question midyear k2 08

8/6/2019 Question Midyear k2 08

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SEKTOR SEKOLAH BERASRAMA PENUH

BAHAGIAN SEKOLAH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERTENGAHAN TAHUN

TINGKATAN LIMA 2008

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian SoalanMarkah

Penuh

Markah

Diperoleh

A

1 3

2 4

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi dua bahagian :Bahagian A dan Bahagian B. Jawab semua

soalan daripada Bahagian A dan empat soalandalam Bahagian B.

2.Jawapan hendaklah ditulis dengan jelas dalam

ruang yang disediakan dalam kertas soalan.Tunjukkan langkah-langkah penting. Ini boleh

membantu anda untuk mendapatkan markah.

3.Rajah yang mengiringi soalan tidak dilukismengikut skala kecuali dinyatakan.

4.Satu senarai rumus disediakan di halaman

2 & 3.

5.Anda dibenarkan menggunakan kalkulatorsaintifik yang tidak boleh diprogram.

3 4

4 4

5 5

6 6

7 6

8 5

9 6

10 5

11 4

B

12 12

13 12

14 12

15 12

16 12

Jumlah

SULIT

1449/2

Matematik

Kertas 2

Mei 2008

2

12 jam

1449/2

NAMA :

TINGKATAN :


2/23

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SULIT 1449/2

Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak

MATHEMATICAL FORMULAE

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

commonly used.RELATIONS

1 am x an = a m+ n

2 am an = a m n

3 ( am )n = a mn

4 A-1 =bcad

1

ac

bd

5 P ( A ) =)(

)(

Sn

An

6 P ( A ) = 1 P(A)

7 Distance = 2 21 2 1 2( ) ( )x x y y +

8 Midpoint, (x, y ) =

++

2

,

2

2121yyxx

9 Average speed =

10 Mean =

11 Mean =

12 Pythagoras Theorem

c2 = a2 + b2

13 m =12

12

xx

yy

14-intercept

-intercept

ym

x=

SHAPES AND SPACE

1449/22008 Hak Cipta Sektor SBP SULIT2

1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT

distance travelled

time takensum of data

number of data

sum of (class mark frequency)

sum of frequencies


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SULIT 1449/2

1 Area of trapezium =2

1 sum of parallel sides height

2 Circumference of circle = d= 2 r

3 Area of circle = r2

4 Curved surface area of cylinder = 2 rh

5 Surface area of sphere = 4 r2

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = r2h

8 Volume of cone =3

1

r2h

9 Volume of sphere =3

4 r3

10 Volume of right pyramid =3

1 base area height

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

12arc length angle subtended at centre

circumference of circle 360=

o

13area of sector angle subtended at centre

area of circle 360=

o

14 Scale factor , k=PA

PA '

15 Area of image = k2 area of object

Section A

[52 marks]

1449/22008 Hak Cipta Sektor SBP [Lihat sebelah

SULIT

3


4/23

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SULIT 1449/2

Answerall questions in this section.

1 The Venn diagram in the answer space shows setsP, Q and R such that the universal set,

RQP = .

On the diagram in the answer space, shade

(a) the set QP .(b) the set (PQ ) R .

[3 marks]

Answer:(a) (b)

2 Calculate the value of v and ofw that satisfy the following simultaneous linear equations:

112 =+wv

733

2= wv

[4 marks]

Answer :

3 Using factorisation, solve the following quadratic equation:


PQ

R

PQ

R


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2

213

=+

x

xx

[4 marks]

Answer :

4 Diagram 1 shows a right prism with a horizontal rectangular basePQRS. VUQR is a

trapezium.


SULIT

5


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Identify and calculate the angle between the plane QWR and the basePQRS.

[4 marks]

Answer :

5 In Diagram 2, straight line TU is parallel to straight line VWand O is the origin .


y

T

U

W

V

P

Q

R

S

8 cm

6 cm

12 cm

5 cm

DIAGRAM 1


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SULIT 1449/2

The equation of straight line VW is 02552 = yx .Find:

(a) the equation of the straight line TU.(b) thex-intercept of the straight line TU.

[5 marks]

Answer:

(a)

(b)

6 Diagram 3 shows two sectors of circle ORQ and OPSwith centre O.


SULIT

7

DIAGRAM 2

x

W

U(1,5)

V

T

O

OP

Q

R

S

1507 cm

12 cm

DIAGRAM 3

7 cm


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By 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)

7 (a) State whether the following statements are true or false.

(i) 2.021and3 == aaaa



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(ii) Number 5 is an odd number or number 2 is a prime number.

(b) State the antecedent and consequent of the implication:

(c) Complete the following argument.

Premise 1 : Ify > 3, then 5y > 15.

Premise 2 : _________________________________________

Conclusion : 5y > 15.

[6 marks]Answer :

(a) (i)

(ii)

(b) Antecedent : ______________________________

Consequent : ______________________________

(c) Premise 2 : ________________________________________________

8 (a) Complete the following statement using the quantifier all or some, to make it a falsestatement.


SULIT

9

Ify is less than zero, theny is a negative number.

____________ polygons have six sides.


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(b) Write down two implications based on the following statement:

(c) Make a general conclusion by induction for the sequence of numbers 2, 14, 34,

which follows the following pattern.

2 = 4(1)2 2

14 = 4(2)2 2

34 = 4(3)2 2

62 = 4(4)2 2

= ..

[ 5 marks]

Answer:

(a) ____________ polygons have six sides.

(b) Implication 1:

____________________________________________________________

Implication 2 :

_____________________________________________________________

(c) _____________________________________________________________

______________________________________________________________


x >y if and only if x < y


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9 (a) The inverse matrix of

45

23is p

35

4 q

Find the value of p and of q.

