maths test 1 spm 2014
DESCRIPTION
test 1TRANSCRIPT
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1449/2
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4
For
Examiners
Use
Section A
[52 marks]
Answer all questions in this section.
1 The Venn diagram in the answer space shows sets K, L and M such that the
universal set, = K L M.
On the diagrams in the answer space, shade
(a) L M ,
(b) ( K M ) L.
[3 marks]
Answer:
(a)
(b)
L
KM
L
KM
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2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.
Right angled triangle MFG is the uniform cross-section of the prism.
S is the midpoint of ND.
DIAGRAM 1
Identify and calculate the angle between the line FS and the base GMND.
[4 marks]
Answer:
For
Examiners
Use
E
G
D
M
S
F
N
5 cm
16 cm6 c
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For
Examiners
Use 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .
The isosceles triangle KLH is the uniform cross-section of the prism.
N is the midpoint of KL.
DIAGRAM 2
Identify and calculate the angle between the plane KLG and the plane KLH.
[4 marks]
Answer:
J
K L
H
G
N
M
6 cm
5 cm
12 cm
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3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.
The height of the cone is 6 cm.
By using722
, calculate the volume, in cm3 , of the combined solid.
[4 marks]
Answer:
For
Examiners
Use
7 cm
12 cm
DIAGRAM 3
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8
For
Examiners
Use
4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.
[4 marks]
Answer:
5 Using factorisation, solve the quadratic equation pp 5
23 2 .
[4 marks]
Answer:
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6 Calculate the value of m and of n that satisfy the following simultaneous
linear equations:
1223166
nmnm
[4 marks]
Answer:
For
Examiners
Use
7 Calculate the value of h and of k that satisfy the following simultaneous
linear equations:
273
6443
hk
hk
[4 marks]
Answer:
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10
For
Examiners
Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.
It is given that POQ = 60.
By using =722 , calculate
(a) the perimeter, in cm, of the whole diagram,
(b) the area, in cm2, of the shaded region.
[ 6 marks ]
Answer:
(a)
(b)
T
Q 14 cm
7 cm
R
S
O
PDIAGRAM 4
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11
9(a) Write down two implications based on the following statement:
m > 6 if and only if m 6 > 0
(b) State the converse of the following statement and hence determine whether the
converse is true or false.
If x is a factor of 5, then x is a factor of 10.
(c) Make a general conclusion by induction for the sequence of numbers
1 , 6 , 15 , 28, . . . which follows the following pattern.
1 = 2 ( 1 )2 1
6 = 2 ( 2 )2 2
15 = 2 ( 3 )2 3
28 = 2 ( 4 )2 4
=
[6 marks]
Answer:
(a) Implication 1:
Implication 2:
(b)
...
(c) ...
For
Examiners
Use
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12
For
Examiners
Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.
Find
(a) the equation of the straight line PQ,
(b) y intercept of the straight line PQ.
[4 marks]
Answer:
(a)
(b)
x
R ( 4 ,12)
DIAGRAM 5
y
P ( 3 , 6 )
O
Q
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11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.
PQ is parallel to RS.
The equation of the straight line KL is 62 xy .
Find
(a) the gradient of the straight line PQ,
(b) the equation of the straight line RS.
[5 marks]
Answer:
(a)
(b)
For
Examiners
Use
xO
KR
S
L
DIAGRAM 6
y
P
Q (3, 3)
3[Turn over
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14
For
Examiners
Use
Section B
[48 marks]
Answer any four questions from this section.
12(a) The Venn diagram in the answer space shows the universal set , sets P, Q
and R. On the diagram in the answer space, shade the region for
(i) P Q ,
(ii) ( P Q ) R.
[3 marks]
Answer:
(i)
(ii)
P
Q
PQ
R
2R
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12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .
Find
(i) the equation of the straight line RN,
(ii) the x intercept of the straight line RN .
[5 marks]
Answer:
(i)
(ii)
For
Examiners
Uses
y
x
R
N ( 4,9 )
Q (3, 4)
O
DIAGRAM 7[Turn over
aCross-Out
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16
For
Examiners
Use
12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.
Trapezium PQGF is the uniform cross-section of the prism.
U, V, and W are midpoints of PS, FE and QR respectively.
DIAGRAM 8
Identify and calculate the angle between the plane QRV and the base PQRS.
