Practise

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

SA-9709-P1-CM-0092 marksL3 ExamCalculatorSegments

A chord

AB

of a circle of radius

10

cm subtends an angle of

1.2

radians at the centre. Find the length of

AB

, correct to 2 decimal places.

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SA-9709-P1-CM3-0023 marksL3 ExamCalculatorSegments

For the same circle (radius

5

cm,

\angle AOB=\dfrac{2\pi}{3}

), find the exact perimeter of the minor segment.

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SA-9709-P1-DF-0113 marksL3 ExamCalculatorRates

The volume of a sphere is increasing at

20

cm³ s⁻¹. Find the rate at which the radius is increasing when the radius is

5

cm. Give an exact answer.

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SA-9709-P1-DF4-0043 marksL3 ExamCalculatorStationary points

Find the coordinates of the stationary point of

y=x+\dfrac4x

for

x>0

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SA-9709-P1-FN1-0034 marksL3 ExamCalculatorRange of quadratics

f(x)=x^2-6x+11

for

0\le x\le4

. The range of

f

p\le f(x)\le q

. Find

p

and

q

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SA-9709-P1-FN1-0043 marksL3 ExamCalculatorRange of quadratics

f(x)=x^2-6x+11

for

4\le x\le7

. The range of

f

p\le f(x)\le q

. Find

p

and

q

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SA-9709-P1-FN2-0063 marksL3 ExamCalculatorExpressions

f(x)=2x+3

and

g(x)=x^2-1

. Solve

gf(x)=0

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SA-9709-P1-FN3-0023 marksL3 ExamCalculatorQuadratic inverses

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

for

x\ge2

. Find

f^{-1}(x)

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SA-9709-P1-FN4-0033 marksL3 ExamCalculatorIntersections

f(x)=x^2-6

for

x\ge0

. Find the

x

-coordinate of the point where the graphs of

y=f(x)

and

y=f^{-1}(x)

meet.

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SA-9709-P1-FN4-0093 marksL3 ExamCalculatorSelf-inverse

f(x)=\dfrac{2x}{x-2}

for

x\ne2

. Show that

f

is self-inverse, and hence find

f^{-1}(6)

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SA-9709-P1-FN5-0062 marksL3 ExamCalculatorImage of a point

The point

(6,4)

lies on

y=f(x)

. Find its image on

y=-f(x+2)

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SA-9709-P1-IN-0114 marksL3 ExamCalculatorAbout the x-axis

The region under

y=x^2+1

from

x=0

x=1

is rotated through

360^\circ

about the

x

-axis. Find the exact volume.

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SA-9709-P1-IN4-0034 marksL3 ExamCalculatorSigns and y-axis

Find the total area of the regions enclosed by

y=x^3-x

and the

x

-axis.

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SA-9709-P1-QD-0063 marksL3 ExamCalculatorCompleting the square

By completing the square, solve

x^2-4x-1=0

. Give your answers in exact form. (Enter both, separated by a comma, or use ±.)

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SA-9709-P1-QD-0204 marksL3 ExamCalculatorQuadratic

Solve the inequality

2x^2+5x-3\ge0

. Give your answer in the form

x\le a

x\ge b

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SA-9709-P1-QD-0215 marksL3 ExamCalculatorSimultaneous

Solve the simultaneous equations

y=x+1

and

x^2+y^2=25

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SA-9709-P1-QD5-0044 marksL3 ExamCalculatorSimultaneous

Solve the simultaneous equations

2x+y=7

and

x^2+xy=6

. Give the values of

x

, then the value of

y

when

x

is larger.

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SA-9709-P1-TR-0092 marksL3 ExamCalculatorIdentities

Simplify

\dfrac{\sin^2x}{1-\cos x}

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SA-9709-P1-TR-0103 marksL3 ExamCalculatorIdentities

Given that

\sin\theta=\dfrac35

and

\theta

is obtuse, find the exact values of

\cos\theta

and

\tan\theta

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SA-9709-P2-AL-0135 marksL3 ExamCalculatorDivision

Find the quotient and the remainder when

x^4-3x^2+2x+1

is divided by

x^2+x+1

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