2011 midyear form5 paper2 math

8/6/2019 2011 Midyear Form5 Paper2 Math

1/15

SMK TAMAN BUKIT INDAHPEPERIKSAAN PERTENGAHUN TAHUN 2011

TINGKATAN 5

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Tuliskan nama dan tingkatan pada ruang yang disediakan.2. Kertas soalan ini mengandungi dua bahagian : Bahagian A

dan Bahagian B. Jawab semua soalan daripada Bahagian A

dan empat soalan dalam Bahagian B.

3. Tulis jawapan anda dengan jelas pada ruang yang disediakandalam kertas soalan. Tunjukkan kerja mengira anda. Ini

boleh membantu anda untuk mendapatkan markah.

4. Rajah yang mengiringi soalan tidak dilukis mengikut skalakecuali dinyatakan.

5. Markah yang diperuntukkan bagi setiap soalan dan ceraiansoalan ditunjukkan dalam kurungan.

6. Satu senarai rumus disediakan .7. Anda dibenarkan menggunakan kalkulator saintifik yang

tidak boleh diprogram.

Kertas soalan ini mengandungi 17 halaman bercetak

MATHEMATICS

Kertas 2

Dua jam tiga puluh minit

Untuk Kegunaan Pemeriksa

Bahagian SoalanMarkah

Penuh

Markah

Diperoleh

A

1 4

2 4

3 4

4 3

5 5

6 6

7 5

8 4

9 6

10 6

11 5

B

12 12

13 12

14 12

15 12

16 12

Jumlah

1449/2

Mathematics

Kertas 2

Mei 2011

2

12 jam

1449/2[Lihat sebelah

SULIT

NAMA :

TINGKATAN : 5


2/15

SULIT

[Lihat sebelah

1449/2 SULIT

2

UntukKegunaanPemeriksa


3/15

SULIT

1449/2 SULIT3

Untuk

KegunaanPemeriksa


4/15

SUL T

Li l

/ SUL T

4

Unt

K

naanPemeri

aSE T[52marks]

Answerall questi ns in t

is secti n

Solv t followi quadrati equation:

h2

= 9( h 1)

2Answer: [4 marks]

2 Cal ulate the value of v danwthat satisfy the following si ultaneous linear equations

2 1v w !

4 3 18v w !

[4 marks]

Answer:

3 Venn Diagram in diagram 1(a) and 1(b) shows set\,P,Q danR . In diagram provided in

the answer space, shade

(a) )( d RQP (b) )( RQP d

Answer:

(a) (b)

[4 marks]

R

QP

\

R

QP

Diagram 1(a) Diagram 1(b)


5/15

SULIT

1449/2 SULIT5

Untuk

KegunaanPemeriksa

4. Diagram 2 shows a right prism. The base ABCD is a horizontal rectangle. Trapezium ABGF is

the uniform cross-section of the prism.

(a)On the diagram 2, mark the angle between the plane BCHG and the base ABCD.(b)Hence, calculate the angle angle between the plane BCHG and the base ABCD.

[3 marks]

Answer :(b)

5. In Diagram 3, PQRS is a parallelogram. O is the origin and R lies on the x-axis. Gi en that PS

= 4 units and the gradient SR= , find

a) the coordinates of the point Rb) the equation of the straight line PQ

[5 marks]

Answer : (a)

(b)

Diagram 3

Diagram 2


6/15

SULIT

[Lihat sebelah

1449/2 SULIT

6

UntukKegunaanPemeriksa

6 (a) Gi en that matrix M = and MN = . Find matrix N.(b) Write the following simultaneous linear equations as matrix equation :

u + 2 = 8

3u = 3

Hence, using matrix method, calculate the alue of u and of . [6 marks]

Answer :(a)

(b)

.

7. (a) Complete the box in the answer space with and / or

(i) This statement is TRUE.

(ii) This statement is FALSE.

(b) (i) Complete the conclusion in the following argument:

Premise 1: All factors of 6 are factors of 24.

Premise 2: 3 is a factor of 6.

Conclusion:.

(ii) Make a general conclusion by induction for the following sequence

..

[5marks]

Answer :

(a) (i)

(ii)


7/15

SUL T

1449/2 SUL T7

Untuk

Kegunaan

Pemeriksa

(b) (i) Conclusion:______________________________________________________

(ii) Conclusion: ______________________________________________________

____________________________________________________

8. The diagram 4 shows a solid formed byjoining a cylinder with a hemisphere. The heightof

the cylinderis 7cm while the diameterofthe cone and the hemisphere is 6 cm.

Using7

22!T , calculate the volume,in cm

3 ,ofthe solid. [4 marks]

Answer:

9. Diagram 5 shows quadrant OPQ and sector ORS,with common centre 0. OQRis a straight

line.

Using7

22!T and give answers correcttotwo decimal places. Calculate

(a) the perimeter,in cm,ofthe whole diagram,(b) the area,in cm2,ofthe whole diagram.

[6 marks]

Diagram 5

Diagram 4

R

QS

O P

60O14cm

7 cm


8/15

SULIT

[Lihat sebelah

1449/2 SULIT

8

UntukKegunaanPemeriksaAnswer

a)

b)

10 (a) On the graph in the answer space, shade the region which satisfy the three inequalities

y x, x 2 andy < 5

(b) State three inequalities which satisfy the shaded region below.

[6marks]

Answer :

(a)

b)


9/15

SULIT

1449/2 SULIT9

Untuk

KegunaanPemeriksa

11 (a) Diagram 6 shows thirteen labeled cards which are placed in a box .

