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Mathematics
Analysis[1449/1][1449/2]
OPICPAPER 1 PAPER 2
08 09 10 11 12 08 09 10 11 12
FOR
M
1-3
1 Polygon I, II 7 6,7 7 7 7,8
2 ransformations I, II 9,1 9,1 9,1 9,1 1,11
3 rigonometry I 11
4 Algebraic Expressions I,II,III 19 19 19 19
5 Algebraic Formulae 21 2 2 21 21
6 Algebraic Fractions 2 21 21 2 2
7 Linear Equations 22 22 22 22 22 4 2 2 2 4
8 Indices 23 23,24 23,24 23,24 24,259 Linear Inequalities 24 25 25 25 25,26 3
1 Graph of Functions I
11 Solid Geometry I,II,III 5 11 4 7 6
12 Circles I,II 8 6 7 9 9
13 Statistics I,II 25,26,27 26,27 26,27 26,27 27,28
FOR
M
4
1 Standard Form 1,2,3,4 1,2,3 1,2,3,4 1,2,3,4 1,2,3,4
2 Quadratic Expressions andEquations
19 3 3 3 3 3
3 Sets 29,3,31 29,3,31 29,3,31 29,3,31 31,32 1 1 1 1
4 Mathematical Reasoning 6 7 5 5 5
5 Te Straight Line 32,33 32,33 32,33 32,33 33,34 1 5 6 6 7
6 Statistics III 29 14 16 14 14 14
7 Probability I 34,35 34,35 34,35 34,35 35,36
8 Circles III 8 8 8 8 9
9 rigonometry II 12,13 11,12,13 11,12,13 11,12,13 12,13
1 Angles of Elevation andDepression
15 15,16 15,16 15,16 15,16
11 Lines and Planes in3-Dimensions
14 14 14 14 14 2 5 11 4 2
FOR
M
5
1 Number Bases 5,6 4,5 5,6 5,6 5,62 Graph of Functions II 28 28 28 28 3 13 1,12 12 12 12
3 ransformations III 12 15 13 13 13
4 Matrices 39,4 39,4 39,4 39,4 39,4 11 9 8 8 11
5 Variations 36,37,4 36,37,4 36,37,4 36,37,38 37,38
6 Gradient and Area under aGraph
9 1 9 11 8
7 Probability II 7 8 1 1 1
8 Bearing 17 16 17 17 17
9 Earth as a Sphere 18 17,18 18 18 18 15 13 15 16 16
1 Plans and Elevations 16 16 16 15 15TOTAL 40 40 40 40 40 16 16 16 16 16
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Mathematic Paper 1 [1449/1]
1 Round of 6.59 correct to two signicant gures.A 6.5 C 6.1B 6.6 D 6.
2 State .38 in standard ormA 38 x 17 C 38 x 1-7B 3.8 x 14 D 3.8 x 1-4
3 A cube with sides o 43 mm. Find its volume, in cm3, correct tothree signicant gures.A 8. C 79.5B 79.5 D 79.5
4
A 1.98 x 13 C 6.6 x 13
B 1.98 x 1
4
D 6.6 x 1
4
5 112
11112
=
A 112
C 112
B 1112
D 1112
6 What is the value o digit 3 in base ve in the number 49 3281
?A 12 C 22B 22 D 222
7 In Diagram 7,PQRSTis a regular polygon.PUTis a straight line.VP = VU
Find the value ox.A 36 C 6
B 54 D 72
( )=
23
2
103
1094.5
om
o
50
P
Q
R
S
T
U
DIAGRAM 7
DIAGRAM 8
9 Diagram 9 shows a circle with centre O.LMandLNare tangentsto the circle at pointsMandNrespectively. Find the value ox.
A 3 C 5B 4 D 6
1 In the diagram, the straight linePQis the image o the line RSunder a reection.
Te axis o reection isA x = 2 C y = 2B x -axis D y-axis
11 Te point A (-5, 7) is the image o point A under atranslation . Find the coordinates o point A
A (3, 1) C (1, 3)B (-3,-1) D (-13, 13)
DIAGRAM 9
6
8
Answer all questions 8 In Diagram 8,PQRTUis a regular pentagon and RSTis astraight line. Find the value om.
