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SEKOLAH MENENGAH KEBANGSAAN AGASEH

PEPERIKSAAN PERTENGAHAN TAHUNTINGKATAN EMPAT 2010

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian SoalanMarkah

Penuh

Markah

Diperoleh

A

1 5

2 3

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi dua bahagian :Bahagian A dan Bahagian B. Jawab semuasoalan daripada Bahagian A dan empat soalan

dalam Bahagian B.

2.Jawapan hendaklah ditulis dengan jelas dalam

ruang yang disediakan dalam kertas soalan.Tunjukkan langkah-langkah penting. Ini bolehmembantu 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 5

5 5

6 4

7 7

8 4

9 5

10 5

11 5

B

12 12

13 12

14 12

15 12

Jumlah

SULIT

1449/2

Matematik

Kertas 2

Mei 2010

2

12 jam

1449/2

NAMA :

TINGKATAN :


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SULIT 50/2

Kertas soalan ini mengandungi 22 halaman bercetak

MATHEMATICAL FORMULAE

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

2121 yyxx

9 Average speed =

10 Mean =

11 Mean =

12 Pythagoras Theorem

c2 = a2 + b2

13 m =12

12

xx

yy

14-intercept

-intercept

ym

x=

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1449/2 [Lihat sebelah

SULIT

distance travelled

time takensum of data

number of data

sum of (class mark frequency)

sum of frequencies


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SHAPES AND SPACE

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 = r2

h

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


SULIT

3


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Answerall questions.

1. (a) (b)4.13

[5 marks]

Answer :

(a)

(b) (i)

(ii)

2 If = {x : 1 x 10 , x is an integer}

E= {x :x is a multiple of 4}

F= {x :x is a factor of 20}

(a) List all the elements in setE,

(b) Find ( )n E F .

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[3 marks]

Answer :

(a)

(b)

3 The Venn diagrams in the answer space show sets P, Q andR. Given thatP Q R.

On the diagram provided in the answer space, shade the region which represents the set

(a) (Q R)',

(b) P' (R Q').


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[4 marks]

Answer :

(a) (b)

4

Diagram 1

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In Diagram 1 , O P Q R is a parallelogram and O is the origin. Find

(a) the gradient of the straight line QR,

(b) the equation of the straight line PR,

(c) the coordinates of the point Q .

[5 marks]

Answer :

a)

b)

c)

5 (a)State whether the following statement is true or false.

3 33 9 or 8 2= =

(b) Write down two implications based on the sentence below.

The inverse matrix of a 2 2 matrix exists if and only if the determinant is 0

(c) Given the number sequence 3, 8, 15, 24, .. and


SULIT

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3 = 1 2 + 2(1)

8 = 2 2 + 2(2)

15 = 3 2 + 2(3)

24 = 4 2 + 2(4)

Make a general conclusion by using the induction method for the numerical

sequence above.

[5 marks]

Answer :

(a)

(b)

(c)

6 Calculate the value of v and of w that satisfy the following simultaneous linearequations:

3 4 8

28 4

3

+ =

=

v w

v w

[4 marks]

Answer:

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.

7 In Diagram 2,PQ andRSare parallel to thex-axis andPSis parallel toRT.


SULIT

9

xO

P Q (5,5)

R (h, 4) S(3,4)

T

DIAGRAM 2

y


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Find the

(a) equation of the linePQ,

(b) gradient of the linePS,

(c) value of h, hence, find the equation of lineRT.

[7 marks]

Answer:

(a)

(b)

(c)

8 Solve the quadratic equation )1(22

)3(3xx

xx

+=+

[4 marks]

Answer:

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9 (a) Find the value of

85

102109

and express the answer in standard form.(b) Express 2.8410-4 as a single number.(c) Calculate the value of 60.12 0.382 0.01, correct to three significant figures.

[5 marks]

Answer :

(a)


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(b)

(c)

10

Diagram 3 shows the frequency polygon of the

marks of a group of students in a test.

(a) State the modal class and the frequency of

the modal class.

(b) Calculate the mean mark.

12 15 18 21 24 27

30 33

Marks

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Diagram 3

[5 marks]

Answer:

(a)

(b)

11

Diagram 4 shows the number of

students who like to play three games. Given = A

B C, set A = {students who like to play

badminton}, set B = {students who like to play

tennis} and set C {students who like to play

squash }. State the number of students who

(a) like to play all the three games,


SULIT

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(a) like to play badminton and squash only,

(b) like to play one game only.

Diagram 4

[5 marks]

Answer:

(a)

(b)

(c)

Section B

[48 marks]

Answerall questions in this section.

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12. (a) Write down two implications based on the following sentence.

k3= 216 if and only ifk = 6.

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

(i) 743 = or 1046 = .

(i)2

1= 0.5 and 87 is a prime number.

(c) Complete the premise in the following argument.

Premise 1 : Alleven numbers are divisible by 2.

Premise 2 : ______________________________

Conclusion : 36 is divisible by 2. [4 marks]

Answer: (a)

(b) (i)

(ii)

(c)Premise 2: ____________________________________________

13 (a) Solve each of the following quadratic equations.

(i) 15

62

=

+x

x

(ii) xx

612

=

[6 marks]

Answer:


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(a) (i)

(ii)

(b)

Diagram 4

In Diagram 4,PQR is a right-angled triangle. If the area of the shaded region is 40 cm2,

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find the value ofx.

[6 marks]

Answer:

(b)

14 The data in Table 1 shows the mass, in kg, for 50 students.

49 54 76 59 55 50 70 70 65 62

45 76 51 63 58 51 63 55 68 67

53 79 46 69 76 64 57 71 63 63

64 45 57 72 55 71 61 60 70 65

56 66 67 52 65 75 60 57 67 54


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17

TABLE 1


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(a) Construct a grouped frequency table for the data using class intervals 45 49,

50 54 and so on.

[3 marks]

Answer:(a)

Mass(kg) Midpoint Frequency45 49

50 54

(b) Using a scale of 2 cm to 5 kg on the horizontal axis and 2 cm to 1 student on the

vertical axis, draw a frequency polygon for the above data.

[5 marks](c) Use the frequency polygon to

(i) find the modal class

(ii) calculate the mean mass of the students.

[4 marks]

Answer:

(b) Refer graph on page 19

(c) (i)

(ii)

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Graph for Question 14


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5 (a) Table 2 shows the number of books read by 45 students in a class.

Books read by the

student

0 1 2 3 4 5 6 7 8

No of students 16 5 6 5 6 4 0 1 2

Find

(i) the median,


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19

TABLE 2


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(ii) the mean.

[4 marks]

Answer:

(a) (i)

(ii)

(b) Table 3 in the answer space shows the marks scored by 200 candidates in a test.

(i) Complete Table 3 by filling in the cumulative frequencies.

[2 marks]

(ii) By using a scale of 2 cm to 10 marks on the x-axis and 2 cm to 20candidates on they-axis, draw an ogive for the given data.

[4 marks]

(iii) Candidates in the first quartile must sit for the examination again.

What is the highest mark for the candidates who reseat the

examination?

[2 marks]

Answer:

(b) (i)

Marks CandidatesCumulative

Frequency

11 20 18

21 30 22

31 40 3541 50 43

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51 60 30

61 70 23

71 80 21

81 90 8

(ii) Refer graph on page 22.

(iii)


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21

TABLE 3

Graph for Question 15

END OF QUESTION PAPER


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