[4 marks]
Answer:
E
P
G
H
Q
R
F
V
US
W8 cm12 cm
5 cm
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13(a) (i) State whether the following sentences is a statement or
non-statement.
(a) 2x + 5y 6
(b) 4 is a prime number.
(ii) Combine the two statements below to form a false statement.
Statement 1 : 3 13 = 39
Statement 2 : 39 is a prime number.
(iii) Write down Premise 1 to complete the following argument:
Premise 1 :
Premise 2 : 3 is a factor of 15
Conclusion : 3 is a factor of 30
(iv) Fill in the blanks with < or > to form
(a) a true statement,
6 3
(b) a false statement.
8 24
[6 marks]
Answer:
(i)(a) _________________________________
(b) _________________________________
(ii) ______________________________________________________
(iii) Premise 1 :______________________________________________
(iv) (a) 6 3
(b) 8 24
For
Examiners
Uses
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18
For
Examiners
Use
13(b) In Diagram 9, ORST is a quadrant and KL is an arc of another circle both
with centre O. ORK and OSL are straight lines.
DIAGRAM 9
OR = RK = 7 cm.
Using722
, calculate
(i) the perimeter, in cm, of the whole diagram,
(ii) the area, in cm 2 , of the shaded region.
. [6 marks]
Answer:
(i)
(ii)
60
R
S
T
L
K
O
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14(a) Using factorisation, solve the quadratic equation mm 6
52 .
[4 marks]
Answer:
14(b) Calculate the value of d and of e that satisfy the following simultaneous linear
equations:
144
10213
ed
ed
[4 marks]
Answer:
For
Examiners
Uses
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20
For
Examiners
Use
14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.
The volume of the remaining solid is 292 cm 3 .
Calculate the width, in cm, of the remaining solid.
(Use =722 )
[4 marks]
Answer:
2 cm
2 cm
8 cm
7 cm
DIAGRAM 10
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15. The data in Diagram 11 shows the ages of 50 runners who took part in a charity run
event.
14 36 12 16 27 31 27 28 30 28
16 18 23 18 24 32 23 14 18 31
22 30 23 20 25 30 31 22 20 37
12 26 36 23 28 30 34 38 33 36
11 23 27 27 34 38 25 12 17 29
DIAGRAM 11
(a) Based on the data in Diagram 11 and by using a class interval of 5, complete
Table 1 in the answer space.
[4marks]
(b) Based on Table 1 in (a),
calculate the estimated mean of the age of the runners.
[3marks]
(c) For this part of the question, use the graph paper provided on page 23.
By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 1
runner on the vertical axis, draw a frequency polygon for the data.
[5marks]
For
Examiners
Use
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22
For
Examiners
Use
Answer:
(a)
Age (years) Midpoint Frequency
11 15
TABLE 1
(b) i)
ii)
(c) Refer graph on page 23.
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For
Examiners
Use
16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.
67 76 91 79 81 82 87 71
79 82 88 83 72 84 71 89
80 86 70 86 62 83 83 80
75 84 84 77 84 86 85 76
80 75 95 77 73 86 77 68
DIAGRAM 12
(a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in
the answer space.
[6 marks]
(b) For this part of the question, use the graph paper provided on page 26.
By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the
y-axis, draw an ogive based on the data.
[5 marks]
(c) From your ogive in (b), find the third quartile.
[1 mark]
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Answer:
a)
Marks Frequency Cumulative Frequency Upper Boundary
61 65
TABLE 2
b) Refer graph on page 26
c)
