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3472/2 Name : ______________________ Class : 5 ( ) Additional

Mathematics SMJK PEREMPUAN CHINA PULAU PINANG

Paper 2 TRIAL EXAMINATION SPM 2010

September 2010

2

hours

ADDITIONAL MATHEMATICS

FORM 5

PAPER 2

2 Hours 30 Minutes

DO NOT OPEN THIS QUESTIONS PAPER UNTIL YOU ARE

INSTRUCTED TO DO SO

1. This question paper consists of three sections : Section A, Section B

and Section C.

2. Answer all questions in Section A, four questions from Section B and

two questions from Section C.

3. Give only one answer/ solution for each question

4. Show your working. It may help you to get marks.

5. The diagrams in the questions provided are not drawn to scale unless

stated.

6. The marks allocated for each question are shown in brackets.

7. A list of formulae is provided on pages 2 and 3.

8. The four-figure mathematical table is provided on page 4.

9. You may use a non-programmable scientific calculator.

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Section A

[ 40 marks ]

Answer all questions

1. Solve the following simultaneous equations and give your answers correct to two

decimal places.

[ 5 marks ]

2.

(a) Diagram1 shows the graph of the quadratic function cut the -axis at the

point and the point . Given the minimum point is , with as

constant.

(i) State the value of .

(ii) Determine the equation of the curve. [ 3 marks ]

(b) Find the range of value p so that the straight line

intersect the curve

at two different points. [ 4 marks ]

3.

Diagram 2 shows a 10cm yoyo is being dropped by a boy. It rebounds to a height of

5cm , 2.5cm and so on as shown in the diagram. Find

(a) The distance of the yoyo from the finger on the 5th bounce. [ 4 marks ]

(b) The distance covered by the yoyo vertically before it stops bouncing.

[ 2 marks ]

Diagram 1

Diagram 2

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4. (a) Prove that . [ 2 marks ]

(b) (i) Sketch the graph of

for .

(ii) Hence, using the same axes, draw a suitable straight line to find the number of

solutions to the equations

– for

[ 6 marks ]

5.

The histogram in Diagram 3 represents the distribution of the time taken by a group of

40 students to travel to school.

(a) Without using an ogive, calculate the median of the times taken. [ 3 marks ]

(b) Calculate the variance of the distribution. [ 4 marks ]

6. Relative to an origin O, the position vector of point and are

and

respectively. Find

(a) The length of [ 2 marks ]

(b) The length of [ 2 marks ]

Given that is a straight line and that the length of is equal to the length of , find

(c) The position vector of the point [ 3 marks ]

Diagram 3

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Section B

[ 40 marks ]

Answer any four questions from this section.

7. The following table shows some of the experiment values of variables x and y.

1.6 2.1 2.5 4.6 5.0 6.0

5.01 0.83 0.51 0.16 0.14 0.11

(a) Plot the graph of

againts and draw a line of best fit using a scale of 2cm

to 1 unit on the x-axis and 2cm to 2 units on the y-axis. [ 5 marks ]

(b) Using the graph obtained in (a),

(i) Find the value of when

(ii) Find the gradient and the

-intercept for the graph and hence, express

in terms of [ 4 marks ]

(c) Calculate the value of when . [ 1 marks ]

8.

(a) Diagram shows a hemispherical bowl of radius cm. The height of the water in the

container is cm from the base , with is the centre of the hemisphere. When

water is flow out from , the water level decrease at the rate of .

(i) Show that the area, , of the water surface in the bowl is given by

(ii) Find the rate of change of in the area of the water surface when cm.

[ 5 marks ]

(b)

Diagram 5 shows the shaded region between the curves and and the

lines and .Find the volume generated, in terms of , when the shaded

region is revolved about the -axis. [ 5 marks ]

Diagram 4

Diagram 5

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9.

