mat_k2_t4_pptsbp07
Transcript of mat_k2_t4_pptsbp07
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Matematik
Kertas 2
Mei
2007
2 jam
SEKTOR SEKOLAH BERASRAMA PENUH
BAHAGIAN SEKOLAH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERTENGAHAN TAHUN
TINGKATAN 4 2007
MATEMATIK
Kertas 2
Dua jam tiga puluh minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1.Kertas soalan ini mengandungi dua
bahagian : Bahagian A dan Bahagian
B. Jawab semua soalan dalam
Bahagian A dan empat soalan
daripadaBahagian 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
dilukis mengikut skala kecuali
dinyatakan.
4.Satu senarai rumus disediakan di halaman
3 dan 4.
5.Anda dibenarkan menggunakan
kalkulator saintifik yang tidak boleh
diprogram.
Pemeriksa
Bahagian SoalanMarkahPenuh
MarkahDiperoleh
A
1 5
2 4
3 4
4 7
5 3
6 5
7 6
8 6
9 3
10 4
11 5
B
12 12
13 12
14 12
15 12
16 12
Jumlah
NAMA : TINGKATAN :
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Kertas soalan ini mengandungi 22 halaman bercetak1449/2 @ 2007 Hak Cipta SBP
INFORMATION FOR CANDIDATES
1. This question paper consists of two sections: Section Aand
Section B. Answerallquestions inSection Aandfourquestions inSection B.
2. Write your answers clearly in the spaces provided in the question paper.
3. Show your working. It may help you to get marks.
4. If you wish to change your answer, neatly cross out the answer that you have
done. Then write down the new answer.
5. The diagrams in the questions provided are not drawn to scale unless stated.
6. The marks allocated for each question and sub-part of a question are shown in
brackets.
7. A list of formulae is provided on pages 3 and4.
8. You may use a non-programmable scientific calculator.
9. This question paper must be handed in at the end of the examination.
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MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols givenare 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
= bcad1
ac
bd
5 P ( A ) =)(
)(
Sn
An
6 P ( A ) = 1 P(A)
7 Distance = 221
2
21)()( yyxx +
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 m =
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distance travelledtime taken
sum of datanumber of data
sum of (class mark frequency)
sum of frequencies
y-interceptx-intercept
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SHAPES AND SPACE
1 Area of trapezium = 2
1
sum of parallel sides height
2 Circumference of circle = d= 2r
3 Area of circle = r2
4 Curved surface area of cylinder = 2rh
5 Surface area of sphere = 4r2
6 Volume of right prism = cross sectional area length
7 Volume of cylinder = r2h
8 Volume of cone =3
1r2h
9 Volume of sphere =3
4r3
10 Volume of right pyramid =31 base area height
11 Sum of interior angles of a polygon = ( n 2) 180
12360
centreatsubtendedangle
circleofncecircumfere
lengtharc=
13360
centreatsubtendedangle
circleofarea
sectorofarea=
14 Scale factor , k=PA
PA'
15 Area of image = k2 area of object
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Section A
[52 marks]
Answerallquestions in this section.
1 (a) Factorise 3k2 2 ( k+ 4 ).
(b) Solve the quadratic equation 13
)4(2+=
+m
mm.
[5 marks]
Answer:
(a)
(b)
2 Calculate the value ofh and kthat satisfy the following simultaneous linear
equations:
3h 4k = 8
2
1h + 2k = 12
[4 marks]
Answer:
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3 Diagram 1shows a solid formed by joining a cylinder and a cone.
The radius of the cylinder and the radius of the base of the cone
are both 6 cm. The height of the cone is 8 cm and the height of
the cylinder is 10 cm.
DIAGRAM 1
Using = 3.142, calculate the volume, in cm3, of the solid.
[4 marks]
Answer:
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4 Diagram 2 shows a quadrantADO with centre O and a sectorBEFwith centreB.
