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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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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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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
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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
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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.
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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,
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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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15
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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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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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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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TABLE 3
Graph for Question 15
END OF QUESTION PAPER
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