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TIMES HIGHER EDUCATION

SOALAN ULANGKAJI SPM 2008MATHEMATIC

Paper 2Nov./Dis

2 hour 30 minutes

DO NOT OPEN UNTILL INTSRUCTED TO

1. Read the instructions carefully

2. Think thoroughly before answering any of the questions. If you need to change your answer, erase the answer properly and thoroughly before remarking the question sheet.

This question paper contains 8 printed pages and 0 non printed pages

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This question paper consists of two sections: Section A and Section B.Answer all the questions in section A and four questions in Section B.

SECTION AAnswers all the questions in this section.

( 52 marks )

1. Using factorization, solve the following quadratic equation: 3x² = 4 ( 2 + x ) - 9 ( 4 marks )

2. Calculate the values of p and q that satisfy the following simultaneous linear equations: 4p – 3q = 10 2p – 5q = 12 ( 4 marks )

3. The Venn diagrams in the answer space show sets P, Q and R. The universal set, ξ = P Q R. On the diagrams provided in the answer space, shade (a) P ∩ (Q R) ′ (b) (P Q) ∩ R ′

( 3 marks )∩ ∩

∩∩

4. (a) State whether each of the following statements is true or false. (i) 4² – 1 = 7 or 3 x 4 + 3 = 15 (ii) A square has two right angles and a square has 4 axes of symmetry.

(b) Write down two implications based on the following sentence. `` 3k² – 5 > 7 if and only if k > 1 (c) Form a general conclusion by induction, given 4 , 7 , 12, 16,……. and 4 = 1² + 3 7 = 2² + 3 12 = 3² + 3 19 = 4² + 3 …………… ( 5 marks )

Q

P

R Q

P

R

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5.

Diagram 1 shows a solid consisting of a cylinder and cone. The diameter of the base of the cylinder is 28cm. The volume of the solid is 16 632 cm³ and the height of the cylinder is 21cm.

By using П = , calculate the height, in cm , of the cone. ( 4 marks )22 7

21 cm

6.

Diagram 2 shows a cuboid with a horizontal rectangular base UVWT. Calculate the angle between the plane WUL and the plane TWLM ( 4 marks )

DIAGRAM 1

DIAGRAM 2

M L

W

VU

H

T

K

8 cm6 cm

7. Table 1 shows numbers of member in three societies from 4 Hidayah.

Table 1

(a) Two members are chosen at random from the Mathematics Society. Calculate the probability that both members are male.

(b) Two members are chosen at random from the Chemistry Society. Calculate the probability that they are from different gender. ( 5 marks )

Students/ Society Mathematics Science ChemistryBoy 10 82 4Girl 5 6 7

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9.

Diagram 3, O is the origin and the point Q lies on the x-axis. The straight line PQ is parallel to the straight line ST.Given that the equation of the straight line QT is y + x + 2 = 0 , find

(a) the gradient of PS

(b) the equation of the straight line ST and hence state its x-intercept. ( 5 marks )

DIAGRAM 3

P (0,3)

S (12,6)

T

Q (-2,0)

y

x

8. It is given that = k (a) Find the value of k .(b) Using matrices, solve the following simultaneous equations: 5x + 6y = -1 2x + 3y = -1 ( 6 marks )

( )5 62 3 ( )3 -6

-2 5 ( )1 00 1

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11.

Diagram 5 shows a semicircle HKL and HLMN is a quadrant with centre H. LMN is an arc of the circle that centred at H.Given that HL = HN = 14 cm. Using П = , calculate

(a) the perimeter , in cm, of the whole diagram

(b) the area, in cm² , of the shaded region ( 6 marks )

22 7

L

M

N

K

H DIAGRAM 5

10. Diagram 4 shows the distance-time graph for the journey of a particle for the period of 30 s.

(a) State the length of time, in seconds, during which the particle is stationary.

(b) Calculate the speed of the particle in the last 5 s.

(c) Calculate the value of d, if the average speed for the whole journey is 2 ms -1 ( 6 marks )

DIAGRAM 4

0 15 25

10

30

dDistance (m)

Time (s)

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SECTION BAnswer four questions from this section.

( 48 marks )

12.

Table 2

(a) Table 2 shows values of x and y which satisfy the equation y = x³ - 5x + 20 ( 2 marks )

x -3 -2 -1 0 1 2 3 4y 22 24 20 16 32 64

(b) For this part of the question, use the graph paper . You may use a flexible curve ruler.

