2010 vs Em4 Prelim2 p1

Class Register Number

Name

4016/01 10/4P2/EM/1

MATHEMATICS PAPER 1 Monday 16 August 2010 2 hours

VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL

VICTORIA SCHOOL

SECOND PRELIMINARY EXAMINATION

SECONDARY FOUR

Candidates answer on the Question Paper

READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid. Answer all the questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. You are expected to use a scientific calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80. This document is intended for internal circulation in Victoria School only. No part of this document may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise, without the prior permission of the Victoria School Internal Exams Committee.

Paper 1 consists of 11 printed pages, including the cover page. [Turn over

2

Mathematical Formulae

Compound interest

Total amount = 1100

nrP +

Mensuration

Curved surface area of a cone = rl Surface area of a sphere = 24 r

Volume of a cone = 213

r h

Volume of a sphere = 343

r

Area of triangle = 1 sin2

ab C

Arc length = r , where is in radians Sector area = 21

2r , where is in radians

Trigonometry

sin sin sina b c

A B C= =

2 2 2 2 cosa b c bc= + A

Statistics

Mean = fxf

Standard deviation = 22fx fx

f f

Victoria School 2010 4016/01/EM4/P2/10

3

1 (a) Evaluate

2

3

71.5 3112

6.15 10

+ , leaving your answer correct to 3 decimal places.

(b) Express 166 : 0.625 : 9 in its simplest form.

Answer (a) [1]

(b) : : [1] 2 One of the interior angles of a polygon is 144 . The remaining interior angles are each

equal to 153 . Find the number of sides of the polygon.

Answer [2]

3 Jeffrey drove for 16 hours from Cape Town and arrived at Johannesburg on Friday at 09 15. Find the time and day when he left Cape Town.

Answer [2]

4 Given that 265 xzy

x+= , express x in term of y and z.

Answer [2]


4

5 Simplify ( )3 252 34ab

ba .

Answer [2] 6 It is given that 7 3x < < and 5 y 1 , where x and y are integers. Find (a) the least value of x

y,

(b) the greatest value of 2 2y x .

Answer (a) [1]

(b) [1]

7 It is given that p is inversely proportional to the cube of q. It is known that for a 540p = particular value of q. Find the value of p when this value of q is increased by 100%.

Answer p = [2]

8 The populations of India, Netherlands, Singapore and Vanuatu are 1.83 billion, 16.6 million, 4.9 million and 240 000 respectively. (a) How many more people are there in Netherlands than in Singapore? Express your answer in standard form. (b) Express the population of Vanuatu as a percentage of the population of India.

Answer (a) [1]

(b) % [2]


5 9 The temperature at the bottom of a mountain was 18 C. The temperature at the top, at a

height of 7 310 m, was C.

16 (a) Find the difference between the two temperatures. (b) The temperature decreases uniformly as the height increases. Find

(i) the temperature when one has climbed half-way up the mountain,

(ii) the height from the bottom of the mountain where the temperature is 3 .

Answer (a) C [1]

(b) (i) C [1]

(ii) m [1]

10 A bank pays compound interest of x % per annum compounded half yearly. Mr Sim deposits $15 000 in the bank and earned an interest of $1 768.61 after 3 years. Find x.

Answer x = [3]

11 (a) Express 12, 40 and 3 960 as a product of their prime factors. Leave your answers in index notation. (b) Find the smallest integer x such that the least common multiple of 12, 40 and x is 3 960.

Answer (a) 12 = .

40 = .

3 960 = [3]

(b) [1] Victoria School 2010 4016/01/EM4/P2/10

6 12

50 40 45 55 35 60 30 Amount of money raised ($) The total amount of money raised by each student in a class for the Presidents Challenge fund-raising project is shown in the dot diagram. Find (a) the modal amount raised, (b) the median amount raised, (c) the mean amount raised.

Answer (a) $ [1]

(b) $ [1]

(c) $ [2] 13 P Q

W

M R

S

N

In the diagram, it is given that ,QPW QNM = MQ is parallel to RS and WP is parallel to NQ. W and S are points on MQ and NQ respectively such that MW WQ RS= = . (a) By stating your reasons clearly, prove that there is a pair of congruent triangles.

(b) Find area of triangle area of figure

SRNPQNMW

.

