jabatan pelajaran negeri sabah filesulit 1449/2 1449/2 [lihat sebelah sulit 4 shapes and space 1...

SULIT 1449/1

1449/1 [Lihat sebelahSULIT

SULIT

1449/2MATHEMATICS

PAPER 2

AUGUST 20082 HOURS 30 MINUTES

JABATAN PELAJARAN NEGERI SABAH

SIJIL PELAJARAN MALAYSIA TAHUN 2008

EXCEL 2

________________________________________________________________________

MATHEMATICS (MATEMATIK)

PAPER 2 (KERTAS 2)

TWO HOURS THIRTY MINUTES (DUA JAM LIMA TIGA PULUH MINIT)

________________________________________________________________________

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Tulis nombor kad pengenalan dan angka giliran anda pada ruangan yang disediakan.2. Kertas soalan ini adalah Bahasa Ingerís.3. Calon dikehendaki membaca maklumat di halaman 2.

________________________________________________________________________This question paper consists of 27 printed pages.

(Kertas soalan ini terdiri daripada 27 halaman bercetak.)

NAMA : _____________________KELAS : _____________________NO K.P : _____________________A. GILIRAN : _____________________

TheMind's Q'Bank - A non-profit community initiative by TheMind Association www.themindassociation.org

TheMind's Q'Bank Note - The Intellectual Property of the question set lies with its original copyright owner.Use the document as a complete set and do not ammend any pages.

SULIT 1449/2


2

INFORMATION FOR CANDIDATES

1. This question paper consists of two sections : Section A and Section B..2. Answer all questions in Section A and four questions from Section B.

3. Write your answers clearly in the space provided in the question paper.

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

5. If you wish to change your answer, neatly cross out the answer that you have done. Thenwrite down the new answer.

.6. The diagram in the questions provided are not drawn to scale unless stated.

7. The marks allocated for each question and sub-part of a question are shown in brackets.

8. A list of formulae is provided on pages 3 to 4.

9. A booklet of four-figure mathematical tables is provided.

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

11. This question paper must be handed in at the end of the examination.

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

RELATIONS



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3

1 nmnm aaa

2 nmnm aaa

3 mnnm aa )(

4

ac

bd

bcadA

11

5)(

)()(

Sn

AnAP

6 )(1)'( APAP

7 Distance = 221

221 )()( yyxx

8 Midpoint,

2,

2),( 2121 yyxx

yx

9 Average speed =distance travelled

time taken

10 Mean =sum of data

number of data

11 Mean =sum of (class mark frequency)

sum of frequencies

12 Pythagoras Theorem222 bac

1312

12

xx

yym

14 m =intercept

intercept

y

x



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SHAPES AND SPACE

1 Area of trapezium =1

sum of parallel sides height2

2 Circumference of circle = 2d r

3 Area of circle = 2r

4 Curved surface area of cylinder = 2 rh

5 Surface area of sphere = 24 r

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = 2r h

8 Volume of cone = 21

3r h

9 Volume of sphere = 34

3r

10 Volume of right pyramid = 3

1base area height

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

120

arc length angle subtended at centre

circumference of circle 360

130

area of sector angle subtended at centre

area of circle 360

14 Scale factor,PA

PAk

'

15 Area of image = 2k area of object



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SECTION A(52 MARKS)

Answer all questions in this section.

1. The Venn diagram in the answer space shows sets X, Y and Z such that the universal set,.X Y Z

On the diagrams in the answer space, shade(a) the set Y Z (b) the set ( ) .X Y Z

[3 marks]

Answer:(a)

(b)



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2. By using factorization, solve the quadratic equation5 2

3n

nn

.

[4 marks]Answer:

3. Calculate the value of x and the value of y which satisfy the following simultaneousequations.

x – 2 y = 141

23

x y

[4 marks]

Answer:



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4. Diagram 1 shows a right prism with a horizontal rectangular base PQRS. PQVU is auniform cross-section of the prism.

