorem
Show that (x+2)(x+2) is a factor of x3−7x−6x^3-7x-6, and hence solve x3−7x−6=0x^3-7x-6=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-0162 marksL2 StandardCalculatorRemainder theorem
Find the remainder when 2x3+3x2−x+42x^3+3x^2-x+4 is divided by (2x−1)(2x-1).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL3-0014 marksL2 StandardCalculatorDivision
Find the quotient and the remainder when 2x3+3x2−5x+62x^3+3x^2-5x+6 is divided by (x+3)(x+3).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL3-0024 marksL2 StandardCalculatorFactor theorem
Solve the equation x3−2x2−5x+6=0x^3-2x^2-5x+6=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-0115 marksL3 ExamCalculatorFactor theorem
The polynomial p(x)=x3+ax2−7x+bp(x)=x^3+ax^2-7x+b has (x−1)(x-1) as a factor. When p(x)p(x) is divided by (x+2)(x+2) the remainder is 1515. Find aa and bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-0135 marksL3 ExamCalculatorDivision
Find the quotient and the remainder when x4−3x2+2x+1x^4-3x^2+2x+1 is divided by x2+x+1x^2+x+1.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-0145 marksL3 ExamCalculatorFactor theorem
(2x−1)(2x-1) is a factor of p(x)=2x3−x2+ax−3p(x)=2x^3-x^2+ax-3. (i) Find aa. (ii) How many real roots does p(x)=0p(x)=0 have?

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-0155 marksL3 ExamCalculatorFactor theorem
p(x)=x3+ax2+bx−2p(x)=x^3+ax^2+bx-2. When p(x)p(x) is divided by (x−1)(x-1) the remainder is 44, and when it is divided by (x+1)(x+1) the remainder is −6-6. Find aa and bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-AL-0055 marksL3 ExamCalculatorFactor theorem
The polynomial p(x)=2x3+ax2+bx−6p(x)=2x^3+ax^2+bx-6 has (x−2)(x-2) as a factor. When p(x)p(x) is divided by (x+1)(x+1) the remainder is −6-6. Find aa and bb.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-AL-0168 marksL5 ExtensionCalculatorFactor theorem
The polynomial p(x)=6x3+ax2+bx−4p(x)=6x^3+ax^2+bx-4 has factors (x−2)(x-2) and (2x+1)(2x+1). (i) Find aa and bb. (ii) Solve p(x)=0p(x)=0. (iii) Hence solve p(∣x∣)=0p(|x|)=0.

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Salam Academy Original Practice · Proposed mark scheme