For
Examiners
Use
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INFORMATION FOR CANDIDATES
1. This question paper consists of two sections: Section A and Section B.
2. Answer all questions in Section A and four questions from Section B.
3. Write your answers in the spaces provided in the question paper.
4. Show your working. It may help you to get marks.
5. If you wish to change your answer, cross out the answer that you have done. Thenwrite down the new answer.
6. The diagrams in the questions provided are not drawn to scale unless stated.
7. The marks allocated for each question and sub-part of a question are shown inbrackets.
8. A list of formulae is provided on page 2 to 3.
9. A booklet of four-figure mathematical tables is provided.
10. You may use a non-programmable scientific calculator.
11. Hand in this question paper to the invigilator at the end of the examination.
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Mathematics Form 4 Final year 2008Section A
[ 52 marks ]
No Marking Scheme Marks
1a)
b)
P1
P2 3
2 a) FSQ
Tan22 86
5
'3426/57.26
b) FSQ
Tan4
12
'3471/57.71
P1
K2
N1
P1
K2
N1
4
4
3 1227
27
722
21
627
27
722
31
21
5.269/21269
627
27
722
31
2112
27
27
722
21
K1
K1
K1
N1 4
L
KM
L
KM
-
No Marking Scheme Marks
4
1,61
01160156 2
x
xxxx K1
K1
N1,N1 4
5
31,2
01320253 2
p
pppp K1
K1
N1,N1 4
6
2,36020
48183
mnn
nm K1K1
N1, N1 4
7
8,35117
24163
khh
hk K1K1
N1, N1 4
8 a) 77
2223606021
7222
36045
0
0
0
0
OR
83.65/6565
777
222360601421
7222
3604521
0
0
0
0
b) 22 77
223606021
722
36045
OR
42.174@125174
77217
722
3606021
722
36045 22
0
0
K1
K1
N1
K1
K1
N1 6
-
No Marking Scheme Marks
9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6
b) If x is a factor of 10, then x is a factor of 5False
c) ,2 2 nn .......,4,3,2,1n
P1P1
P1P1
P1P1 6
10 a) 304012
ORPQ mm
15315336
xycORc
b) 15y
K1
K1N1
N1 4
11 a)21
3303
PQm
621
6)0(216
21
xy
cORc
mm RSPQ
K1, N1
K1
K1
N1 5
-
Section B[48 marks]
No Marking Scheme Marks
12 a)i
ii.
b)i.34
m
834
)9(344
xy
c
ii. 8340 x
6x
c) VWU
Tan125
P1
P2
K1
K1
N1
K1
N1
P1
K2
P Q
R
PQ
R
'3722/62.22 N1 12
-
No Marking Scheme Marks
13 a) i) a) Non-statementb) Statement
ii) andiii) all factors of 15 are factors of 30iv) a )
(b) i) 147222
36060
0
0
OR 77222
36030
0
0
147222
36060
0
0
+ 77222
36030
0
0
+14+7+7
3146 OR 46.34
ii) 1414722
36060
0
0
OR 77722
360300
1414722
36060
0
0
+ 77722
360300
= 89.83 2cm or6589
P1P1
P1P1P1P1
K1
K1
N1
K1
K1
N112
14
5,1051
056)( 2
mmmmma
2362206)(
edd
edb
cm
cmw
wc
6292298
292727
222187
87)(
22
K1N1N1,N1
K1K1N1N1
K1
K1, K1
N112
-
No Marking Scheme Marks
15 (a)
Age(years) Midpoint Frequency
11 - 15 13 6
16 20 18 8
21 25 23 10
26 30 28 13
31 35 33 7
36 40 38 6
All values in Column 1 correctAll values in Column 2 correctAll values in Column 3 correct
(b)
5.2550
127550
)6(38)7(33)13(28)10(23)8(18)6(13
(c) Refer to the graph
Axes drawn in the correct direction , uniform scale for 438 xand 130 y .Horizontal axis labeled using midpoint / upper boundary / classinterval6 points plotted correctly(8,0) and (43,0).Straight line passing 8 point.
P1P1P2
K2
N1
K1
P1P1P1P1
12
-
No Marking Scheme Marks
16 Marks Frequency Cumulativefrequency
Upperboundary
I55 60
II0
III0
IV60.5
61 65 1 1 65.566 70 3 4 70.571 75 6 10 75.576 80 10 20 80.581 85 11 31 85.586 90 7 38 90.591 - 95 2 40 95.5
All values in Column ( I ) correctAll values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correctAll values in Column ( IV ) correct
(b) x-axis and y-axis are drawn with the right direction and inuniform scale from 60.5 5.95 x , 110 y
All eight points* plotted correctly.Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed throughAll the right eight points plotted correctly and ogive is drawnsmoothly passing through all the points.
(c) 85 0.5
P1P2P2P1
K1
K2
K1N1
N112
-
8 13 18 23 28 330
2
4
6
8
10
12
14
Graph is not drawn to scale.
38
43
Frequency
Mid-point
Graph for Question 15.
-
655605 705 755 805 855 905
0
5
10
15
20
25
30
35
40
Graph is not drawn to scale.
Graph for Question 16.
