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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2730 questions · page 28 of 137 · choose a topic above to narrow them down

SA-9709-P1-DF3-0013 marksL1 FoundationCalculatorTangents and normals

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-9709-P1-DF3-G013 marksL1 FoundationCalculatorTangents and normals

Find the equation of the tangent to

y=x^2+1

at the point

(1,2)

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF4-G013 marksL1 FoundationCalculatorStationary points

Find the coordinates of the stationary point of

y=x^2-6x+1

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SA-9709-P1-DF5-G013 marksL1 FoundationCalculatorRates

The radius of a circle increases at

2

cm s⁻¹. Find the rate at which the area is increasing when the radius is

3

cm. Give an exact answer.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-G013 marksL1 FoundationCalculatorPower rule

Given

y=4x^3-6x+\dfrac{2}{x}

, find

\dfrac{dy}{dx}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-G012 marksL1 FoundationCalculatorRange on an interval

f(x)=3x+1

for

-2\le x\le3

. The range of

f

p\le f(x)\le q

. Find

p

and

q

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-0012 marksL1 FoundationCalculatorEvaluate fg(a)

f(x)=2x+3

and

g(x)=x^2-1

. Find

gf(2)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN2-G012 marksL1 FoundationCalculatorEvaluate fg(a)

f(x)=2x+3

and

g(x)=x^2-1

. Find

fg(2)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-G012 marksL1 FoundationCalculatorFind the inverse

f(x)=3x-5

x\in\mathbb{R}

. Find

f^{-1}(x)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-G012 marksL1 FoundationCalculatorReflect in y = x

The point

(2,7)

lies on the graph of

y=f(x)

. State the coordinates of the corresponding point on the graph of

y=f^{-1}(x)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN5-0011 markL1 FoundationCalculatorDescribe

The transformation that maps

y=f(x)

onto

y=f(x+4)

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SA-9709-P1-FN5-G012 marksL1 FoundationCalculatorImage of a point

f(x)=x^2

. State the coordinates of the vertex of

y=f(x-3)+2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN-0013 marksL1 FoundationCalculatorIndefinite

Find

\displaystyle\int(8x^3-6x+5)\,dx

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SA-9709-P1-IN-0063 marksL1 FoundationCalculatorDefinite

Evaluate

\displaystyle\int_1^3(3x^2-2x)\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN1-0011 markL1 FoundationCalculatorIndefinite

Find

\displaystyle\int6x^2\,dx

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SA-9709-P1-IN1-0022 marksL1 FoundationCalculatorIndefinite

Find

\displaystyle\int(x^3-4x+1)\,dx

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SA-9709-P1-IN2-0012 marksL1 FoundationCalculator(ax + b)ⁿ

Find

\displaystyle\int(2x-5)^3\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN2-G012 marksL1 FoundationCalculator(ax + b)ⁿ

Find

\displaystyle\int(3x+1)^4\,dx

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SA-9709-P1-IN3-0012 marksL1 FoundationCalculatorDefinite

Evaluate

\displaystyle\int_1^4(2x+1)\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN3-G012 marksL1 FoundationCalculatorDefinite

Evaluate

\displaystyle\int_0^2 3x^2\,dx

Salam Academy Original Practice · Proposed mark scheme