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1 (a) Express ]5 as a percentage.

Answer (a) % [1]

(b) Express 171% as a fraction in its simplest form.

3 Factorise fully 3x3 - 12xY.

For

Examiner's

Use

Answer (b) [1]

Answer [2]

Answer [2]

Answer all the questions.

3.93

(7.47 +3.02) 5.67

Give your answer correct to 2 significant figures.

Calculate2

For

Examiner's

Use

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For

Examiner's

Use

4 (a) Given that

(b) Simplify 1 +- 2x-5

find k.

Answer (a) k= [1]

Answer (b) [1]

Exa

5 The temperature, in DC, at noon, on three successive days was -3, 5 and t.Find an expression, in terms of t, for

(a) the difference in temperature between the first and third days,

Answer (a) DC [1]

(b) the mean temperature for the three days.

Answer (b) 0 C [1]

6 A sum of money was divided between A, Band C in the ratio 2 : 3 : 4.

If, instead, this money had been divided equally between them, A would have received an

extra $20.

What was the total sum of money?

Answer $ [2]

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Show your solution on the number line below.

8 Solve the inequality -2 ~ 2x +4

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1111111111111111111111111111111111111111111111111111111

For

Examiners

Use

9 In the diagram, A, Band C

lie on a circle, centre O.

The tangents at A and C

meet at T.

Angle OAC == 28.

Find

(a) AGC,

(b) ABC,

Answer (a) AOC == [1]

For

Examin

Use

Answer (b) ABC == [1]

(c) ATe.

Answer (c) ATC == [1]

10 Written as the product of its prime factors 4900 == 22 x 52 x 72.

(a) Express 168 as the product of its prime factors.

Answer (a) 168 == [1]

(b) Hence write down

(i) the LCM of 4900 and 168, giving your answer as the

product of its prime factors,

*.

Answer (b)(i) [1]

(ii) the greatest integer that will divide both 4900 and 168 exactly.

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Answer (a) [I]

Answer (c) [1]

Answer (a) [1]

For

Examiner's

Use

Answer (c) [1]

Answer (b) [1]*,

List the elements in

(a) the total of the three numbers shown is 18,

Answer (b) [1]

(b) the three dice show the same number,

(a) A',

(c) AU B.

(c) the total of the three numbers shown is 17?

(b) An B,

12 cg = {x is an integer: -3 ~ x ~ 3}

A = {x: -3 < x

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1111111111111111111111111111111111111111111111111111111

For

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13 The volume, V, of a given mass of gas is inversely proportional to the pressure, P.

When V =3 m3, P =200 N/m2.

(a) Find V when P =150 N/m2

Answer (a) m3 [2]

(b) Find the pressure when the volume is 5m3.

Answer (b) N/m2 [1]

14 The speed of Iight is 3 x 105 km/s.

(a) Express this speed in metres per second.

Give your answer in standard form.

Answer (a) m/s [1]

(b) How long does light take to travel one metre?

Express this answer in nanoseconds.

Answer b nanoseconds 2

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Answer (b) [1 ]

Answer (a)

(b) Explain what your answer to (a) represents.

For

Examiners

Use

[2]

Answer (a) [2]

1

2x- 3

2x

(2x - 3)2

Won Drawn Lost Points

City ( ~2 ~)Won

( 0United 6

Drawn

Lost

(a) Find ( ~2 ~)0)-6

(b) Simplify

3a2 . 9a16 (a) Simplify tbc -:-14b .

15 The matrices below show the results for two football teams and the points awarded.For

Examiners

Use

Answer (b) [2]

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For

Examiner's

Use

17 The graph shows Alison's journey from home to school.She left home at 0800, walked to the bus stop and travelled the rest of the way on the bus.

For

Examiner's

Use

Answer (d)

(d) Alison's brother, Sam, also left home at 0800.

He 'cycled to school at a constant speed of 20 km/h.

Show his journey on the above graph.

(b) How far was she from school at 0815?

[1]

08200815

Answer (a) minutes [1]

Answer (b) km [I]

Answer (c) km/h [1]

0810Time

0805

1

Home 0

0800

6

School5

4

Distance from

home (km) 3

2

(c) Find the speed ofthe bus.

