UJIAN_PENGESANAN__AHKIR_TAHUN_PAPER_2[1].pdf

8/18/2019 UJIAN_PENGESANAN__AHKIR_TAHUN_PAPER_2[1].pdf

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1449/2©2008 HakCipta JPM [Lihat sebelah

UJIAN PENGESANAN PERTENGAHAN TAHUNSIJIL PELAJARAN MALAYSIA 2008

This question paper consist of 17 printed paper

MATHEMATICS

Paper 2Two hour and thirty minutes

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU

ARE TOLD TO DO SO

1. This question paper consist of two section: Section A and SectionB. Answer all question in Section A and Section B.

2. This question paper is bilingual.

3. Write your answers in the spaces provided in the question paper.

4. Working step must be written clearly.

5. Diagrams given are not according to scale unless stated.

6. Marks for each question are given in bracket.

7. A list of formulae is given in pages 2 and 3.

8. Non programmable scientific calculator are allowed.

9 This question paper must be hand up at the end of the exam.

Section Question Full

Marks

Mark

Obtain1 3

2 4

3 4

4 4

5 5

6 5

7 4

8 6

9 6

10 5

A

11 6

12 12

13 12

14 12B

15 12

Total

1449/2

Mathematics

Paper 2

NOV

2008

JABATAN PELAJARAN MELAKA

Name :……………………………………….

Form :………………………………………..

http://sahatmozac.blogspot.com

http: mathsmozac blogspot com


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MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols given are the

ones commonly used..

RELATIONS1 nmnm aaa

2 nmnm aaa

3 mnnm

aa )(

4

ac

bd

bcad A

11

5 S n An

A P )(

)(

6 )(1)'( A P A P

7 2122

12 )()(Distance y y x x

8 Midpoint ,

2,

2),( 2121

y y x x y x

9 Average speed =takentime

travelleddistance

10 Mean =dataf umber

dataof sum

11 Meansfrequencieof sum

frequency)mark of(classsum

12 Pythagoras Theorem222

bac

1312

12

x x

y ym

14erceptint

erceptint

x

ym




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3

SHAPES AND SPACE

1 Area of trapezium = 1

sum of parallel sides height

2 Circumference of circle = r d 2

3 Area of circle = 2r

4 Curved surface area of cylinder = rh 2

5 Surface area of sphere = 24 r

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = h j 2

8 Volume of cone = hr 21

9 Volume of sphere = 3

3

4r

10 Volume of right pyramid = 1

base area height

11 Sum of interior angles of a polygon = (n – 2) 180º

12o

360

center atsubtendedangle

circleof ncecircumfere

lengtharc

13o

60

centreatsubtendedangle

circleof area

sector of area

14 Scale factor, k = PA

PA'

15 Area of image = k 2 area of object




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Bahagian A[52 markah]

Answer all questions in this section.

1 The Venn diagram in the answer space shows sets P , Q and R such that the

universal set, = P Q R. On the diagrams in the answer space, shade

(a) the set P' R' ,

(b) the set ( P Q ) R.[ 3 marks ]

Answer:

(a)

(b)

Q

P

R

Q

P

R




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2. Diagram 1 shows a cuboid with a horizontal base ABCD. E , F, G, H are the

midpoints of AD , JM , KL and BC respectively .

.

Identify and calculate the angle between the plane KLE and the plane ABCD.

[ 4 marks ]

Answer:

DIAGRAM 1

K

C

B A

L M

D

J

10 cm

2 cm

5 cm

•H

••

•

G

E

F




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3 Solve the quadratic equation 9 x ( x – 3) = –21 x + 15 [4 marks].

Answer:

4 Calculate the values of x and y that satisfy the following simultaneous linear

equations:

x − 3 y = 9

4 x − y = 6

[ 4 marks]

Answer:




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5 Diagram I shows a cylindrical solid of height h cm with a base radius of 7 cm. A

conical cavity PQR of the same height is hollowed out. The volume of the remaining

solid is 2772 cm3.

Calculate the height, in cm of the solid.

7

22 Use [ 5 marks ]

Answer:

Q

P R

Diagram I




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6 (a) State whether the following statement is true or false ?

‘ k – 3k = 2k or 6482 ’

(b) Write down two implications based on the following sentence :.“m + 3 = 10 if and only if m = 7”

(c) 1 = 2(1)2 – 1

7 = 2(2)2

– 1

17 = 2(3)2

– 1

.

.

Based on the information above, make a general conclusion by induction

[5 marks]

Answer :

(a) ……………….………………………………………………………….

(b) Implication 1 :

……………………………………………………………

Implication 2 :

………………………………………………………….

(c) ……………………………………..……………………………………

……………….…………………………………………………………

7 A box contains 4 red balls,6 black balls and 2 yellow balls.

(a) If a ball is picked at random from the box, state the probability that it is red incolour.

(b) The ball that was picked is returned into the box and 4 black balls are added intothe box. If a ball is picked at random from the box, state the probability that it is

black in colour [ 4 marks]

Answer :

(a)




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(b)

8. Diagram 3 shows two sectors, PQR and TUV , with the same centre O. The angle of

each sector is 270

. OSR is a semicircle with centre V . PTO is a straight line and

OP = 14 cm.

