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-0122 marksL1 FoundationCalculatorSketching

Find the

x

-coordinates of the points where the curve

y=x(x-2)(x+3)

meets the

x

-axis.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL3-0011 markL1 FoundationNon-calculatorSketching

Find the

y

-coordinate of the point where

y=(x-1)^2(x+2)

meets the

y

-axis.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL3-0021 markL1 FoundationNon-calculatorSketching

Write down the equation of the horizontal asymptote of

y=\dfrac3x+1

, in the form

y=b

. State

b

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL3-0032 marksL1 FoundationNon-calculatorTransformations

y=f(x)

has a maximum at

(1,4)

. Write down the coordinates of the maximum of

y=f(x)+2

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL3-0061 markL1 FoundationCalculatorSketching

For

k>0

, the graph of

y=\dfrac k{x^2}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-Q031 markL1 FoundationCalculatorTransformations

The graph of

y=f(x)-4

is the graph of

y=f(x)

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0132 marksL2 StandardCalculatorTransformations

The curve

y=f(x)

has a maximum point at

(2,5)

. Write down the coordinates of the maximum point of

y=f(x+3)

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0144 marksL2 StandardCalculatorTransformations

The curve

y=f(x)

has a minimum point at

(4,-3)

. Write down the coordinates of the minimum point of (i)

y=f(2x)

and (ii)

y=3f(x)

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0152 marksL2 StandardCalculatorSketching

The curve

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

has asymptotes

x=a

and

y=b

. Write down

a

and

b

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL3-0042 marksL2 StandardNon-calculatorTransformations

y=f(x)

passes through

(3,-2)

. Write down the corresponding point on

y=f(-x)

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL3-0052 marksL2 StandardNon-calculatorTransformations

y=f(x)

has a minimum at

(3,1)

. Write down the coordinates of the minimum of

y=f\left(\tfrac12x\right)

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0163 marksL3 ExamCalculatorSketching

By sketching

y=x^2(x-3)

and

y=\dfrac2x

on the same axes, state the number of real solutions of

x^2(x-3)=\dfrac2x

Salam Academy Original Practice · Proposed mark scheme