(a) How long did she wait at the bus stop?

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Answer (c) The performed better because .

(c) Explain briefly whether the boys or the girls performed better in the test.

18 Twenty boys and fifteen girls took a Mathematics test.

The marks are shown in the stem-and-Ieaf diagram.For

Exominer

Use

Girls

8

8 9 9

4 7 8 9

3 5 6 8 9

0

Key (Girls)

318 means 38

3

4

6

7

5

2

9

2

o 8

o2

5

45

4

5

5

Key (Boys)

913 means 39

Boys

........................................................................................................................ [1]

Answer (a) [1]

Answer (b) [1]

8

9

5

9

7

(a) Write down the mode of the boys' marks.

(b) Write down the median of the girls' marks.

7

For

rominers

Use:

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For

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Use

19 (a) Sketch the graph of y = 4 - (x - 1)2.

Answer (a)

(b) (i) Sketch the graph of y = (x - I)(x +4).

Answer (b)(i)

y

o

y

o

x

x

[2]

[2]

(ii) Write down the equation of the line of symmetry of y = (x - 1)(x +4).

Answer (b )(ii) [l]

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(a) Find the area of triangle ABC.

20 A, Band C are the points (3, 1), (6, 1) and (9, 5).For

Examiner

Use

10 X8642o

Answer (b) ( , ) [2]

Answer (a) units2 [1]

2

............................

Ai

y

8 T" ~ f..T..T.., T' ; : .[""[":TTr..: : --:- .

6 i11:]lilk4 ijt!T-r : ! : .

Answer (c) k = or [2]

2 :.~tI-r j : ( : .- ! [""["I"]""T rr--:-...

r[T:..TTrrr:-4 ;trt:..i!:t:

......... ~ ~ ~ ~ ,.~ i ~ ; ; ~

-6 ~ ; :. ; ; ; : ~ :

(b) ABCD is a trapezium with AB parallel to DC.

The area of the trapezium is 14 units2.

Find the coordinates of the point D.

(c) E is the point (2, k) and the area of triangle ABE is 9 units2.

Find the two possible values of k.

For

taminers

Use

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For

Examiner's

Use

21 A man walks 1000 m at an average speed of 4 km/h and then runs 1.3 km in 5 minutes.

CalculateFor

Examine

Use

(a) the time, in minutes, he takes to walk the 1000 m,

Answer (a) minutes [1]

(b) his running speed in kilometres per hour,

Answer (b) km/h [2]

(c) his average speed for the whole distance.

Answer (c) km/h [2]

22 Given that n is an integer,

(a) write down expressions for the next two odd numbers after 2n - 1,

Answer (a) and [1]

(b) (i) find, in its simplest form, the expression for the sum of these three odd numbers,

Answer (b)(i) [1]

(ii) explain why the sum is a multiple of 3,

Answer (b)(ii) .

....................................................................................................... [1]

(c) fiQd, in its simplest form, an expression for the sum of the squares of these three odd

numbers.

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(a) Show that triangles ALB and NLD are similar.

........................................................................................................................ [2]

For

Examiner's

Use

A

Answer (d)(i) [1]

Answer (d)(i i) [1]

Areaof~MLBArea of~ALD

Areaof~ABL

Area of ~ ADL '

Answer (c) and [1]

Answer (a) In ~s ALB and NLD .

Answer (b) [1]

(ii)

(iii)

(c) Name two triangles that are congruent.

(b) Name a triangle similar to triangle NCM.

(d) Given that DL = 3LB, find

(i) ABCN'

N

s a para e ogram an s a po nt on .

The line AL produced meets BC at M and DC produced at N.For

Examiner's

Use:

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24 Three points A, Band C are shown below.For

Examiners

UseAnswer (a), (b) and (d)

For

Examine r

Use

C

B

(a) Construct the perpendicular bisector ofBe. [1]

Answer (c) The point P is equidistant from the lines : and .

and equidistant from the points and . [1]

(d) The point D is such that BCD = 1300 andAD = 7.5em.

Find the two possible positions of D and label them D) and D2

[2]

[1]

(c) These two bisectors meet at P.

Complete the statement below.

(b) Construct the bisector of angle ABe.

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