3

CONFIDENTIAL MM315

MMM3152015 Hak Cipta Terpelihara MRSM Pendang [Lihat halaman sebelah]

SULIT

[100 MARKS]

Answer All Questions

1. (a) In diagram 1(a), AB and CD are straight lines. EF is a transversal. Match the correct

answers.

Diagram 1(a)

Answer:

[3 marks]

(i)

po, ro Alternate

angles

(ii)

qo, so Interior

angles

(iii)

qo, ro Corresponding

angles

For

Examiners Use

F

B

s E

D

C

A

rq

p

3

4

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For

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(b)(i)

(b)(ii)

Based on diagram 1(b)(i), identify the straight line which is parallel to CD.

Diagram 1(b)(i)

The straight line which is parallel to CD is ______________.

[1 marks]

Answer:

In diagram 1(b)(ii), PQR and SQT are straight lines.

Diagram 1(b)(ii)

Find the value of x.

[2 marks]

Answer:

x

110

150

R

TQ

P

S

120

10

15

45

20

SRQP

D

CBA

5

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(b)(iii)

(c)

In diagram 1(b)(iii), PRT and QRS are straight lines. Find the value of x.

Diagram 1(b)(iii)

[1 mark]

Answer:

A 25o

B 35o

C 43o

D 45o

In diagram 1(c), ABC, AD, DE and FG are straight lines.

Diagram 1(c)

Calculate the value of sr . [3 marks]

Answer:

For

Examiners Use

G

F

ED

CBA

65

s

r

4

x

43

78

TS

R

QP

3

6

CONFIDENTIAL MM315

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For

Examiners Use

2. (a)

(b)(i)

(b)(ii)

By using a pair of compasses, a protractor and a ruler, construct a regular hexagon with

sides of 3 cm.

[3 marks]

Answer:

What is the sum of the exterior angles of a polygon.

Answer:

In diagram 2(b)(ii), ABCDEF is a hexagon, GAB is a straight line.

Diagram 2(b)(ii)

Find the value of x.

Answer:

[4 marks]

75

101

80

x

120

G

F

E

DC

B

A

4

3

7

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(c) Diagram 2(c) is a combination of a half hexagon and a half octagon. ABCD are vertices

of a regular hexagon and DEFGH are vertices of a regular octagon. ADH is a straight line.

Diagram 2(c)

Find the value of x.

[3 marks]

Answer:

For

Examiners Use

3

8

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3.(a)

In diagram 3(a), PQRS is a circumference with centre O.

Diagram 3(a)

Find:

(i) the length of RS (ii) the value of x

[3 marks]

Answer:

(a)

(b)

3

9

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(b)(i)

(b)(ii)

In diagram 3(b)(i), ABC is a chord of the circle with centre O. OB = 6 cm, AC= 16 cm

and AB = BC.

Diagram 3 (b)(i)

State the value of

(i) x

(ii) y

[2 marks]

Answer :

(i)

(ii)

In diagram 3(b)(ii), PQRS is a circle.

Diagram 3(b)(ii)

Find the value of x.

[2 marks]

Answer:

For

Examiners Use

4

10

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For

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(c) In diagram 3(c), PQR is a straight line and PT = PQ.

Diagram 3 (c)

Find the value of x.

[3 marks]

Answer:

3

11

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4. (a) The pie chart in Diagram 4(a) shows the ratio of a cake which is divided among five people,

P, Q, R, S and T.

Diagram 4(a)

Given the weight of the cake is 2400g and T gets 800g of it, find the value of x, in degrees.

[3 marks]

Answer:

For

Examiners Use

40

60

60

xT

S

R

Q

P

3

12

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For

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(b)

(c)

The table shows the score obtained by a group of the students in a quiz.

Table 4(b)

(i) It is given that the modal score is 3. Find the minimum value of n.

(ii) If 3n , calculate the mean score of the quiz.

[4 marks]

Answer:

(i)

(ii)

The data below shows the masses, in kg, of parcels collected in a post office on a particular

day.

2 10 9 10 4

7 16 13 8 10

(i) Based on the data above, find the mode of the parcels. (ii) Find the median of the parcels.

[3 marks]

Answer:

(i)

(ii)

Score 0 1 2 3 4 5

Frequency 6 4 6 n 10 3

4

3

13

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5. (a)

State whether each of the following statement is true or false.

(i) 7 x 7 x 7 x 7 x 7 x 7 = 67

Answer : ____________

(ii) 1138 zz

Answer : ____________

(iii) 030

Answer : ____________

[3 marks]

For

Examiners Use

(b)(i)

(b)(ii)

Simplify 3

2

3

2

gg

[2 marks]

Answer:

Given 3221 x , calculate the value of x.

[2 marks]

Answer:

3

4

14

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For

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(c)(i)

(c)(ii)

Circle the correct answer.

Answer:

305 kk A 3k

B 2k

C 2k

D 8k

Simplify 483

3

21812 abba

[3 marks]

Answer:

3

15

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6.(a) Expand each of the following :

(i) ba 25305

1

(ii) 48 yy

[3 marks]

Answer:

(i)

(ii)

For

Examiners Use

(b) Factorise each of the following expression completely :

(i) 22 816 kjkj

(ii) 49

232

k

k

[4 marks]

Answer:

(i)

(ii)

3

4

16

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For

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(c) Express y

x

y

x

5

32

as a single fraction.

