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Mathematic

43

J A W A P A N b o l e h d i d a p a t i d

i l a m a n w e b h t t p : / / w w w

. t i m e s . m y

SOALAN ULANGKAJI SPM 2008

TOPICSPAPER 1

2004 2005 2006 2007

F

O

R

M

1-3

1

2

3

4

5

6

7

8

9

10

11

12

13

F

O

R

M

4

1

2

3

4

5

6

7

8

9

10

11

FO

R

M

5

1

2

3

4

5

6

7

8

9

10

TOTAL 40 40 40 40

Polygon 1 ,11

Transformations 1, 11

Trigonometry 1

Algebraic Expressions 1,11,111

Algebraic Formulae

Algebraic Fractions

Linear Equations 1,11

Indices

Linear Inequalities

Graph of Functions 1

Solid Geometry 1,11,111

Circles 1,11

Statistics 1,11

Standard Forms

Quadratic Expressions and Equations

Set

Mathematical Reasoning

The Straight Lines

Statistics III

Probability I

Circles III

Trigonometry II

Angles of Elevation and Depression

Lines and Plane in 3-Dimension

Number Base

Graph of Functions II

Transformations III

Matrices

Variations

Gradient and the Area under a Graph

Probability II

Bearing

The Earth as a Sphere

Plan and Elevation

7

19,10

13

20

21

19

22

23,24

25,26

-

-

-

27,28

1,2,3,4

-

30,31,32

-

33,34

-

-

8

11,12

15,16

14

5,6

28

-

40

38,39

-

35,36,37

18

17

-

6,7

9,10

-

-

21

20

22

23,24

25

-

-

-

27

1,2,3

19

29,30,31

-

32,33

26

-

8

11,12,13

15

14

4,5

28

-

39,40

36,37,38

-

34,35

16

17,18

-

7

9,10

-

19,20

21

-

22

23

24

-

-

-

25,26

1,2,3,4

-

29,30,31

-

32,33

27

34,35

8

11,12,13

15,16

14

5,6

28

-

39.40

36,37,38

-

-

17

18

-

6,7

9,10

-

19

20

21

22

23,24

25

-

-

-

26,27

1,2,3

-

29,30,31

-

32,33

-

34,35

8

11,12,13

15

14

4,5

28

-

39,40

36,37,38

-

-

16

17,18

-

Analysis Of Mathematic

(2004-2007)

http://edu.joshuatly.com http://www.joshuatly.co



SPM2008

[ 1449/1 ] [ 1449/2 ]

Mathematic


TOPICSPAPER 1

2004 2005 2006 2007

F

O

R

M

1-3

1

2

3

4

5

6

7

8

9

10

11

12

13

F

O

R

M

4

1

2

3

4

5

6

7

8

9

10

11

FO

R

M

5

1

2

3

4

5

6

7

8

9

10

TOTAL 40 40 40 40

Polygon 1 ,11

Transformations 1, 11

Trigonometry 1

Algebraic Expressions 1,11,111

Algebraic Formulae

Algebraic Fractions

Linear Equations 1,11

Indices

Linear Inequalities

Graph of Functions 1

Solid Geometry 1,11,111

Circles 1,11

Statistics 1,11

Standard Forms

Quadratic Expressions and Equations

Set

Mathematical Reasoning

The Straight Lines

Statistics III

Probability I

Circles III

Trigonometry II

Angles of Elevation and Depression

Lines and Plane in 3-Dimension

Number Base

Graph of Functions II

Transformations III

Matrices

Variations

Gradient and the Area under a Graph

Probability II

Bearing

The Earth as a Sphere

Plan and Elevation

5

2

9

7

1

4

6

14

3

12

13

8

11

10

16

15

2

3

6

7

1

8

5

14

4

12

13

11

10

9

16

15

4

5

8

3

1

6

10

14

2

13

12

11

9

7

16

15

2

11

6

3

7

5

16

4

1,12

15

9

10

8

14

13




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45



. t i m e s . m y


1449/1

TIMES HIGHER EDUCATION


MATHEMATICPaper 1

Nov./Dis

1 hour 15 minutes

DO NOT OPEN UNTILL INTSRUCTED TO

1. Answer all the questions

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 6 printed pages and 0 non printed pages




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1. Round off 3.0364 correct to three signicant gures.