A card is chosen at random from a box. By listing the possible outcomes of the e ent , find the

probability that(i) the card labeled with owel are chosen.(ii) the card labeled with R is chosen.

(b) Table 1 shows the marks scored by 140 students in a Mathematics tests.

A students is selected at random from the group. Find the probability that the mark is :

(i) in the class inter al 61 65

(ii) less than 61 marks.

[5 marks]

Answer :

(a) (i)

(ii)

(b) (i)

(ii)

Marks Number of Students

51-55 11

56-60 45

61-65 67

66-70 17

Diagram 6

Table 1


10/15

SUL T

[Li at sebelah

1449/2 SUL T

10

Untuk

KegunaanPemeriksa

Table 1

Table 2

Sectio B

[48 marks]

Answerfo questi nsfrom t

is section.

12 (a) Complete Table 2inthe answer space fothe equation 4y

!

[2marks]

Fort

is partoft

e question, use t

e graph paper provi

ed on page 11. You may use a

flexi

le curve rule.

(b)By using a scale of2 cm to 1 unitonthe x-axis and 2 cm kepada 2 unit onthe-yaxis,drawthe graph

4y

x! for 4 4x e e .

[4 marks]

( c ) From yourgraph, find

( i) the value ofywhenx = 1.8

(ii) the value ofxwhen y = 3.4

[2marks]

(d) Draw a suitable straightline on yourgraph to find allthe value of x which satisfy the

equation 3x 2x2

= 4 for 4 4x e e . State these values of x.

[4 marks]

Answer:

(a)x 4 2.5 1 -0.5 0.5 1 2 3.2 4

y 1 1.6 8 -8 -4 -1.25 -1

(b) Refergraph on page 11.

(c) ( i ) y = ____________________

( ii) x =_____________________

(c)x = _______________________,_______________________

x 4 2.5 1 -0.5 0.5 1 2 3.2 4

y 1 1.6 8 -8 -4 -1.25 -1

Table 2


11/15


12/15

SUL T

[Lihat sebelah

1449/2 SUL T

12

Untuk

KegunaanPemeriksa(ii)

(c) (i)

(ii)

14 The data in diagram 8 shows the donations,inRM,of families totheir childrens school

welfared fund.

40 24 17 30 22 26 35 19

23 28 33 33 39 34 39 28

27 35 45 21 38 22 27 35

30 34 31 37 40 32 14 28

20 32 29 26 32 22 38 44

(a) Using data in diagram 8 and a class intervalof RM 5 , complete the table 3 in theanswer space. [5marks]

(b) Forthis partofthe questions, use the graph paper providedon page 15.

By using a scale of2 cm toRM5onthex- axis and 2 cm to5 families onthe y-axis,

draw anogive based onthe data. [4 marks]

( c ) From yourogive in (b)

( i ) Find the third quartile

(ii ) hence, explain briefly the meaningofthe third quartile. [3 marks]

Answer:

(a)

Donations (RM) Frequency Cumulative

frequency

11 - 15

16 20

Table 3

Diagram 8


13/15

SUL T

1449/2 SUL T13

Untuk

Kegunaan

Pemeriksa

(b) Refergraph on page 15.

( c )

(i)

(ii)

15. Diagram 9 shows the number of tickets sold by a group of 32 students in a fund raising

project.

51 45 73 56 98 68 75 79

62 53 80 78 58 89 71 36

76 48 65 54 60 76 55 84

84 34 71 85 70 65 42 75

(a) Based onthe data in Diagram 9, complete Table 4 inthe answer space.[5 marks]

(b) Calculate the estimated mean forthe numberoftickets sold by the group of students. [3 marks]

(c) Forthis partofthe question, use the graph paper provided on page 16.By usingthe scale of2 cm to 10 tickets onthe hori ontal axis and 2 cm to 1 studentonthe vertical axis, draw a frequency polygon forthe data. [4 marks]

Answer:(a)

Class Interval Frequency Midpoint

21-30 0 25.5

31-40

101-110 0 105.5

(b)

(c) Refergraph on page 16.

Diagram 9

Table 4


14/15

SUL T

[Lihat sebelah

1449/2 SUL T

14

Untuk

KegunaanPemeriksa16. (a) Diagram below shows a right prism solid with rectangular baseABCD on a hori ontal

plane.ABGFEis the uniform cross sectionofthe prism. RectanglesFGHJandEFJKare

inclined planes. GiventhatGF=FE.JFis 4 cm above the base ofABCD.

Drawto full scale,the elevationofthe solid on a vertical plane paralleltoAB as viewed

from X. [3 marks]

(b) A solid semi cylinderisjoined tothe prism atthe vertical planeADKE. The combinedsolid is as shownin diagram below. The heightofthe semi cylinderis 7 cm.

Drawto full scale,

(i) the planofthe combined solid, [4 marks](ii) the elevationofthe combined solid on a vertical plane paralleltoBCas viewed from Y.[5 marks]

D

6 cm

5 cm

4 cm

H J

K

E

FG

C

B

A

X

D

6 cm

5 cm

4 cm

H J

K

E

FG

C

B

A

Y


15/15

SUL T

1449/2 SUL T15

Untuk

Kegunaan

Pemeriksa

Answer:

(a)

(b) (i)

(ii)

Prepared by Certified by

NORA BINTI ABDUL JALIL CIK LOI LAI FONG

Head ofMathematics Panel

2011 midyear form5 paper2 math

Documents