Diagram 1

Calculate the angle between the plane TQR and the plane PQRS.[3 marks]

Answer:



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5. In diagram 2, PQ and SR are parallel lines. The equation of the straight line QRis 3y = x + 9.

Diagram 2Find(a) the value of t,(b) the equation of the straight line RS.(c) the y-intercept of RS.

[5 marks]

Answer:(a)

(b)

Q(-3,2)

R(6, t)

x

y

P

-4 S



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(c)

6. Diagram 3 shows two sectors OTS and ORQ with centre O. It is given that OQ = 21 cm andOT = 14 cm.

Diagram 3

By using22

7 , calculate

(a) the perimeter of the whole diagram,(b) the area, in cm2, of the shaded region.

[6 marks]

Answer :

(a)



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(b)

7. (a) Combine the following statements with the word “and” or “or” to form a truestatement.

I : 3 is an odd number.II : 14 ( 2) 7

(b) Complete the conclusion in the following argument.Premise 1 : If is less than 180o , then sin is positive.

Premise 2 : is 135o.

Conclusion : ………………………………………………………..

(c) Identify the antecedent and the consequent of the implication below:

“If 090 , then andA B A B are complementary angles.”

[5 marks]

Answer:

(a) …………………………………………………………………………................

……………………………………………………………………………………

(b) Conclusion : ……. ………………………………………………………..

………………………………………………………………



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(c) Antecedent : ………………………………………………………………

Consequent : ………………………………………………………………

8. The matrix G =1 3

.2 4

(a) Given that the inverse matrix of G is41

2 12

n

mn

, find the value of m and of n.

(b) Hence, using matrices, calculate the value of p and of q that satisfy the followingequation.

G6

2

p

q

[7 marks]

Answer:

(a)

(b)



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9. Diagram 4 shows 10 labeled cards in two boxes.

Box P

Box Q

Diagram 4

A card is picked at random from each of the boxes.By listing the outcomes, find the probability that(a) both cards are labeled with a number,(b) one card is labeled with a number and the other card is labeled with a consonant.

[5 marks]

Answer:

(a)

A 4 B F

G 8 I 9 J K



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(b)

10. Diagram 5 shows the speed-time graph of a particle for a period of t seconds.

Speed (ms-1)

22

10

0 4 16 t Time (s)

Diagram 5

(a) State the length of time, in s, when the particle moves with uniform speed.(b) Calculate the rate of change of speed, in ms-2, in the first 4 seconds.(c) Calculate the value of t , if the total distance travelled in t seconds is 306 m.

[6 marks]Answer:(a)

(b)

3



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(c)

11. Diagram 6 shows a solid cylinder with hemisphere PQR removed form one end. Both thecylinder and the hemisphere have the same radius of 3 cm.

Diagram 6

Using22

7 , calculate the length, t cm, of the cylinder if the volume of the

remaining solid is6

2827

cm3.

[4 marks]

Answer:



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1449/2

15

Section B[48 marks]

Answer any four questions from this section.

12 Diagram 7 shows quadrilateral JIGH, EFGH and ABCD drawn on aCartesian plane.

12 (a) M is a translation

2

3

coordinates of the image

(i) MN(ii) NM

(b) EFGH is the image of J

2

4

6

8

10

y

x0

-2

2 4 6 8-2-4-6

A B

C

D

E F

G

H J

I


TheMind's Q'Bank Note - The Intellectual Property of the question set lies w

[Lihat sebelahSULIT

. N is a reflection in the line x = 3. State the

of point H under each transformation below:

[ 4 marks]IGH under a transformation U. ABCD is the

Diagram 7

ith its original copyright owner.Use the document as a complete set and do not ammend any pages.

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image of EFGH under a transformation V. Describe in full

(i) the transformation U(ii) the transformation V

[ 5 marks]

(c) Given that the area of ABCD is 336 unit2, calculate the area, in unit2.of JIGH.

Answer :(a) (i)

(ii)

(b) (i)

(ii)

U :

V :

(c)



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13 (a) Complete Table 1 in the answer space for the equation

754 2 xxy by writing down the values of y when x = –1 and

x = 2.5.