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 units on the y-axis, draw the y = x³ – 5x + 20 - 3 < x < 4 ( 3 marks )

(c) From your graph, find (i) the value of y when x = - 1.5 ( 1 marks ) (ii) the value of x when y = 20 ( 2 marks )

(d) Draw a suitable line on your graph to find the value of x which satisfies the equation x³ – 15x + 10 = 0 for - 3 < x < 4. State this values of x . ( 4 marks )

13 (a) Transformation T represents a translation and R represents clockwise rotation of 90 0 about the point (1,3). State

the coordinates of point ( 3,2 ) under the transformations

(i) R (ii) TR (iii) RT ( 5 marks )

(b) Diagram 6 shows a polygon ABCD being mapped to ABPQRD under a transformation M (i) State (a) the centre of enlargement (b) the scale factor, k

DIAGRAM 6-1

3 -2( )

(ii) If the area of ABCD is 8 unit², find the area of BPQRDC ( 7 marks )

BA P

QR

-2 -1 0 1 2 3 4 5 6 7 8

1

2

3

4

5y

x

-4 -3

D C

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SOALAN ULANGKAJI SPM 2008

14. The data in Diagram 7 shows the ages, in years, of 48 participants in a mathematics competition.

18 13 12 30 21 19 17 23 23 20 18 17 22 27 14 38 28 29 34 28 37 22 26 25 18 24 21 16 27 31 24 11 21 21 29 30 27 30 27 23 22 35 25 22 14 10 18 25

DIAGRAM 7

(a) Based on the data in Diagram 7, complete the Table 3 provided in the answer space. ( 4 marks )

Age (years) Frequency Upper Boundary Cumulative frequency5 - 9 0 9.5 0

10 - 14

(b) For this part of the question, use graph paper. By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 5 participants on the y-axis, draw the ogive for the data. ( 4 marks )(c) From your ogive in (b), (i) find third quartile (ii) hence, explain briefly the meaning at the third quartile. ( 4 marks )

15. (a) Diagram 8(i) shows a solid right prism with a rectangular base, PQRS, on a horizontal table. CDPST is the uniform cross-section of the prism and BCTU is an inclined plane. Rectangle ABCD is a horizontal plane and AQ, DP, UR and TS are vertical edges.

Draw to full scale, the plan of the solid. ( 3 marks )

U

T

B

C

R

S

Q

P

A

D

6 cm

8 cm

3 cm

3 cm

7 cm

DIAGRAM 8(i)

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Accountingis muchsought afterDespite the perception that accounting is dull, many may not be aware of the wide job scopes available until after they graduate. Times Guides spoke to Madam Lee Mee Chu, Senior Lecturer from Segi College and she gives her take on where an accounting degree can lead one to.

What are the career options in the field of accountancy? Career options in the field of accountancy are not restricted to jobs relating to accountancy. Other than becoming an accountant, one can consider financial or cost or management, become a financial controller, auditor, treasurer, fund manager, tax consultant, risk management consultant. There are other job opportunities in other sectors such as human resources management and operation management among others. Therefore, the prospects in the field of accountancy, is extremely wide and there is no doubt that every organisation will need expertise in this field.

What advice would you give to prospective students who are thinking about careers in accountancy? Especially SPM students.Prospective students, who are considering an accountancy programme, should have a target in mind and a desire to achieve a certain level of success in a particular career. This will provide the prospective students the determination to work hard and to study diligently, in achieving their goals. Before pursuing the programme, the prospective students should ensure that they are able to have a good command of the English language and mathematics, especially.

What qualities do students need to succeed in the field of accountancy? Students do not need to have specialist skills to undertake a programme in the field of accountancy. As long as students have an interest in business, focus and determination to excel in their abilities, and the willingness to face and overcome challenges, the students should be able to succeed.

What is currently the most popular accounting course among Malaysian students? There are a number of degree programmes in accountancy offered by both local and foreign universities. In addition, there are also professional programmes in accountancy such as the Association of Chartered Certified Accountants, and the Chartered Institute of Management Accountants among others.

What core areas are covered by the programme?The entry route varies with entry qualification. Students who have completed their SPM will need to either take up a foundation programme or a diploma programme in business or accountancy before enrolling for a degree in or professional accountancy programme. Upon the completion of an undergraduate programme, students can continue with the postgraduate programme either in business or accountancy.

How much emphasis is placed on theoretical knowledge and practical skills? More emphasis is placed on theoretical knowledge at the lower level of studies to build the knowledge requirement before a more practical or application based approach is adopted at the higher level.