A 36 C 65B 58 D 72
N
L
xo
50o
40o
M
O
2 S
Q
R
P4
0-2
-2
2-4
-4
4
S
Q
R
P
0-2
-2
-4
2-4 4
-4
2
4
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13 Diagram 13 shows the graph oy = sin x.
Te value op isA 9 C 27
B 36 D 18
14 Diagram 14, shows a pyramidPQRS. Te horizontal basePQRis a right-angled triangle. VertexP is vertically above S.
Name the angle between the linePRand the planePSQ.A C
B D
DIAGRAM 13
DIAGRAM 14
S
P
Q
R
RPS PRS
RPQ PRQ
Q
R
DIAGRAM 15
DIAGRAM 12
S
R
U
P Q
T
20 y
1213
12 In Diagram 12, SPQandPRUare right angle triangles. STQandPTUare straight lines.
It is given that cosyo = andPQ= QR. Calculate the length incm, oPTU
A 7.17 C 27.67B 65.94 D 25.54
15 In Diagram 15, Qand S are two points on a horizontal plane.Ris the top o a vertical agpole SR.
Te angle o elevation oRrom Qis 520 . Te distance betweenQand S is 14 m. Calculate the height, in m, o agpole RS.A 1.94 C 11.3B 15.59 D 17.92
16 Diagram 16 shows two towers on a horizontal plane
P and Qare two points on the top o the towers as shown. Risa point vertically belowQ. Te angle o elevation oQromP is550 and the angle o elevation oRromP is 40. Calculate thedistance, in m, rom Qto R.A 1.58 C 15.53B 35.34 D 29.5
DIAGRAM 16
P
Q
R
60m
17 In Diagram 17,P, Qand Rare three points on a horizontal
plane such thatPR = RQ = QP
Given that Qis due east oP, nd the bearing oQrom R.A 33 C 12B 15 D 6
18 P and Qare two points on the surace o the earth and thelatitude oP is 55N. Given that Qis located 15 south oP,nd the latitude oQ.A 4 S C 4NB 7 S D 7 N
19
A C
B D
P
R
Q
DIAGRAM 17
Q S
p
O
-1
1
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31 Diagram 31 is an incomplete Venn diagram showing the numbero elements in setsP, Qand R.
It is given that the universal set and .Find .
A 5 C 12B 6 D 17
P Q
R
46
2
3 1
7
DIAGRAM 31
2 Express as a single raction in its simplestrom.
21 Given that , express rin terms op.
22 Given that , calculate the value oa.
23 Given that , nd the value ox.
24 Simpliy
25 Which o the ollowing inequalities satisy the simultaneous
linear inequalities and ?
26 List all the integers x which satisy the inequality .
A 3, 4 C 2, 3, 4B 2, 3, 4, 5 D 1, 2, 3, 4, 5
27 able 27 is a requency table which shows the scores o students
in a test.
Calculate the mean score o the students.A 11.36 C 1.36B 9.36 D 9.17
Score Frequency
1-3 8
4-6 9
7-9 11
10-12 16
13-15 14
16-18 12
TABLE 27
28 Diagram 28 is a pie chart showing how Adam uses his incomeeach month. Adams income is RM3 5 per month. Adamssavings is RM35 and he spends 4% o his income onmiscellaneous.
It is given that x :y = 2 : 3. Find the value ox.A 72 C 18B 144 D 216
29 able 29 shows the requency distribution o the scores obtainedby a group o pupils in a game.
I 2 is the modal score, the minimum value ok isA 6 C 1B 9 D 11
3 Which o the ollowing graphs represents ?
A C
B D
DIAGRAM 28
TABLE 29
o
x House
o
y
Miscellaneous
Savings
Car
Score 1 2 3 4 5 6
Frequency 6 k 9 9 8 6
O
y
xO
y
x
O
y
x
J
O
y
x
5
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32 Diagram 32 is a Venn Diagram showing the universal set , setP,set Qand set R.
Which region,A, B, C or D represents the set ?
33 In Diagram 33,PORis a straight line and O is the origin.
Find the gradient oPOR.
34 Te gradient o the straight line is
35 24 students in a class are computer club members. A student ischosen at random rom the class. Te probability o choosing a
student who is not a computer club member is . Find the totalnumber o students in the class
A 32 C 4B 36 D 72
x y
4 8
25 20
TABLE 38
EnDOFQUESTIOnPAPER
37 It is given thaty varies inversely as the cube root ox andy = 6when x =8. Calculate the value ox wheny = 4.
A 3 C 12B 9 D 27
38 able 38 shows some values o the variables x andy such thaty varies directly as the square root ox.Find the relationshipbetweeny and x.