95.5
CumulativeFrequency
UpperBoundary
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SULIT 1449/11449/1MatematikKertas1PeraturanPemarkahanOktober2008
SEKTOR SEKOLAH BERASRAMA PENUHBAHAGIAN SEKOLAH
KEMENTERIAN PELAJARANMALAYSIA
PERATURAN PEMARKAHANPEPERIKSAAN AKHIR TAHUN TAHUN 2008
TINGKATAN 4
MATEMATIK
KERTAS 1 & 2
1449/1/2
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QUESTION ANSWER QUESTION ANSWER
1 D 21 C
2 C 22 B
3 C 23 D
4 D 24 A
5 A 25 B
6 A 26 B
7 C 27 A
8 D 28 D
9 C 29 D
10 C 30 D
11 A 31 B
12 C 32 B
13 A 33 D
14 B 34 C
15 B 35 D
16 C 36 A
17 B 37 B
18 A 38 A
19 A 39 A
20 B 40 C
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1449/2 Form Four1
NAMA : ___________________________________
TINGKATAN : _____________________________
BAHAGIAN PENGURUSANSEKOLAH BERASRAMA PENUH / KLUSTER
BAHAGIAN SEKOLAHKEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPATMATHEMATICSKertas 2Oktober2 jam Dua jam tiga puluh minit
MATEMATIK
Kertas 2
Dua jam tiga puluh minit
Pemeriksa
Bahagian Soalan MarkahPenuhMarkah
Diperoleh
A
1 3
2 8
JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU
1. Kertas soalan ini mengandungi dua bahagian :Bahagian A dan Bahagian B. Jawab semuasoalan daripada Bahagian A dan empat soalandalam Bahagian B.
2. Jawapan hendaklah ditulis dengan jelas dalamruang 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 halaman2 & 3.
5. Anda dibenarkan menggunakan kalkulatorsaintifik yang tidak boleh diprogram.
3 44 4
5 4
6 4
7 4
8 6
9 6
10 4
11 5
B
12 12
13 12
14 12
15 12
16 12
Jumlah[Turn over1449/2Maths / F4 / P2 /2008
Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak
1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT
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1449/2 Form Four
1449/2 Form FourMaths / F4 / P2 /2008
2
MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols given are theones commonly used.
RELATIONS
1 am an = am + n 12 Pythagoras Theoremc2 = a2 + b2
2 am an = am n 13
12
12
xxyym
3 (am )n = am n 14interceptintercept
xym
4
acbd
bcadA 11
5)()()(
SnAnAP
6 )(1)'( APAP
7 Distance = 2122
12 )()( yyxx
8Midpoint,
2,
2),( 2121 yyxxyx
9takentimetravelleddistancespeedAverage
10dataofnumber
dataofsumMean
11sfrequencieofsum
frequency)marks(classofsumMean
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1449/2 Form Four
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3
SHAPES AND SPACE
1heightsidesparallelofsum
21trapeziumofArea
2 Circumference of circle = d = 2 r
3 Area of circle = r 2
4 Curved surface area of cylinder = 2 r h
5 Surface area of sphere = 4 r 2
6 Volume of right prism = cross sectional area length
7 Volume of cylinder = r 2 h
8Volume of cone hr 2
31
9Volume of sphere 3
34 r
10Volume of right pyramid heightareabase
31
11 Sum of interior angles of polygon = (n 2)180
12o360
centreatsubtendedanglecircleofncecircumfere
lengtharc
13o360
centreatsubtendedanglecircleofareasectorofarea
14PAPA'k ,factorScale
15 Area of image = k2 area of object
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1449/2 Form Four
1449/2 Form FourMaths / F4 / P2 /2008
4
For
Examiners
Use
Section A
[52 marks]
Answer all questions in this section.
1 The Venn diagram in the answer space shows sets K, L and M such that the
universal set, = K L M.
On the diagrams in the answer space, shade
(a) L M ,
(b) ( K M ) L.
[3 marks]
Answer:
(a)
(b)
L
KM
L
KM
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1449/2 Form Four
[Turn over1449/2Maths / F4 / P2 /2008
5
2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.
Right angled triangle MFG is the uniform cross-section of the prism.
S is the midpoint of ND.
DIAGRAM 1
Identify and calculate the angle between the line FS and the base GMND.
