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

SA-4024-AL-0082 marksL2 StandardNon-calculatorInequalities

Solve

5-2x<11

, and write down the smallest integer that satisfies it.

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SA-4024-AL-0123 marksL2 StandardNon-calculatorDirect proportion

y

is directly proportional to

x^2

, and

y=18

when

x=3

. Find

y

when

x=5

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SA-4024-AL1-0043 marksL2 StandardCalculatorFormulae

Make

x

the subject of

y=\dfrac{3x-2}{5}

, and hence find

x

when

y=8

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SA-4024-AL11-0023 marksL2 StandardNon-calculatorDirect proportion

y

is directly proportional to

x^3

, and

y=16

when

x=2

. Find

y

when

x=3

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SA-4024-AL12-0032 marksL2 StandardNon-calculatorFunctions

f(x)=3x+1

and

g(x)=x-4

. Find

gf(2)

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SA-4024-AL2-0043 marksL2 StandardCalculatorSolving quadratics

Solve

x^2+4x-2=0

, giving your answers correct to 2 decimal places.

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SA-4024-AL2-0053 marksL2 StandardCalculatorLinear equations

Solve

\dfrac{x+1}{3}=\dfrac{x-2}{2}

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SA-4024-AL3-0022 marksL2 StandardCalculatorInequalities

Find the largest integer

x

that satisfies

4-3x\ge-8

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SA-4024-AL3-0052 marksL2 StandardCalculatorLinear sequences

The sequence

20,\ 17,\ 14,\ 11,\ldots

has nth term

23-3n

. Find the position of the first negative term.

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SA-4024-AL4-0042 marksL2 StandardCalculatorInverses

f(x)=4x-3

. Find

f^{-1}(9)

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SA-4024-AL8-0022 marksL2 StandardNon-calculatorSolving quadratics

Solve

2x^2+x-6=0

. Give the positive solution.

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SA-4024-AL8-0032 marksL2 StandardNon-calculatorCompleting the square

x^2+8x+3=(x+a)^2+b

. Find

a

and

b

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SA-4024-CG-0053 marksL2 StandardNon-calculatorPerpendicular

Find the equation of the line perpendicular to

y=2x+1

that passes through

(4,3)

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SA-4024-CG-0084 marksL2 StandardCalculatorTravel graphs

A car accelerates uniformly from rest to

12

m/s in

8

s, travels at

12

m/s for

20

s, then slows uniformly to rest in

4

s. Find (a) its acceleration in the first

8

s (b) the total distance travelled.

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SA-4024-CG-0092 marksL2 StandardCalculatorTravel graphs

Ali walks

6

km to a shop in

1\tfrac12

hours, stays there for

30

minutes, then walks home in

1

hour. Find his average speed for the whole trip, in km/h.

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SA-4024-CG2-0062 marksL2 StandardCalculatorParallel

The line

y=kx+1

is parallel to the line

4x-2y=5

. Find

k

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SA-4024-CG3-0043 marksL2 StandardCalculatorTravel graphs

A car travelling at

20

m/s slows uniformly to rest in

5

s. Find (a) its deceleration (b) the distance it travels while slowing.

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SA-4024-CG4-0042 marksL2 StandardNon-calculatorTangents

The tangent to

y=x^2

(3,9)

also passes through

(1,-3)

. Find the gradient of the curve at

(3,9)

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SA-4024-CG4-0052 marksL2 StandardNon-calculatorTangents

A tangent is drawn to a curve at

(2,5)

. The tangent crosses the

y

-axis at

(0,1)

. Find the gradient of the curve at

(2,5)

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SA-4024-GE-0052 marksL2 StandardNon-calculatorCircle angles

A

B

and

C

lie on a circle with centre

O

C

is on the major arc, and angle

AOB=140^\circ

. Find angle

ACB

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