39 Given calculate the value ok .
A -3 C 4B -8 D 7
4 Find the value oh and ok in the ollowing matrix equation:
DIAGRAM 32
PQ
R
A
B
C
D
DIAGRAM 33
)5,3R
x
y
O
P
Pass Fail
Boy 8 4
Gr 20 x
TABLE 36
36 able 36 shows the result o a Mathematics test or a group ostudents.
A student is chosen at random rom the group. Te probability ochoosing a student who ailed the test is . Find the value ox.
A 1 B 3 C 4 D 5
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3 Solve the quadratic equation [4 marks]
Asw :
4 Calculate the values oe and ofwhich satisy the ollowing simultaneous linear equations :[4 marks]
Answer:
5 (a) State whether the ollowing sentence is a statement or a non-statement.
All multiples o 2 are divisible by 4
(b) Write down a true statement using both o the ollowing statements:
Statement 1 :
Statement 2 :
(c) Write down two implications based on the ollowing sentence:
y < x i and only i[4 marks]
Answer:
(a) ______________________________________________________________________________
(b) ______________________________________________________________________________
(c) Implication I : _________________________________________________________________
_________________________________________________________________
Implication II: _________________________________________________________________
_________________________________________________________________
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6 Diagram 6 shows a solid, ormed by joining a cylinder to a right prism. rapeziumAFGB is the uniorm cross-section o the prism.AB =BC = 9 cm. Te height o the cylinder is 6 cm and its diameter is 7 cm. Calculate the volume, in cm3, o the combined solid.
Use . [4 marks]
DIAGRAM 6
7 In diagram 7, O is the origin.
Te gradient o the linePQis . Find,
(a) the value ok.
(b) the equation o the straight line QR.
(c) the x-intercept o the straight line QR.[5 marks]
y
Q (k, 8)
6
-4
x0
R
P
DIAGRAM 7
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8 Diagram 8 shows the speed-time graph o a vehicle or a period o 15 seconds.
DIAGRAM 8
Calculate the(a) distance traveled during the rst 12 second.(b) value ov, i the rate o change o speed during the last 3 seconds is 5 ms-2. [6 marks]
9 In diagram 9,LKis an arc o a circle with centreP andPQRS is an arc o a circle with centre O.PORL is a straight line.
Giv KOL = 600,PK = 21 cm and OP = 7 cm. Using , calculate
a) the area , in cm2 o the shaded regionb) the perimeter in cm, o the whole diagram. [7 marks]
Answer:
P O R L
S
K
Q
60
DIAGRAM 9
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1 Diagram 1 shows six labelled cards in two boxes,P and Q,
A card is picked at random rom boxP and then a card is picked at random rom boxQ. By listing the sample o all the possible outcomes
o the event, nd the probability that
(a) a card with an odd number and the card labelledJare picked,
(b) a card with a number which is multiple o 2 or the card labelled Hare picked. [5 marks]
Answer:
DIAGRAM 10
11 (a) It is given that matrixM= and matrix such that .
Find the values op and q.
(b) Using matrices, calculate the values ox andy that satisy the ollowing matrix equation:
2x - 3y = 134x +y = 5
[7 marks]
Answer
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Graph or question 12
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13 (a) Te transormationRrepresents a 90 anticlockwise rotation about the center (3, 2).Te transormation Trepresents a translation . State the coordinates o the image o the point (1, 1) under the ollowingtransormations.
(i) R(ii) RT [3 marks]
Answer:(a) (i)
(ii)
(b) Diagram 13 shows three quadrilateralEFGH,ABCD and OFJK on a Cartesian plane.EFGH is the image oABCD under thetransormation U andEJKO is the image oEFGHunder the transormationV.
Describe completely the transormation,(i) U,(ii) V. [6 marks]
(c) Given that the shaded area is 12 unit2 , nd the area oABCD. [3 marks]
Answer:(b) (i)
(ii)
(c)
DIAGRAM 13
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14 Te data in the table shows the weight o 4 students in a class.
