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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2401 questions · page 47 of 121 · choose a topic above to narrow them down

SA-IAL-P1-AL-0012 marksL1 FoundationCalculatorIndices

Find the value of

27^{-\frac23}

Salam Academy Original Practice · Proposed mark scheme

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-AL1-0012 marksL1 FoundationNon-calculatorIndices

Find the value of

16^{\frac34}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL2-0012 marksL1 FoundationNon-calculatorDiscriminant

Write

x^2+6x+11

in the form

(x+p)^2+q

. Find

p

and

q

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL2-0022 marksL1 FoundationNon-calculatorDiscriminant

Find the value of the discriminant of

2x^2-3x+5

, and hence state the number of real roots of

2x^2-3x+5=0

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-AL-G012 marksL1 FoundationCalculatorIndices

Find the value of

8^{\frac23}

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SA-IAL-P1-DF-0022 marksL1 FoundationCalculatorPower rule

Given

y=(2x+5)(x-1)

, find

\dfrac{dy}{dx}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-0052 marksL1 FoundationCalculatorGradients

Find the gradient of

y=x^3-3x^2+2

at the point where

x=-1

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF1-0011 markL1 FoundationNon-calculatorPower rule

Given

y=5x^4

, find

\dfrac{dy}{dx}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF1-0022 marksL1 FoundationNon-calculatorPower rule

Given

y=\dfrac3x

, find

\dfrac{dy}{dx}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF1-0032 marksL1 FoundationNon-calculatorPower rule

Given

y=x\sqrt x

, find

\dfrac{dy}{dx}

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF2-0012 marksL1 FoundationNon-calculatorGradients

Find the gradient of

y=2x^3

at the point where

x=-1

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF2-0042 marksL1 FoundationNon-calculatorGradients

Find the

x

-coordinate of the point on

y=x^2-6x

where the gradient is zero.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF3-0012 marksL1 FoundationNon-calculatorNormals

Find the gradient of the normal to

y=x^2

at the point where

x=2

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF3-0023 marksL1 FoundationNon-calculatorTangents

Find the equation of the tangent to

y=x^3

at the point where

x=1

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-G012 marksL1 FoundationCalculatorPower rule

Given

y=4x^3-5x^2+2

, find

\dfrac{dy}{dx}

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SA-IAL-P1-IN1-0011 markL1 FoundationNon-calculatorPower rule

Find

\displaystyle\int8x^3\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-IN1-0022 marksL1 FoundationNon-calculatorPower rule

Find

\displaystyle\int x^{-\frac12}\,dx

Salam Academy Original Practice · Proposed mark scheme