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-FP-RAT-0011 markL1 FoundationNon-calculatorAsymptotes

State the value

c

for the horizontal asymptote

y=c

y=\dfrac{2x+1}{x-3}

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-G011 markL1 FoundationNon-calculatorAsymptotes

State the equation of the vertical asymptote of

y=\dfrac{2x+1}{x-3}

, giving the value

x=k

. State

k

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-Q011 markL1 FoundationNon-calculatorAsymptotes

The horizontal asymptote of

y=\dfrac{3x-1}{x+2}

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-X011 markL1 FoundationNon-calculatorAsymptotes

Find the equation

x=k

of the vertical asymptote of

y=\frac{2x+1}{x-3}

. Give

k

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-X021 markL1 FoundationNon-calculatorAsymptotes

Find the horizontal asymptote

y=c

y=\frac{2x+1}{x-3}

. Give

c

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-X051 markL1 FoundationNon-calculatorAsymptotes

Find the horizontal asymptote

y=c

y=\frac{x^2-4}{x^2-1}

. Give

c

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-0023 marksL2 StandardNon-calculatorAsymptotes

Find the oblique asymptote of

y=\dfrac{x^2+3x+4}{x+1}

, giving

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-0042 marksL2 StandardNon-calculatorAsymptotes

Find the

x

-values of the vertical asymptotes of

y=\dfrac{x^2-4}{x^2-1}

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-X032 marksL2 StandardNon-calculatorAsymptotes

y=\frac{x^2+1}{x-1}

has an oblique asymptote

y=x+c

. Find

c

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-0033 marksL3 ExamNon-calculatorRange

Find the greatest value of

y=\dfrac{x}{x^2+1}

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-X043 marksL3 ExamNon-calculatorRange

Find the greatest value of

y=\frac x{x^2+1}

Salam Academy Original Practice · Proposed mark scheme

SA-FP-RAT-0054 marksL4 ChallengingNon-calculatorRange

Find the

y

-coordinates of the turning points of

y=\dfrac{x^2-5}{x-3}

Salam Academy Original Practice · Proposed mark scheme