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

SA-9709-P1-FN4-0051 markL2 StandardCalculatorReflect in y = x

f(x)=\dfrac{1}{x-2}+3

for

x>2

. The graph of

y=f^{-1}(x)

has a vertical asymptote

x=k

. State

k

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN5-0031 markL2 StandardCalculatorDescribe

The transformation that maps

y=f(x)

onto

y=f(2x)

is a stretch parallel to the

x

-axis with scale factor

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN5-0073 marksL2 StandardCalculatorNew equation

f(x)=x^2-4x

. The graph of

y=f(x)

is translated by

\dbinom{1}{3}

. Find the equation of the new graph in the form

y=x^2+bx+c

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN-0032 marksL2 StandardCalculator(ax + b)ⁿ

Find

\displaystyle\int(2x+3)^4\,dx

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SA-9709-P1-IN-0084 marksL2 StandardCalculatorArea under

Find the area of the region enclosed by the curve

y=x^2-4x

and the

x

-axis.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN-0103 marksL2 StandardCalculatorAbout the x-axis

The region under

y=\sqrt{x}

from

x=0

x=4

is rotated through

360^\circ

about the

x

-axis. Find the exact volume.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN1-0032 marksL2 StandardCalculatorRewriting

Find

\displaystyle\int\frac{3}{x^2}\,dx

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SA-9709-P1-IN2-0022 marksL2 StandardCalculator(ax + b)ⁿ

Find

\displaystyle\int(1-x)^5\,dx

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SA-9709-P1-IN2-0032 marksL2 StandardCalculatorRoots and reciprocals

Find

\displaystyle\int\sqrt{2x+1}\,dx

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SA-9709-P1-IN3-0022 marksL2 StandardCalculatorDefinite

Evaluate

\displaystyle\int_1^2\frac{6}{x^2}\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN3-0033 marksL2 StandardCalculatorDefinite

Evaluate

\displaystyle\int_0^1(2x+1)^3\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN4-0023 marksL2 StandardCalculatorArea under

Find the area of the region enclosed by

y=4-x^2

and the

x

-axis.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN5-0013 marksL2 StandardCalculatorAbout the x-axis

The region under

y=x^2

from

x=0

x=2

is rotated through

360^\circ

about the

x

-axis. Find the exact volume.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-IN5-0023 marksL2 StandardCalculatorAbout the x-axis

The region under

y=\dfrac2x

from

x=1

x=4

is rotated through

360^\circ

about the

x

-axis. Find the exact volume.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0033 marksL2 StandardCalculatora = 1

Express

x^2+5x-3

in the form

(x+a)^2+b

, giving

a

and

b

as exact fractions.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0043 marksL2 StandardCalculatora ≠ 1

Express

2x^2-12x+5

in the form

a(x+b)^2+c

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0052 marksL2 StandardCalculatorVertex

Find the coordinates of the minimum point of the curve

y=x^2-8x+19

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SA-9709-P1-QD-0163 marksL2 StandardCalculatorNature of roots

Find the set of values of

k

for which

x^2+kx+9=0

has two distinct real roots. Give your answer in the form

k<a

k>b

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0193 marksL2 StandardCalculatorQuadratic

Solve the inequality

x^2-x-12<0

. Give your answer in the form

a<x<b

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD2-0023 marksL2 StandardCalculatorFactorising

Solve

3x^2+10x-8=0

Salam Academy Original Practice · Proposed mark scheme