In Diagram 6 , the straight line intersect the -axis and the -axis at

points and respectively. is a point that lies on the . Find

(a) the coordinates of points and [ 2 marks ]

(b) the equation of the straight line such that is perpendicular to

[ 3 marks ]

(c) the area of triangle . [ 3 marks ]

(d) the equation of the locus of point which moves in such a way that its distance

from point is always 5 units. [ 2 marks ]

10.

Diagram 7 shows a circle, with centre and radius is an arc of a

circle with centre . Given is parallel to and .

(a) Calculate the perimeter of the segment in term of π. [ 5 marks ]

(b) Show that the area of the shaded region is

[ 5 marks ]

11. (a) The Mathematics test marks of the students in a matriculation centre are normally

distributed with a mean of 55marks and standard deviation of 10marks. There are 500

students from the matriculation centre sat for the Mathematics test.

(i) If the passing mark for the test is 35. Find the probability that a student chosen at

random pass the test.

(ii) Find the number of students who pass the test if the passing mark is 35.

(iii) If 13% of the students pass the test with gred A, find the minimum mark for

obtained gred A in the test. [ 7 marks ]

Diagram 7

Diagram 6

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(b) In a shooting practice, the probability of Azmi hitting the target is 0.75. Find the

minimum number of shots required in order that the probability of hitting the target at

least 1 times is more than 0.92. [ 3 marks ]

Section C

[20 marks ]

Answer any two question form this section.

12. A particle moves in a straight line, starting form a fixed point O. Its velocity , ,

is given by , where is the time in seconds after it starts to move from O.

(a) Find the displacement from O when it reverse its direction of motion.

[ 4 marks ]

(b) Find the maximum velocity of the particle.

[ 3 marks ]

(c) Find the acceleration when it comes to rest for an instant.

[ 3 marks ]

(Assume the motion to the right is positive.)

13. Diagram 8 shows a pyramid with a right-angled triangle base lying on horizontal

ground. represents a tree with a height of m standing vertically at . Calculate

(a) The values of and [ 3 marks ]

(b) The length of and [ 3 marks ]

(c) The value of [ 2 marks ]

(d) The area of triangle [ 2 marks ]

Diagram 8

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14. Rosli bought packets of normal rice which costs RM40 a packet and packets of

fragrant rice which costs RM80 a packet. Rosli orders packets of normal rice and

packets of fragrant rice subject to the following conditions:

I : Rosli had only RM 16 000 to purchase the rice.

II : The number of packets of normal rice bought must be at least two times the number

of packets of fragrant rice bought.

III : Rosli sold a packet of normal rice at RM 56 and a packet of fragrant rice at RM 120.

After all the rice is sold, Rosli made a profit of at least RM 4 000.

(a) Write three inequalities, other than and , which satisfy the above

constraints. [ 3

marks ]

(b) Using a scale of 2cm to 50 packets on the -axis and 2cm to 20 packets on the –

axis, draw the graph for the three inequalities. Hence, shade the region R which

satisfies the above constraints. [ 3 marks ]

(c) Based on your graph , find

(i) The maximum and the minimum profit made by Rosli if 50 packets of

fragrant rice were sold.

(ii) The number of packets of normal rice and fragrant rice that must sold so

that the profit made is maximum. [ 4 marks ]

15.

(a) Using 1994 as the base year, the price indices of an article in 1999 and 2002 are 115

and 108 respectively. Show that the price of the article decrease by 6.1% from 1999

to 2002. [ 4 marks ]

(b)

Table shows the price indices and weightage of four items in 1998 based on 1995

(i) Find the composite price index in 1998 using 1995 as the base year.

[3 marks ]

(ii) If the composite price index increase at the same rate from 1998 to 2001 as

from 1995 to 1998, find the composite price index in 2001 using 1998 as

the base year. [ 3 marks ]

Prepared by: Checked by : Certified by :

OGL .

Item Price Index Weightage

A 125 2

B 110 1

C 120 4

D 105 3