[4 marks]
Answer:
For
Examiners
Use
E
G
D
M
S
F
N
5 cm
16 cm6 cm
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1449/2 Form Four
1449/2 Form FourMaths / F4 / P2 /2008
6
For
Examiners
Use 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .
The isosceles triangle KLH is the uniform cross-section of the prism.
N is the midpoint of KL.
DIAGRAM 2
Identify and calculate the angle between the plane KLG and the plane KLH.
[4 marks]
Answer:
J
K L
H
G
N
M
6 cm
5 cm
12 cm
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1449/2 Form Four
[Turn over1449/2Maths / F4 / P2 /2008
7
3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.
The height of the cone is 6 cm.
By using722
, calculate the volume, in cm3 , of the combined solid.
[4 marks]
Answer:
For
Examiners
Use
7 cm
12 cm
DIAGRAM 3
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1449/2 Form FourMaths / F4 / P2 /2008
8
For
Examiners
Use
4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.
[4 marks]
Answer:
5 Using factorisation, solve the quadratic equation pp 5
23 2 .
[4 marks]
Answer:
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1449/2 Form Four
[Turn over1449/2Maths / F4 / P2 /2008
9
6 Calculate the value of m and of n that satisfy the following simultaneous
linear equations:
1223166
nmnm
[4 marks]
Answer:
For
Examiners
Use
7 Calculate the value of h and of k that satisfy the following simultaneous
linear equations:
273
6443
hk
hk
[4 marks]
Answer:
-
1449/2 Form Four
1449/2Maths / F4 / P2 /2008
10
For
Examiners
Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.
It is given that POQ = 60.
By using =722 , calculate
(a) the perimeter, in cm, of the whole diagram,
(b) the area, in cm2, of the shaded region.
[ 6 marks ]
Answer:
(a)
(b)
T
Q 14 cm
7 cm
R
S
O
PDIAGRAM 4Form Four
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1449/2 Form Four
[Turn over1449/2Maths / F4 / P2 /2008
11
9(a) Write down two implications based on the following statement:
m > 6 if and only if m 6 > 0
(b) State the converse of the following statement and hence determine whether the
converse is true or false.
If x is a factor of 5, then x is a factor of 10.
(c) Make a general conclusion by induction for the sequence of numbers
1 , 6 , 15 , 28, . . . which follows the following pattern.
1 = 2 ( 1 )2 1
6 = 2 ( 2 )2 2
15 = 2 ( 3 )2 3
28 = 2 ( 4 )2 4
=
[6 marks]
Answer:
(a) Implication 1:
Implication 2:
(b)
...
(c) ...
For
Examiners
Use
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1449/2 Form Four
1449/2 Form FourMaths / F4 / P2 /2008
12
For
Examiners
Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.
Find
(a) the equation of the straight line PQ,
(b) y intercept of the straight line PQ.
[4 marks]
Answer:
(a)
(b)
x
R ( 4 ,12)
DIAGRAM 5
y
P ( 3 , 6 )
O
Q
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1449/2 Form Four
1449/2Maths / F4 / P2 /2008
13
11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.
PQ is parallel to RS.
The equation of the straight line KL is 62 xy .
Find
(a) the gradient of the straight line PQ,
(b) the equation of the straight line RS.
[5 marks]
Answer:
(a)
(b)
For
Examiners
Use
xO
KR
S
L
DIAGRAM 6
y
P
Q (3, 3)
3[Turn over
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1449/2 Form Four
1449/Maths
14
For
Examiners
Use
Section B
[48 marks]
Answer any four questions from this section.
12(a) The Venn diagram in the answer space shows the universal set , sets P, Q
and R. On the diagram in the answer space, shade the region for
(i) P Q ,
(ii) ( P Q ) R.
[3 marks]
Answer:
(i)
(ii)
P
Q
PQ
R
2/ F4 / P2 /Form Four2008
R
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15
12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .
Find
(i) the equation of the straight line RN,
(ii) the x intercept of the straight line RN .
[5 marks]
Answer:
(i)
(ii)
For
Examiners
Uses
y
x
R
N ( 4,9 )
Q (3, 4)
O
DIAGRAM 7[Turn over
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16
For
Examiners
Use
12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.
Trapezium PQGF is the uniform cross-section of the prism.
U, V, and W are midpoints of PS, FE and QR respectively.
DIAGRAM 8
Identify and calculate the angle between the plane QRV and the base PQRS.
