Practise

Question bank

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

TopicSkillDifficulty

12 questions

SA-IAL-P1-AL-0012 marksL1 FoundationCalculatorIndices

Find the value of

27^{-\frac23}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0042 marksL1 FoundationCalculatorSurds

Simplify

\sqrt{75}-\sqrt{12}

, giving your answer in the form

k\sqrt3

. State

k

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL1-0012 marksL1 FoundationNon-calculatorIndices

Find the value of

16^{\frac34}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL1-0032 marksL1 FoundationNon-calculatorSurds

Simplify

\sqrt{48}+\sqrt{27}

, giving your answer in the form

k\sqrt3

. State

k

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL1-0042 marksL1 FoundationNon-calculatorSurds

Find the value of

(2+\sqrt3)(2-\sqrt3)

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL1-0052 marksL1 FoundationNon-calculatorSurds

Write

\dfrac{10}{\sqrt5}

in the form

k\sqrt5

. State

k

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-G012 marksL1 FoundationCalculatorIndices

Find the value of

8^{\frac23}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-Q011 markL1 FoundationCalculatorIndices

a^{-\frac12}=

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0022 marksL2 StandardCalculatorIndices

Write

\dfrac{x^2\sqrt x}{x^{-1}}

as a single power of

x

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0033 marksL2 StandardCalculatorSurds

Express

\dfrac{6}{3-\sqrt3}

in the form

a+b\sqrt3

, where

a

and

b

are integers.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL1-0023 marksL2 StandardNon-calculatorIndices

Solve

3^{2x-1}=27

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0054 marksL3 ExamCalculatorSurds

Express

\dfrac{2+\sqrt5}{\sqrt5-1}

in the form

a+b\sqrt5

, where

a

and

b

are rational.

Salam Academy Original Practice · Proposed mark scheme