Answer (a) .

.

[3]

(b) [2]


7 14 The first four rows of a sequence are given below.

Row 1 1 21= Row 2 2 3 4+ + 23= Row 3 3 4 5 6 7+ + + + 25= Row 4 4 5 6 7 8 9 10+ + + + + + 27=

: :

: :

: :

Row R 75 .......................................... L+ + S=

(a) Write down the 5th row of the sequence. (b) In Row R, it is given that the first term is 75. Find

(i) R, (ii) L,

(iii) S.

Answer (a) [1]

(b)(i) R = [1]

(ii) L = [1]

(iii) S = [2]

15 Factorise the following completely. (a) 281 6 45x x+ (b) 2 2 22 25 50r pqs s pqr+ 2

Answer (a) [2]

(b) [3]


8

16 (a) Express 29 6y x x= + in the form ( )2 .y q x p= (b) Sketch the graph of 29 6 .y x x= +

Answer (a) [2] (b)

[3]

17 The points , and( )4, 3A ( )3, 7B ( )3, 2C are shown in the diagram. Find

x

yA

B

C O

(a) the area of triangle ABC, (b) the perpendicular distance from C to AB, (c) sin .CAB

Answer (a) unit2 [2]

(b) units [2]

(c) [3]


9 18 The facilities in a fitness area is in the shape of a triangle PSC. The parallel bar station at P is 120 m due east of the sit-up station at S. The chin-up station at C is at a distance of 105 m and on a bearing of 050o from S. (a) Using a scale of 1 cm to represent 10 m, construct an accurate scale drawing of the fitness area PSC. (b) A bench, B, is placed such that it is

equidistant from CP and SP, equidistant from P and S.

By using ruler and compasses only, find and label the position of B. Answer for (a) and (b)

[5]


10 19 The diagram shows the speed-time graph for the first t seconds of a cars journey. speed (m/s)

0 8

6.4 time, T (s)

t14 (a) The car travelled 41.2 m for the first 14 seconds. Find the initial speed of the car. (b) Find the speed of the car when T = 12 s. (c) The car decelerates at 2.5 m/s2 after 14 seconds. Find the value of t. (d) On the axes in the answer space, sketch the distance-time graph of the car.

Answer (a) m/s [2]

(b) m/s [2]

(c) t = [2]

distance (m)

0 time, T (s)

8 14 t

(d)

[3]


11 20

C B

A

D

15

12 9

O

The figure shows a sector OAB with centre O, and an arc BD of a circle with centre C. It is given that OC 15 cm= , and CD12 cmOD = 9 cm= . Find (a) angle in radians, AOB (b) the length of arc AB, (c) the area of the shaded region, (d) the perimeter of the shaded region.

Answer (a) [2]

(b) cm [1]

(c) cm2 [3]

(d) cm [2]

End of Paper


12 2010 Sec 4 Elementary Mathematics Prelim 2 Paper 1 Answers

1a 1.648 14a 25 6 7 8 9 10 11 12 13 9+ + + + + + + + = 1b 144 : 15 : 220 14bi 75 2 13 14bii 223 3 17 15 on Thursday 14biii 22 201

15a ( )( )3 9 2 3 1 x x 4 ( )( )

65 5

= + x y z y z 15b ( )( )( )2 5 + 5pq r s r s 5 12 56 a b 16a ( )218 3= y x 6a 2 6b 25 7 67.5 8a 71.17 10 8b 0.0131 9a 34 9bi 1 9bii 4515

16b

10 3.75 17a 1217 17b 2.87 17c 0.333 19a 2 19b 14154

11a

2

3

3 2

12 2 340 2 53960 2 3 5 11

= = =

19c 142516 or 16.56 11b 99 12a 45 12b 42.50 12c 42.69

19d

20a 0.644 20b 15.4 20c 41.7

13a

(corr. s, / / ) (alt. s, / / )

(given)

(given)

(AAS)

= = = = =

NSR NQM MQ RSNQM QWP WP NQ

NSR QWP

WQ RS

QPW SNR

WPQ SNR

20d 47.4 13b

15

1.24 7.240 3

18

y

x

9

distance (m)

0 time, T (s)

8 14 t

16

41.2

49.392


MATHEMATICS16 August 2010

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2010 vs Em4 Prelim2 p1