[3 marks]

Answer:

3

17

CONFIDENTIAL MM315

MMM3152015 Hak Cipta Terpelihara MRSM Pendang [Lihat halaman sebelah]

SULIT

7. (a) Determine the variables in the following situations and represent them with a suitable

letters.

[3 marks]

(i) Temperature throughout last Thursday in January in Kuala Kubu.

Answer : Variable : _______________ Letter : ________________

(ii) Decrease in the mass of an adult from 30 kg to 40kg over a period.

Answer : Variable :_________________ Letter : _______________

(iii)Number of days of emergency leave of an employee in twelve month.

Answer : Variable :_________________ Letter : _______________

For

Examiners

Use

(b)(i)

(b)(ii)

Given 2

42n

mnP . Find the value of P when m = 3, and n = 2.

[2 marks]

Answer:

Given atrts2

1 . Find the value of t if s = 8, r = 5 and a = 6.

[2 marks]

Answer:

3

4

18

CONFIDENTIAL MM315

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For

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(c) Given 2

2 gtfm

.When f = 4, 3m and 2t , calculate the value of g.

[3 marks]

Answer :

3

19

CONFIDENTIAL MM315

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SULIT

8. (a)

Diagram 8(a)

Convert the volume of water in the diagram into:

Answer:

(i) ____________cm3

(ii) ____________l

(iii) ____________mm3

[3 marks]

For

Examiners Use

3

20

CONFIDENTIAL MM315

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For

Examiners Use

(b)

Diagram 8(b)(i) Diagram 8(b)(ii)

Diagram 8(b)(i) shows a composite solid of a sphere and a right pyramid that were designed by

a group of students for their Innovation Project. The solid is made of iron.

(i) If the total volume of a composite solid is 5467 cm3, find the height of the right pyramid,

in cm.

(ii) In the Innovation Project, the students need to transform the right pyramid into a cuboid

shown in Diagram 8(b)(ii). By using your answer in (b)(i), give the ratio height of right

pyramid to height of that cuboid in the diagram.

(Use 7

22 )

[4 marks]

Answer:

(i)

(ii)

14 cm

11 cm

10.5 cm

4

h

10.5 cm

14 cm

11 cm

21

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(c)

Diagram 8(c)

Ali made a right pyramid as shown using plasticine. He then reformed the pyramid into a

right cone of the same height. Calculate the base radius of the cone. (Use 7

22 )

[3 marks]

Answer:

For

Examiners Use

3

11 cm

14 cm

21 cm

22

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3 cm 8 cm

6 cm 16 cm

20 cm

10 cm

2 cm 1 cm

For

Examiners Use

9.(a) State the scales of the following scale drawings.

[3 marks]

Answer:

Object Scale drawing

Scale

( n:1 )

a)

b)

c)

3

2 cm

12 cm

23

CONFIDENTIAL MM315

MMM3152015 Hak Cipta Terpelihara MRSM Pendang [Lihat halaman sebelah]

SULIT

(b) Diagram 9(b) shows a picture with dimension of 40 cm by 20 cm.

Diagram 9(b)

(i) Using scale of 1 : 4, calculate the perimeter of the drawing.

(ii) If Abu wants to draw a picture with 8 cm by 4 cm, calculate the scale used by Abu.

[4 marks]

Answer:

(i)

(ii)

For

Examiners Use

40 cm

20 cm

4

24

CONFIDENTIAL MM315

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For

Examiners Use

(c) Diagram 9(c) shows a polygon.

Diagram 9(c)

On the grid in the answer space, redraw the polygon using the scale 1: 500. The grid has equal

squares with sides of 1 unit.

[3 marks]

Answer :

3

25

CONFIDENTIAL MM315

MMM3152015 Hak Cipta Terpelihara MRSM Pendang [Lihat halaman sebelah]

SULIT

10.(a)

OABCDE is the image of OABCDE under an enlargement.

(i) State the scale factor.

(ii) Given the area of the OABCDE is 20 cm2, find the area of OABCDE.

[3 marks]

Answer:

(i)

(ii)

For

Examiners Use

3

Diagram 10(a)

26

CONFIDENTIAL MM315

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(b) Diagram 10(b) shows the elevation of a flyover of a highway.

The vertical lines represent the pillars of the flyover. The pillars are placed 20 m apart and

the height of the first pillar is 15 m.

(i) Determine whether triangle ABC and ADE are similar. Circle the correct answer.

Answer : Yes / No

(ii) If triangle ABC and ADE are similar, find the total height of the first 4 pillars.

[4 marks]

Answer:

(i)

(ii)

F

H

20 m

15 m

20 m20 mA C

D

E G

B

I

4

Diagram 10(b)

27

CONFIDENTIAL MM315

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SULIT

(c) Diagram shows the object PQRS of an enlargement. Construct the image of PQRS with centre

O and scale factor of 2.

[3 marks]

Answer:

Diagram 10(c)

-END OF QUESTIONS-

For

Examiners Use

3