[4 marks]
Answer:
E
P
G
H
Q
R
F
V
US
W8 cm12 cm
5 cm
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13(a) (i) State whether the following sentences is a statement or
non-statement.
(a) 2x + 5y 6
(b) 4 is a prime number.
(ii) Combine the two statements below to form a false statement.
Statement 1 : 3 13 = 39
Statement 2 : 39 is a prime number.
(iii) Write down Premise 1 to complete the following argument:
Premise 1 :
Premise 2 : 3 is a factor of 15
Conclusion : 3 is a factor of 30
(iv) Fill in the blanks with < or > to form
(a) a true statement,
6 3
(b) a false statement.
8 24
[6 marks]
Answer:
(i)(a) _________________________________
(b) _________________________________
(ii) ______________________________________________________
(iii) Premise 1 :______________________________________________
(iv) (a) 6 3
(b) 8 24
For
Examiners
Uses
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18
For
Examiners
Use
13(b) In Diagram 9, ORST is a quadrant and KL is an arc of another circle both
with centre O. ORK and OSL are straight lines.
DIAGRAM 9
OR = RK = 7 cm.
Using722
, calculate
(i) the perimeter, in cm, of the whole diagram,
(ii) the area, in cm 2 , of the shaded region.
. [6 marks]
Answer:
(i)
(ii)
60
R
S
T
L
K
O
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1449/2 Form Four
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19
14(a) Using factorisation, solve the quadratic equation mm 6
52 .
[4 marks]
Answer:
14(b) Calculate the value of d and of e that satisfy the following simultaneous linear
equations:
144
10213
ed
ed
[4 marks]
Answer:
For
Examiners
Uses
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For
Examiners
Use
14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.
The volume of the remaining solid is 292 cm 3 .
Calculate the width, in cm, of the remaining solid.
(Use =722 )
[4 marks]
Answer:
2 cm
2 cm
8 cm
7 cm
DIAGRAM 10
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15. The data in Diagram 11 shows the ages of 50 runners who took part in a charity run
event.
14 36 12 16 27 31 27 28 30 28
16 18 23 18 24 32 23 14 18 31
22 30 23 20 25 30 31 22 20 37
12 26 36 23 28 30 34 38 33 36
11 23 27 27 34 38 25 12 17 29
DIAGRAM 11
(a) Based on the data in Diagram 11 and by using a class interval of 5, complete
Table 1 in the answer space.
[4marks]
(b) Based on Table 1 in (a),
calculate the estimated mean of the age of the runners.
[3marks]
(c) For this part of the question, use the graph paper provided on page 23.
By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 1
runner on the vertical axis, draw a frequency polygon for the data.
[5marks]
For
Examiners
Use
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22
For
Examiners
Use
Answer:
(a)
Age (years) Midpoint Frequency
11 15
TABLE 1
(b) i)
ii)
(c) Refer graph on page 23.
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For
Examiners
Use
16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.
67 76 91 79 81 82 87 71
79 82 88 83 72 84 71 89
80 86 70 86 62 83 83 80
75 84 84 77 84 86 85 76
80 75 95 77 73 86 77 68
DIAGRAM 12
(a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in
the answer space.
[6 marks]
(b) For this part of the question, use the graph paper provided on page 26.
By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the
y-axis, draw an ogive based on the data.
[5 marks]
(c) From your ogive in (b), find the third quartile.
[1 mark]
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25
Answer:
a)
Marks Frequency Cumulative Frequency Upper Boundary
61 65
TABLE 2
b) Refer graph on page 26
c)