A 3.036

B 3.04

C 3.03

D 3.037

2 Express 1.354 x 10 – 5

as a single number

A 0.001354

B 0.0001354

C 0.00001354D 135400

3 =

A 5 x 102

B 5 x 10-2

C 5 x 10-4

D 5 x 10-6

4. Given 5 x 8

3

+ 6 x 8

2

+ 8k = 56708, nd the value of k.

A 0

B 6

C 7

D 561

5. 110102 + 11112 =

A 100112

B 110102

C 1010012

D 1100012

6.

Diagram 1, LMNTUV is a regular hexagon. KLM and HVL

are straight lines. Find the value of x + y .

MATHEMATICS

Paper 1

1 hour 15 minutes

Answer all question

0.35

70 000

DIAGRAM 1

HU

V

N

MLK

760

x y

A 64o

B 74o

C 104o

D 106o

7.

P Q R

In diagram 2, PQR is the tangent to the circle at Q.

Find the value of y.

A 30o

B 45o

C 55o

D 75o

S

750

8.

Diagram 3, PQRSTU is a regular hexagon. H and K are

midpoints of TS and UT respectively. The value of x is

A 106.5o

B 140o

C 150.5o

D 175o

DIAGRAM 2

DIAGRAM 3

27o

x

T H S

R

QP

U

K

T

y




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10

Diagram 5, UVWM is given a clockwise rotation of 270o

about point R, the coordinates of the image of point U are

A (4,3)

B (5,6)

C (7,2)

D (8,5)

9. Diagram 4 shows seven points on a square grid. L is the

image of K under a reection.

The axis of reection is the straight line that joins P and

A Q B R C S D T

DIAGRAM 4

P

L

Q

K

R

T

S

DIAGRAM 5

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11

1

2

3

4

56

-1

-2

-3

-4

U

M

W

VR

y

x

11. It is given that cos = 0.3420 and 180º < < 360º,

nd the value of .

A 70º

B 110º

C 250ºD 290º

0 0

0

12. Diagram 6 shows the graph of y = - sin . The value of is

A 90º

B 180º

C 270º

D 360º

0 0

00

-1

1

DIAGRAM 6

13. Factorise k ( 3 + 2k ) – 35 completely

A ( 2k – 7 )( k – 5 )

B ( 2k – 7 )( k + 5 )

C ( 2k + 7 )( k – 5 )D ( 2k + 7 )( k + 5 )

14

DIAGRAM 7

Diagram 7 shows a cuboid. Name the angle between the

planes HKRT and PQKH.

A THK

B QRK

C QKR

D TRK

S T R

H K

P Q

M L




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26. Pictograph in Table 1 shows the total marks obtained by

four classes in a quiz.

15. Diagram 8, K and L are on a horizontal ground. H is 20 m

vertically above L. Find the angle of depression of K from

H.

A 38.7º

B 43º

C 50.7º

D 51.3º

DIAGRAM 8

20 m

H

K L25 m

16. Diagram 9 shows the position of points P and Q. Find the

bearing of point P from point Q

A 050º B 130º C 250º D 310º

DIAGRAM 9

230ºP

Q

North

North

17. P (37º N,76º W) and Q are two points on the earth`s surface.

PQ is the diameter of the earth. Find the location of Q .

A ( 37º S , 76º E )

B ( 143º S , 76º W )

C ( 37º S , 104º E )

D ( 143º S, 104º E )

18. H ( 50º N, 20º E) and K are two points on the surface

of the earth. K lies 3 600 nautical miles to the south of H.

The latitude of point K is

A 10º S B 60º S C 60º N D 110º S

19. ( 4k – 1 )² =

A 16k² + 8k – 1

B 16k² – 8k + 1

C 16k² – 8k – 1

D 16k² + 1

20. Given that m + = mn, express m in terms of n.

A C

B D

2

n

2

n²-1

2

1-n²

2

n²-n

2

n-n²

21. - =

A C

B D

h+3

3hk

2+3k

6k

2-hk

2hk

2+hk

2hk

hk-2

2hk

6+3hk

6hk

22. If y = 6 y -2, then y =

A C

B D

2

31

43

8

2

31

3

23. can be written as

A 3 x-7 C x7

B 3 x7 D x-7

3

x-7

2

3

2

3

24. It is given that 37

÷ 3n = 9 , nd the value of n.

