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 83 of 137 · choose a topic above to narrow them down

SA-9709-P1-TR2-0031 markL2 StandardCalculatorGraphs

State the period of

y=\tan2x

, in degrees.

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SA-9709-P1-TR3-0021 markL2 StandardCalculatorPrincipal values

Find the exact value of

\cos^{-1}\left(-\dfrac{\sqrt3}{2}\right)

in radians.

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SA-9709-P1-TR4-0033 marksL2 StandardCalculatorExact ratios

Given that

\sin\theta=\dfrac13

and

\theta

is acute, find the exact values of

\cos\theta

and

\tan\theta

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SA-9709-P1-TR5-0023 marksL2 StandardCalculatorTransformed angles

Solve

\cos2x=0.5

for

0^\circ\le x\le180^\circ

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SA-9709-P2-AL-0014 marksL2 StandardCalculatorEquations

Solve the equation

|x+1|=|3x-5|

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SA-9709-P2-AL-0073 marksL2 StandardCalculatorSimple

The solution of

|x-2|\ge3

x\le a

x\ge b

. Find

a

and

b

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SA-9709-P2-AL-0102 marksL2 StandardCalculatorRemainder theorem

Find the remainder when

4x^3-2x^2+x-3

is divided by

(2x+1)

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SA-9709-P2-DF-0013 marksL2 StandardCalculatorProduct rule

Differentiate

y=x^2e^{2x}

with respect to

x

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SA-9709-P2-DF-0083 marksL2 StandardCalculatorTangents and normals

Find the equation of the tangent to

y=e^{2x}

at the point where

x=0

. Give your answer in the form

y=mx+c

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SA-9709-P2-DF-0104 marksL2 StandardCalculatorImplicit

The curve

x^2+y^2+2x-4y=20

passes through

(2,6)

. Find the gradient of the curve at this point.

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SA-9709-P2-DF-0153 marksL2 StandardCalculatorParametric

A curve has parametric equations

x=3\cos t

y=2\sin t

. Find the gradient at the point where

t=\tfrac\pi4

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SA-9709-P2-IN-0043 marksL2 StandardCalculatorLog results

Find the exact value of

\displaystyle\int_1^3\frac{2}{3x-1}\,dx

, giving your answer in the form

k\ln4

. State

k

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SA-9709-P2-IN-0053 marksL2 StandardCalculatorExact integrals

Find the exact value of

\displaystyle\int_0^{\pi/6}\sin2x\,dx

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SA-9709-P2-IN-0063 marksL2 StandardCalculatorSquares

Find

\displaystyle\int\sin^2x\,dx

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SA-9709-P2-IN-0083 marksL2 StandardCalculatorSquares

Find

\displaystyle\int\tan^2x\,dx

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SA-9709-P2-IN-0154 marksL2 StandardCalculatorOver or under

Use the trapezium rule with 2 intervals to estimate

\displaystyle\int_1^3\ln x\,dx

, giving your answer to 2 decimal places. State whether this is an overestimate or an underestimate.

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SA-9709-P2-IN-0164 marksL2 StandardCalculatorTrapezium rule

Use the trapezium rule with 4 intervals to estimate

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

, giving your answer to 2 decimal places. State whether this is an overestimate or an underestimate.

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SA-9709-P3-AL-0014 marksL2 StandardCalculatorEquations

Solve the equation

|x-2|=|2x+1|

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SA-9709-P3-AL-0113 marksL2 StandardCalculatorExpanding

Expand

(1+x)^{-2}

in ascending powers of

x

, up to and including the term in

x^3

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SA-9709-P3-AL-0124 marksL2 StandardCalculatorValidity

Expand

\sqrt{1-4x}

in ascending powers of

x

, up to and including the term in

x^2

. The expansion is valid for

|x|<k

. State

k

Salam Academy Original Practice · Proposed mark scheme