OBC is a right angled triangle andD is the midpoint of the straight line OC.Given OC= OB =BE = 14 cm.
DIAGRAM 2
Using =7
22, calculate
(a) the perimeter, in cm, of the whole diagram,
(b) the area, in cm2, of the shaded region.
. [7 marks]
Answer:
(a)
(b)
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5 The Venn diagramin the answer space shows setP, set Q and set
R with the universal set = PQ R.
On the diagram in the answer space, shade
(a) PQ R
(b) P ( Q R)
[3 marks]
Answer:
(a)
(b)
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Q
P R
R
Q
P
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6 In Diagram 3, O is the origin, pointR lies on thex-axis and point Q lies on they-axis. Straight linePQ is parallel to thex-axis and straight line RQ is parallel to
ST. The equation ofRQ is 3y x = 12.
DIAGRAM 3
(a) State the equation ofPQ.
(b) Find the equation of the straight line STand hence, state itsx-intercept.
[5 marks]
Answer:
(a)
(b)
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P Q
R
T
S(3, 10)
O
y
x
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7 (a) State whether each of the following statement is true or
false.
(i) 6 is a factor of 36 and 1 is a prime number.
(ii) 2 ( 5) = 10 or 3 ( 6) = 18.
(b) Write down two implications based on the following statement.
(c) Complete the premise in the following argument:
Premise 1 :
Premise 2 : 2m + 5 13.
Conclusion : m 4.
Answer:
(a) (i)
(ii)
(b) Implication 1 : .
Implication 2 : .
(c) Premise 1: .
[6 marks]
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x2 < 25 if and only if 5
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8 The width of a rectangle is (2y 1) cm and its length is (4y + 3) cm.
(a) Express the area of the rectangle in terms ofy.
(b) Given the area of the rectangle is 18 cm2 , find the width of the rectangle.
[6 marks]
Answer:
(a)
(b)
9 480 pieces of A4 size paper make up one ream of paper. The mass of one ream of
paper in grams is 1.26 102. Find the mass of each piece of paper in milligrams.Express your answer in standard form.
[3 marks]
Answer:
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10 Diagram 4 shows an incomplete Venn diagram that represents thenumber of students from a class of 30, according to the subjects
they have studied. Each student studied at least one of the three
subjects Physics, Chemistry and Biology.
Given the universal set, =PCB, P= {students who studied Physics}
C= {students who studied Chemistry}
B = {students who studied Biology}
DIAGRAM 4
20 students studied Chemistry and 12 students studied Biology. Based on thisinformation, find
(a) the number of students who studied Chemistry and Biology but not
Physics.
(b) the number of students who studied Biologyonly.
(c) the number of students who studied Physics.
[4 marks]
Answer:
(a)
(b)
(c)
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C P
B
1
6
25
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x
y
R(4, 6)
S
P( 6, 1)
Q(0, 2)
(a) the equation of the straight line QR,
(b) they-intercept ofthe straight linePS.
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Diagram 5,PQRSis a parallelogram. Point Q lies on they-axis.
DIAGRAM 5
Find
[5 marks]
Answer:
(a)
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(b)
Section B
[48 marks]
Answerfourquestions in this section.
12 (a) Factorise completely 2p3 50p.
[2 marks]
(b) ABCis a triangular plot of land in which angleACB is a right angle.
Given thatAB = (3x 5) m,AC= (x + 5) m andBC= 2x m.
(i) Use Pythagoras Theorem to form a quadratic equation in general
form.
(ii) Solve this equation and hence find the perimeter of the triangular plot
ABC.
[5 marks]
(c) In Diagram 6, O is the origin, the straight linesPR and STintersect at
pointM.
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2y =x
=
y = 2x + 9
=
x
=O
P
R
S
T
y
=
M
DIAGRAM 6
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(i) Find the coordinates ofM.
(ii) Given that the straight line PR passes through the point (h, h +12),
find the value of h.