(b) Hence, using matrices, calculate the value ofx and ofy that satisfy the following

simultaneous linear equations :

3x 2y = 85x 4y = 13

[6marks]

Answer :

(a)

(b)


SULIT

11


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SULIT 1449/2

10 Diagram 4 shows the speed-time graph of a particle for a period of 50 seconds.

(a) Calculate the rate of change of speed, in ms -2, in the first 10 seconds.

(b) Calculate the value of u, if the total distance traveled in the last 40 seconds is750 m.

[5 marks]

Answer :

(a)

(b)


Speed (ms-1)

Time (s)0

5

10 30

v

20

50

DIAGRAM 4

u


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SULIT 1449/2

11 Diagram 5 shows a solid formed by joining a prism to a right pyramid. Trapezium

ABGFis the uniform cross-section of the prism.

FG = GH= 7 cm. The height of the pyramid is 6 cm.

Calculate the volume, in cm3, of the solid.

[ Use =7

22]

[4 marks]

Answer:


SULIT

13

DIAGRAM 5

8 cm

11 cmA B

CD

E

F G

H

V


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Section B

[48 marks]

Answerfour questions from this section.

12 (a) Complete Table 1 in the answer space for the equationy = 2x2 + 4x + 16.

x 4 3 2 1 0 1 2 3 4y 32 h 0 10 16 18 k 10 0

Calculate the values of h and of k.

[2 marks]

(b) For this part of the question, use the graph paper on pag15 .You may us flexible curve ruler.

By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on they-axis ,draw the graph ofy = 2x2 + 4x + 16 for 4 x 4.

[4 marks](c) From your graph, find

(i) the value ofy when x = 2.2

(ii) the value ofx when y = 5 [3 marks]

(d) Draw a suitable straight line on your graph to find all the values ofx which satisfytheequation 2x2 +x 11 = 0 for 4 x 4.

State these values ofx.

[3 marks]

Answer:

(a) h =

k=

(b) Refer graph on page 15


TABLE 1


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SULIT 1449/2

(c) (i) y =

(ii) x = .

(d) x =


SULIT

15

Graph for Question 12


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13 (a) Transformation T is a translation

3

2

and transformation P is an anticlockwise

rotation of 90o about the centre (5, 0).

State the coordinates of the image of point (9, 4) under each of the following

transformations:

(i) P,

(ii) TP,

(iii) T2

[4 marks]

(b) Diagram 6 shows three quadrilaterals A,B and C, drawn on a Cartesian plane.

(i) Cis the image ofA under the combined transformations WV.Descibe in full,:

(a) the transformation V

(b) the transformation W

[5 marks]


0 2 4 6 8 10 12x

2

4

8

y

C A

DIAGRAM 6

B

6


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(ii) It is given thatB represents a region of area 180 cm2.Calculate the area, in cm2, of the region represented byA.

[3 marks]

Answer:

(a) (i)

(ii)

(iii)

(b) (i) (a)

(b)

(ii)


SULIT

17


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SULIT 1449/2

14 The data in Table 2 shows the mass, in kg, of a group of 32 members of Science andMathematics societies.

44 64 59 49 35 40 50 51

60 50 40 43 47 45 57 53

54 49 58 54 48 47 53 45

51 52 62 59 56 46 51 56

(a) Based on the data in Table 2 and by using a class interval of 5 kg,complete the following table.

[4 marks]

Answer:

(a)

Mass (kg) Frequency Midpoint

35 39

(b) Calculate the estimated mean of the mass of the members.

[3 marks]

(c) Using a scale of 2 cm to 5 kg on thex-axis and 2 cm to 1 member on they-axis, draw

a frequency polygon for the above data.[5 marks]

Answer:

(b)

(c) Refer graph on page 19


TABLE 2


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SULIT 1449/2


SULIT

19



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SULIT 1449/2

15 (a) Complete Table 3 in the answer space for the equationy = x

2by writing down the

values ofy whenx = 0.5 andx = 2. [2 marks]

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

You may use a flexible curve rule.

By using a scale of 2 cm to 1 unit on both the axes, draw the graph ofy = x

2for

4 x 4. [5 marks]

(c) From your graph, find

(i) the value ofx wheny = 1.2 ,

(ii) the value ofy whenx = 2.3. [2 marks]

(d) Draw a suitable straight line on your graph to find values ofx which satisfies the

equation x + 1 =x

2for4 x 4.

State these values ofx.

[3 marks]

Answer:

(a)

x 4 3 2 1 0.5 0.5 1 2 3 4y 0.5 0.67 1 2 4 2 0.67 0.5

TABLE 3

(b) Refer graph on page 21

(c) (i) x = .

(ii) y = .

(d) x = ............................................................................



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SULIT

21



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SULIT 1449/2

16 (a) Transformation U is a translation

21

.

Transformation V is a reflection in the straight line y = 1.

State the coordinates of the image of point (3, -2) under each of the following

transformations :

) U,(ii) UV.

[3 marks]

(b) Diagram 7 shows three quadrilateralsABCD,HGFE and KJIE on aCartesian plane.

5 10 15

x

J

K

I

H

G

B

DC

E

F

A

- 2

- 4

6

- 8

4

- 10

2

- 6 - 4 - 2 6420

DIAGRAM 7

HGFEis an image ofABCD under transformation W and KJIEis an image of

HGFE under transformation Z.

(i) Describe in full,

(a) the transformation W,

(b) the transformation Z.

[6 marks]

(ii) Given that quadrilateralHGFErepresents a region of area 26 cm2,calculate the area, in cm2, of the region represented by the shaded region.

[3 marks]

Answer:


x


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SULIT 1449/2

(a) (i)

(ii)

(b) (i) (a)

(b)

(ii)


SULIT

23

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question midyear k2 08

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