Diagram 3

Using =7

22, calculate

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

(b) the area, in cm2

, of the shaded region.

[ 6 marks ]

Answer:

(a)

(b)




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9 Table 1 shows the ages 200 of participants in the charity run.

Age (year) Frequency Midpoint

15 – 19 25

20 – 24 3725 - 29 58

30 – 34 32

35 – 39 20

40 – 44 17

45 - 50 11

Table 1

(a) State the class size and modal class based on the grouped data in table1.[2 marks]

(b) Complete the table 1 and find the mean age of the participants.[4 marks]

Answer :

(a) Class size = ……………………………….

Modal class = ……………………………….

(b)

Age (year) Frequency Midpoint

15 – 19 25

20 – 24 37

25 - 29 58

30 – 34 32

35 – 39 20

40 – 44 17

45 - 50 11

Mean age = …………………………………..




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10

DIAGRAM 4

In Diagram 4, straight line QP is parallel to RT. QR is parallel to x-axis . P and S is

located on the x-axis. Gradient of QP is -3.

Calculate

(a) the value of c

(b) the RT equation’s

(c) x - intercept of RT

[ 5 mark ]

Answer :

(a)

(b)

(c)

R ( 2, -3 )

O

Q ( −6, c)

SP

T

x

y




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11. (a) The diagram 1 shows two vertical poles, DE and FSH

SD

E F

H

The angle of depression of peak D from peak H is 550. The length of

EF is 13 m and the height of DE is 7 m. Calculate the height in m, of

the pole of FSH.

[ 3 marks ](b)

F

A

B

E

C

D

The diagram shows a prism with horizontal base ABCD. Given thatAB = 6 ,BC = 8 and AF = 5. Calculate the angle between line FC and

the plane ABCD.

[ 3 marks ]

Answer : ( a )

( b )




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Section B[48 marks]

Answer all questions from this section.

12 (a) Given that sin = sin 59° and 90 360, find the value of .

(b) Given that x is an angle in quadrant III and sin x = -0.2924, find

the value of tan x correct to two decimal places.

In the diagram above, ABC is a straight line. Calculate the

(i) length of AD,

(ii) value of cos y .

(d) Given that x = sin 270°, y = cos 240° and z = tan 360°, find the

value of

(i) y x z ,(ii) z y x,(iii) x ( y + z ),(iv) z x + y z . ( 12 marks)

Answer :

(a)

(b)




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(c) ( i )

( ii )

(d) ( i )

( ii )

( iii )

( iv )




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13. (a) Given the universal set ξ = W X Y. WhereSet W = {a, b, c }

Set Y = {c, d, e, f, g}

Set X = {g}I. In the Venn diagram below, fill in set W, set Y and Set X

II. List all the elements of (W X) III. Find n( X ∩ Y )

(b) Given that the universal set ξ = {x: 20≤ x ≤ 50}

Set K = { x: x is multiple of 5}

Set L = { x: x is prime number}

Set H = { x: x is greater that 30}

I. Write down all the elements of set K and set L

II. Write down the elements of (K L) ∩ H

III. Find n(L∩H)

Answer:(a) I

W Y

X

II ………………………………………………………………….

III ………………………………………………………………….

(b) I …………………………………………………………………….

II …………………………………………………………………….

III. …………………………………………………………………….




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14 Table 2 shows the distribution of the weight of 40 students in a class.

TABLE 2

(a) State the modal class for the data in the Table 2 [1 mark]

(b) (i) Construct a cumulative frequency table for the data in Table 2[3 marks]

(ii) Using the scale of 2cm to 5cm on the x-axis and 2cm to 5 students to

y-axis, draw an ogive for the data.

[5 marks]

(c) From the graph, find

(i) median(ii) interquartile range

[3 marks]

Answer :

(a)

(b)

(c) (i)

(ii)

Weight ( kg ) Frequency

35 – 39 2

40 – 44 545 – 49 850 – 54 10

55 – 59 7

60 – 64 465 – 69 3

70 – 74 1

Weight ( kg ) Frequency Upper Boundary CumulativeFrequency

35 – 39 240 – 44 5

45 – 49 850 – 54 10

55 – 59 7

60 – 64 465 – 69 3

70 – 74 1




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15 ( a ) Find the equation of the straight line that passes through the point ( 2, -5 ) andis parallel to y = 4 – 3x.

[2 marks]

( b ) In the diagram above, the gradient of the straight line AB is 2. Find

( i ) the value of h, [1 marks]

( ii ) the x-intercept of the straight line AB, [2 marks]

( iii ) the gradient of BC, [1 marks]

( iv ) the y-intercept of the straight line of BC. [2 marks]

(c) If M is the midpoint of AC, find the equation of the straight line BM. Hence,state its y-intercept.

[4 marks]

Answer :

(a)

(b) (i)

(ii)

B ( 1, h )

A( 0 , 2 )

x




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(iii)

(iv)

(c)


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UJIAN_PENGESANAN__AHKIR_TAHUN_PAPER_2[1].pdf