[5
marks]
Answer:
12 (a)
(b) (i)
(ii)
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(c) (i)
(ii)
13 (a) Given that = {x:x is an integer and 7 x 15},A = {x: x is a multiple of 3 },
B = {x :x is an odd number} and
C= {x: 10 x 13 }.
(i) List the elements of the set C .(ii) Find n(AB).(iii) List all the possible subsets of setA.(iv) Find the elementx such thatx (BC ) andxA. [7 marks]
(b) Given that n() = 50. G andHare two sets for which n( GH) = 6,n(G) = 18 and n(H) = 14.
(i) Draw a Venn diagram to represent the relationship between sets G
andHand write the number of elements in each region.
(ii) Find n(GH) . [3 marks]
(c) On the Venn diagram in the answer space, draw a setN such that N
L andN M= .[2 marks]
Answer:
(a) (i)
(ii)
(iii)
(iv)
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A BO
210o
B
A
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(b) (i)
(ii)
(c)
14 (a) In Diagram 7, the shaded region represents the part of the flat
windscreen of a van which is being wiped by the windscreen wiperAB. The
wiper rotates through an angle of 210o about the centre O. Given that OA = 7
cm andAB = 28 cm.
DIAGRAM 7
Using =7
22, calculate
(i) the length of arcBB ,
(ii) the ratio of arc lengths , AA : BB
(iii) the area of the shaded region. [7 marks]
Answer:
(a) (i)
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L M
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(ii)
(iii)
14 (b) In Diagram 8, the pointsA,B, CandD lie on a circleABCD with centre O.
ABD = 50o and DBC = 60o.
DIAGRAM 8
Calculate
(i)
COD,
(ii)
ADC,
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D
B
A
C
O
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(iii) ADO.
[5 marks]
Answer:
(b) (i)
(ii)
(iii)
15 (a) Diagram 9 shows a solid right cylinder of radius 7 cm and length 10 cm
with hemispheres of radius 7 cm attached at each end.
DIAGRAM 9
Calculate the total surface area, in cm2, of the combined solids.
(Use =7
22)
[4 marks]
(b) (i) Complete each of the following statements with the quantifier
all or some so that it will become a true statement.
(a) .. sets with 2 elements will have 4 subsets.
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(b) .. prime numbers are divisible by 3.
(ii)
(a) State the antecedent and consequent of the aboveimplication.
(b) Write the converse of the above implication and hence
determine whether its converse is true or false.
(c) Based on the information below, make a general conclusion by
induction.
12 = 2 (2) (2 + 1)
24 = 2 (3) (3 + 1)
40 = 2 (4) (4 + 1)
60 = 2(5) (5 + 1)
..
[8 marks]
Answer:
15 (a)
(b) (i) (a) ................................................................................................
(b) .....................................................................................................
(ii) (a) Antecedent: ................................................................................
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Ifx < 2, thenx < 7.
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Consequent: ...............................................................................
(b) ....................................................................................................
...................................................................................................
(c) ....................................................................................................................
16 The data below shows the Chemistry test marks scored by a group of
40 students in Form 4 Wawasan.
TABLE 1
(a) Using the given data and a class interval of 10, complete Table 2 in the
answer space.
[4 marks]
(b) From the table in (a),
(i) state the modal class,
(ii) calculate the mean mark.
[4 marks]
Answer:
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68 40 65 66 60 46 53 56 49 58
53 57 73 53 69 51 56 64 58 62
47 65 67 66 67 36 56 53 38 37
62 61 37 74 48 41 75 63 69 55
Marks scored Midpoint Frequency
20 29
30 39
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TABLE 2
(b) (i)
(ii)
(c) For this part of the question, use the graph paper.
By using a scale of 2 cm to 10 marks on the horizontal axis and 2 cm to 2
students on the vertical axis, draw a frequency polygon for the data.
[4 marks]
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