Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

13 questions

SA-9709-P3-AL5-G013 marksL1 FoundationCalculatorExpanding

Expand

(1+x)^{-1}

in ascending powers of

x

, up to and including the term in

x^3

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-Q011 markL1 FoundationCalculatorExpanding

The binomial expansion of

(1+x)^{\frac12}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-Q021 markL1 FoundationCalculatorValidity

The expansion of

(1+2x)^{-1}

is valid for

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-0113 marksL2 StandardCalculatorExpanding

Expand

(1+x)^{-2}

in ascending powers of

x

, up to and including the term in

x^3

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-0124 marksL2 StandardCalculatorValidity

Expand

\sqrt{1-4x}

in ascending powers of

x

, up to and including the term in

x^2

. The expansion is valid for

|x|<k

. State

k

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-0013 marksL2 StandardCalculatorExpanding

Expand

(1+3x)^{-2}

in ascending powers of

x

, up to and including the term in

x^2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-0031 markL2 StandardCalculatorValidity

The expansion of

(2-3x)^{-1}

in ascending powers of

x

is valid for

|x|<k

. State

k

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-0042 marksL2 StandardCalculatorApplications

Use the first three terms of the expansion of

(1+x)^{\frac12}

to estimate

\sqrt{1.02}

, giving your answer to 5 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-0134 marksL3 ExamCalculatorValidity

Expand

\dfrac{1}{2+x}

in ascending powers of

x

, up to and including the term in

x^2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-0024 marksL3 ExamCalculatorValidity

Expand

\sqrt[3]{8+x}

in ascending powers of

x

, up to and including the term in

x^2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-0054 marksL3 ExamCalculatorApplications

Expand

\dfrac{1+x}{(1-x)^2}

in ascending powers of

x

, up to and including the term in

x^2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL-0146 marksL5 ExtensionCalculatorApplications

Given

f(x)=\dfrac{5x+1}{(x-1)(x+2)}=\dfrac{2}{x-1}+\dfrac{3}{x+2}

, find the expansion of

f(x)

in ascending powers of

x

, up to and including the term in

x^2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-AL5-0065 marksL5 ExtensionCalculatorExpanding

The expansion of

(1+ax)^n

begins

1-6x+27x^2+\cdots

. Find

a

and

n

Salam Academy Original Practice · Proposed mark scheme