Can students complete the programme overseas or is it possible to take everything in Malaysia? Students may choose to complete the programme either overseas or complete everything in Malaysia. There are a number of 3+0 accountancy programmes offered by private colleges here in Malaysia.

Other thoughts? In considering a field, students should learn more about the programme in terms of the subjects involved, assessment basis, job opportunities, basic requirement or pre-requisites before enrolling in it. Information can be obtained through the internet, speaking to those who have completed the programme or they can seek advice from the programme consultant in the universities or colleges.

Career options after SPM

BAC.indd 3 6/11/2008 9:51:00 AM

U

T

B

C

R

S

Q

P

A

D

6 cm

3 cm

V

W

L

K

DIAGRAM 8(ii)(b)

A solid cuboid is joined to the prism in Diagram 8(i). The combined solid is as shown in Diagram 8(ii).

Draw to full scale (i) the elevation of the combined solid on a vertical plane parallel to KL as viewed from X ( 4 marks ) (ii) the elevation of the combined solid on a vertical plane parallel PSK as viewed from Y . ( 5 marks )

X

Y

16. H ( 60º S, 40º E), K ( 60º S, 30º W) , L and M are four points on the surface of the earth. HL is the diameter of the parallel of latitude 60º S. M lies due north of H.

(a) State the longitude of L

(b) Find the shortest distance, in nautical miles, from H to L measured along the surface of the earth.

(c) Calculate the distance, in nautical miles, from H to K measured along the parallel of latitude.

(d) An aeroplane took off from H and flew due north to M along the surface of the earth. Given that its average speed for the whole flight was 480 knots and the total time taken for the whole flight was 5 hours, find the latitude of M. ( 12 marks )

Accountingis muchsought afterDespite the perception that accounting is dull, many may not be aware of the wide job scopes available until after they graduate. Times Guides spoke to Madam Lee Mee Chu, Senior Lecturer from Segi College and she gives her take on where an accounting degree can lead one to.

What are the career options in the field of accountancy? Career options in the field of accountancy are not restricted to jobs relating to accountancy. Other than becoming an accountant, one can consider financial or cost or management, become a financial controller, auditor, treasurer, fund manager, tax consultant, risk management consultant. There are other job opportunities in other sectors such as human resources management and operation management among others. Therefore, the prospects in the field of accountancy, is extremely wide and there is no doubt that every organisation will need expertise in this field.

What advice would you give to prospective students who are thinking about careers in accountancy? Especially SPM students.Prospective students, who are considering an accountancy programme, should have a target in mind and a desire to achieve a certain level of success in a particular career. This will provide the prospective students the determination to work hard and to study diligently, in achieving their goals. Before pursuing the programme, the prospective students should ensure that they are able to have a good command of the English language and mathematics, especially.

What qualities do students need to succeed in the field of accountancy? Students do not need to have specialist skills to undertake a programme in the field of accountancy. As long as students have an interest in business, focus and determination to excel in their abilities, and the willingness to face and overcome challenges, the students should be able to succeed.

What is currently the most popular accounting course among Malaysian students? There are a number of degree programmes in accountancy offered by both local and foreign universities. In addition, there are also professional programmes in accountancy such as the Association of Chartered Certified Accountants, and the Chartered Institute of Management Accountants among others.

What core areas are covered by the programme?The entry route varies with entry qualification. Students who have completed their SPM will need to either take up a foundation programme or a diploma programme in business or accountancy before enrolling for a degree in or professional accountancy programme. Upon the completion of an undergraduate programme, students can continue with the postgraduate programme either in business or accountancy.

How much emphasis is placed on theoretical knowledge and practical skills? More emphasis is placed on theoretical knowledge at the lower level of studies to build the knowledge requirement before a more practical or application based approach is adopted at the higher level.

Can students complete the programme overseas or is it possible to take everything in Malaysia? Students may choose to complete the programme either overseas or complete everything in Malaysia. There are a number of 3+0 accountancy programmes offered by private colleges here in Malaysia.

Other thoughts? In considering a field, students should learn more about the programme in terms of the subjects involved, assessment basis, job opportunities, basic requirement or pre-requisites before enrolling in it. Information can be obtained through the internet, speaking to those who have completed the programme or they can seek advice from the programme consultant in the universities or colleges.

Career options after SPM

BAC.indd 3 6/11/2008 9:51:00 AM