A - 6 B 4 C 5 D 6

12

25. List all the integres x that satisfy the inequalities

3 < 2x – 4 ≤ 14 - x

A 4,5 B 3,4,5 C 4,5,6 D 3,4,5,6

5 Tauk * *5 Hidayah * * * *

5 Rahmah *

5 Ikhtiar * * *

* represents 25 marks

If the data in Table 1 is represented by a pie chart, nd theangle of a sector which represent the total marks obtained

by 5 Ikhtiar.

A 75 B 108 C 144 D 216

Table 1




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Score 1 2 3 4 5 6

Number

of pupils

5 8 2 20 4 6

Table 2

Table 2 shows scores obtained by a group of students in a

game. Number of pupils who get score less than the mode

score is

A 6 B 10 C 15 D 25

27

28. Diagram 10 shows the graph of the function y = x³ + 5

Find the value of k .

A 3 B 4 C 5 D 6

(1,k )

y = x³ + 5

y

x0

DIAGRAM 10

29. Diagram 11 is a Venn diagram which shows the number

of elements in set P, and set Q.

ξ

If ∩ (ξ) = 30, find ∩ ( P Q )′

A 12 B 15 C 14 D 18

∩

30. Given the universal set, ξ = K L, set K = {2,6,7} andset L = {3,5,6,7,8,9}. nd the value of ∩ (ξ).

A 2 B 3 C 7 D 9

∩

6 4 2

QP

DIAGRAM 11

31. List all the subsets of P = {h,k }

A {h},{k }B {},{h},{k }C {h},{k },{h,k }

D {},{h},{k },{h,k }

32. Find the y-intercept of the straight line 2 x + 4 y = 8

A - 4 B 2 C 4 D 8

33 Diagram 12 shows a straight line HK on a Cartesian lane.

0

12

H

-4

K

The gradient of HK is

A - 3 B - 2 C 3 D 4

24 12 33 48 52 60 19 76

DIAGRAM 13

34. Diagram 13 shows 8 cards . A card is picked at random.

State the probability that a number that is divisible by 6 is

picked.

A B C D1

2

1

4

1

8

3

8

35. A box contains of 10 blue marbles and 15 black marbles.

Two marbles are picked At random from the box. The

probability of picking two different colours of marbles is

A B C D1

41

2

2

5

3

5

36. If p α and p = 6, q = - 8 and h = 2 , nd the value of v

when p = 12 and q = 1.

A - B 6 C 15.5 D 18

1

2

√q

v

y

x

DIAGRAM 12




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37. Table 3 shows some value of the variables y , u and v

which satisfy the relationship vα u , nd the value of m.

A 10 B 20 C 25 D 30

√ y

y 9 36

u 3 12

v 5 m

Table 3

38. Diagram 14 shows two objects P and Q on a Cartesian plane. Q is the image of P under a reection.

The line of reection is

A the x-axis

B the y-axis

C x = 1

D y = x

DIAGRAM 14

-2 0 2 4 6 8

2

4

6

Q

y

x

8

P

39. It is given that (3 6) = (96), nd the value of h + k .

A - 1 B 2 C 4 D 8

( )4h

2k

40. Find the matrix P such that -2P =

A C

B D

( )1 32 -4 ( )3 -5

4 -2

( )-1 4

-1 1

( )-1 4

-1 -1 ( )-1 1

-1 -1

( )-2 8

-2 -2

END OF QUESTION PAPER




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TIMES HIGHER EDUCATION


MATHEMATICPaper 2

Nov./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 A

Answers 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 providedin 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 cm

6 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 Chemistry

Boy 10 82 4

Girl 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 , nd

(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 6

2 3 ( )3 -6

-2 5 ( )1 0

0 1






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SECTION B

Answer 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 4

y 22 24 20 16 32 64

(b) For this part of the question, use the graph paper . You may use a exible 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, nd(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 nd the value of x which satises theequation 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, nd the area of BPQRDC ( 7 marks )

BA P

QR

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

1

2

3

4

5

y

x

-4 -3

D C




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57



. t i m e s . m y


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 2322 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 frequency

5 - 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) nd third quartile(ii) hence, explain briey 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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