[ 2 marks](b) For this part of the question, use the graph paper provided on page

18. You may use a flexible curve rule.By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on

the y-axis, draw the graph of 754 2 xxy for .35.2 x

[ 4 marks]

(c) From your graph, find(i) the value of y when x = -1.5,(ii) the value of x when y = 22.

[ 2 marks]

(d) Draw a suitable straight line on your graph to find a value of x which

satisfies the equation 0224 2 xx for .35.2 xState these values of x.

[ 4 marks]Answer :

(a) x –2.5 –2 –1 0 1 2 2.5 3

y 30.5 19 -7 -8 -1 14

TABLE 1

(b) Refer graph on page 18.

(c) (i) y = ……………………………………..

(ii) x = …………………………………….

(d) x = …………………………………………….

Graph for Question 13




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14

(a) The table 2 shows the masses, in kilogram, of waste paper collected by40 students.

5 12 7 3 32 17 22 29 35 34

29 4 9 14 20 18 15 23 21 8

26 38 25 13 19 24 27 1 30 21

10 25 27 24 16 11 4 26 23 17

TABLE 2

(a) Based on the data above and by using a size class of 5, complete the tableon page 20.

[ 4 marks]

(b) Based on the table 2 in (a), find the estimated mean for the mass of wastepaper collected by each student.

[ 3 marks]

(c) For this part of the question, use the graph paper provided on page 21.

By using a scale of 2 cm to 5 kg on the x-axis and 2 cm to 1 student onthe y-axis, draw a histogram for the data.

[ 4 marks](d) Based on the histogram in (c), state one information related to the mass of

waste paper collected by the students.[ 1 mark]



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Answer :(a)

Mass (g) Frequency Midpoint

1 - 5 5 3

(b)

(c) Refer graph on page 21.

(d)



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15 You are not allowed to use graph paper to answer this question.

(a) The diagram shows two prisms joined together at the vertical plane BMQG. Thebase AFGNKB is a rectangle lying on a horizontal table. ABCDE and BKLM arethe uniform cross sections of the respective prisms. AE and BMC are verticaledges of the same length. EJID and IHCD are inclined planes. MLPQ is ahorizontal plane. ED = CD and DI is 6cm vertically above the base of the solid.

Draw to full scale, the plan of the solid. [ 3 marks]

Answer :

B

A

N

P

K

C

D

G

Q

E

I

F

L

4cm

6cm

7cm

3cm

5cm

M

H

J



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(a)



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(b) A triangular prism is joined to the solid in (a) at the horizontal plane PQML. Thecombined solid is as shown in the diagram below. LMR is the uniform crosssection of the triangular prism. RM = RL and RS is 2 cm vertically above theplane PQML.

Draw to full scale,

(i) The elevation on a vertical plane parallel to ABK as viewed from X. [4 marks]

(ii) The elevation on a vertical plane parallel to KN as viewed from Y. [5 marks]

B

A

N

P

K

C

D

G

Q

E

I

F

L

4cm

6cm

7cm

3cm

5cm

M

Y

X

R

S

H

J



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Answer :

(b)(i)

(ii)



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16 A (54oS, 5oW), B (54oS, 25oE), C and D are four points on the earth’s surface. AC is adiameter of a parallel of latitude and D is due north of A.

(a) Find the longitude of C.[ 2 marks]

(b) Calculate the shortest distance, in nautical miles, from A to C.[ 3 marks]

(c) Calculate the distance of AB, in nautical miles, measured along the commonparallel of latitude.

[ 3 marks]

(d) A plane took off from A due north at a speed of 550 knots and took 6 hours toreach D. Find the latitude of D.

[ 4 marks]Answer :

(a)

(b)

(c)



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(d)

END OF QUESTION PAPER



jabatan pelajaran negeri sabah filesulit 1449/2 1449/2 [lihat sebelah sulit 4 shapes and space 1...

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