For
Examiners
Use
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INFORMATION FOR CANDIDATES
1. This question paper consists of two sections: Section A and Section B.
2. Answer all questions in Section A and four questions from Section B.
3. Write your answers in the spaces provided in the question paper.
4. Show your working. It may help you to get marks.
5. If you wish to change your answer, cross out the answer that you have done. Thenwrite down the new answer.
6. The diagrams in the questions provided are not drawn to scale unless stated.
7. The marks allocated for each question and sub-part of a question are shown inbrackets.
8. A list of formulae is provided on page 2 to 3.
9. A booklet of four-figure mathematical tables is provided.
10. You may use a non-programmable scientific calculator.
11. Hand in this question paper to the invigilator at the end of the examination.
-
Mathematics Form 4 Final year 2008Section A
[ 52 marks ]
No Marking Scheme Marks
1a)
b)
P1
P2 3
2 a) FSQ
Tan22 86
5
'3426/57.26
b) FSQ
Tan4
12
'3471/57.71
P1
K2
N1
P1
K2
N1
4
4
3 1227
27
722
21
627
27
722
31
21
5.269/21269
627
27
722
31
2112
27
27
722
21
K1
K1
K1
N1 4
L
KM
L
KM
-
No Marking Scheme Marks
4
1,61
01160156 2
x
xxxx K1
K1
N1,N1 4
5
31,2
01320253 2
p
pppp K1
K1
N1,N1 4
6
2,36020
48183
mnn
nm K1K1
N1, N1 4
7
8,35117
24163
khh
hk K1K1
N1, N1 4
8 a) 77
2223606021
7222
36045
0
0
0
0
OR
83.65/6565
777
222360601421
7222
3604521
0
0
0
0
b) 22 77
223606021
722
36045
OR
42.174@125174
77217
722
3606021
722
36045 22
0
0
K1
K1
N1
K1
K1
N1 6
-
No Marking Scheme Marks
9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6
b) If x is a factor of 10, then x is a factor of 5False
c) ,2 2 nn .......,4,3,2,1n
P1P1
P1P1
P1P1 6
10 a) 304012
ORPQ mm
15315336
xycORc
b) 15y
K1
K1N1
N1 4
11 a)21
3303
PQm
621
6)0(216
21
xy
cORc
mm RSPQ
K1, N1
K1
K1
N1 5
-
Section B[48 marks]
No Marking Scheme Marks
12 a)i
ii.
b)i.34
m
834
)9(344
xy
c
ii. 8340 x
6x
c) VWU
Tan125
P1
P2
K1
K1
N1
K1
N1
P1
K2
P Q
R
PQ
R
'3722/62.22 N1 12
-
No Marking Scheme Marks
13 a) i) a) Non-statementb) Statement
ii) andiii) all factors of 15 are factors of 30iv) a )
(b) i) 147222
36060
0
0
OR 77222
36030
0
0
147222
36060
0
0
+ 77222
36030
0
0
+14+7+7
3146 OR 46.34
ii) 1414722
36060
0
0
OR 77722
360300
1414722
36060
0
0
+ 77722
360300
= 89.83 2cm or6589
P1P1
P1P1P1P1
K1
K1
N1
K1
K1
N112
14
5,1051
056)( 2
mmmmma
2362206)(
edd
edb
cm
cmw
wc
6292298
292727
222187
87)(
22
K1N1N1,N1
K1K1N1N1
K1
K1, K1
N112
-
No Marking Scheme Marks
15 (a)
Age(years) Midpoint Frequency
11 - 15 13 6
16 20 18 8
21 25 23 10
26 30 28 13
31 35 33 7
36 40 38 6
All values in Column 1 correctAll values in Column 2 correctAll values in Column 3 correct
(b)
5.2550
127550
)6(38)7(33)13(28)10(23)8(18)6(13
(c) Refer to the graph
Axes drawn in the correct direction , uniform scale for 438 xand 130 y .Horizontal axis labeled using midpoint / upper boundary / classinterval6 points plotted correctly(8,0) and (43,0).Straight line passing 8 point.
P1P1P2
K2
N1
K1
P1P1P1P1
12
-
No Marking Scheme Marks
16 Marks Frequency Cumulativefrequency
Upperboundary
I55 60
II0
III0
IV60.5
61 65 1 1 65.566 70 3 4 70.571 75 6 10 75.576 80 10 20 80.581 85 11 31 85.586 90 7 38 90.591 - 95 2 40 95.5
All values in Column ( I ) correctAll values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correctAll values in Column ( IV ) correct
(b) x-axis and y-axis are drawn with the right direction and inuniform scale from 60.5 5.95 x , 110 y
All eight points* plotted correctly.Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed throughAll the right eight points plotted correctly and ogive is drawnsmoothly passing through all the points.
(c) 85 0.5
P1P2P2P1
K1
K2
K1N1
N112
-
8 13 18 23 28 330
2
4
6
8
10
12
14
Graph is not drawn to scale.
38
43
Frequency
Mid-point
Graph for Question 15.
-
655605 705 755 805 855 905
0
5
10
15
20
25
30
35
40
Graph is not drawn to scale.
Graph for Question 16.
95.5
CumulativeFrequency
UpperBoundary