60 45 50 56 66 51 44 46 54 4753 48 49 49 48 65 52 50 51 5152 52 42 51 41 54 46 54 56 6058 39 53 59 58 63 47 64 43 59
(a) Based on the data in the table above, complete the table provided in the answer space using 5 kg as the size o the class interval.[4 marks]
(b) By using a scale o 2 cm to 5 kg on the x-axis and 2 cm to 5 students on they-axis, draw an ogive or the data.[4 marks]
(c) Based on the ogive in (b),i) Find the inter quartile range.ii) Briey explain the meaning o the third quartile in the graph. [4 marks]
Answer:(a)
c) (i) _________________________________________________________________
(ii) _________________________________________________________________
_________________________________________________________________
ClassIterval FrequecyCumulativeFrequecy
3 35
36 4
41 45
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Graph or question 14
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15 (a) Diagram 15(i) shows a solid prism with rectangular baseJKLMon a horizontal plane.ADEHJKis the uniorm cross-sectiono the prism. Te rectanglesABCD andAFGHare horizontal planes.AK,BI, CF,DE, GMand HJare vertical edges.Draw to ull scale, the plan o the solid.
[3 marks]
(b) A solid prism is joined to the prism in Diagram 15(i) at the vertical planeBCFGML to orm a combined solid as shown inDiagram 15(ii). Te trapeziumMNRS is the uniorm cross-section o the prism. TBL, SGM, RNand QP are vertical edges.
Draw to ull scale,
(i) Te elevation o the combined solid on a vertical plane parallel toKJas viewed romX. [5 marks]
(ii) Te elevation o the combined solid on a vertical plane parallel toJMNas viewed rom Y. [4 marks]
DIAGRAM 15 (i)
DIAGRAM 15 (ii)
G(.- (
A
B
3 cm
4 cm
5 cm
3 cm
2 cmL
H
G
J
K
M
N
P
T
S
R
D
FC
E
YX
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16 J(7S,37E),KandL are three points on the surace o the earth such thatJKis the diameter o the parallel o latitude 7S. Anaeroplane takes of romJand ies due east along its parallel o latitude until it reaches townK. Upon arrival in townKthe planechanges its crew and ies back toJusing the shortest distance measured along the surace o the earth. Aer reueling inJ,the aeroplane is instructed to y to townL which is located 54 nautical miles due north oJ.
(a) Find the longitude o townK. [2 marks]
(b) Find the latitude o townL. [3 marks]
(c) Calculate the distance, in nautical miles, traveled by the plane,
(i) From Jto K, measured along the parallel latitude.
(ii) FromKback toJ. [5 marks]
(d) Calculate the average speed, in knots, or the whole journey o the plane i the time taken to reachL is 22 hours. [2 marks]
Answer:
(a)
(b)
(c) (i)
(ii)
(d)
EnDOFQUESTIOnPAPER
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SOALAN ULANGKJI SPM 201314
Mathematic Paper 2
5m
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SOALAN ULANGKJI SPM 201316
10
a) 1/8
b) 7/8
1
2
2 5
11a)
b)
= 2, y= -3
1
1 1
1
1
1 1 6
(a) 16
-8
(b) Axes drawn in correct direction and correct scales
in
6 points and *2 points correctly plotted or curve passes through the points for
A smooth and continuous curve without any straight line and passes
through all 9 correct points for .
1
1
1
2
1
1
y
x
y = 15
x : x Intercept ( 0, 0)
y=-3x+5
y=-15/x
y = 2 - 3x
33 x
xy
16=
33 x
12
x
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SOALAN ULANGKJI SPM 2013 17
(c) (i)
(ii)
(d) Drawing
1
1 1
1 112
13 (a) (i) ( 4 , -2 )
(ii) ( 1 ,0 )
(b) (i) U 90o clockwise with centre ( 1 , 1 ).
(ii) V : Enlargement with scale factor 2 at F or( 4 , 0 ).
(c) 2
2
120 + AreaABCD = 2
2 ABCD
40
1
2
3
3
1
1
1
12
2726 y
4.131 x
xy 32=
15.205.2 x , 752652 x
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SOALAN ULANGKJI SPM 201318
14
a)
Marks Upper B Frequency Cumula ve
30 35 35.5 0 0
36 40 40.5 1 1
41 45 45.5 5 6
46 50 50.5 10 1 6
51 55 55.5 12 2 8
56 60 60.5 8 36
61 65 65.5 3 39
66 70 70.5 1 40
b) i)
c)(i) Q1 = 48, Q3 = 56.3 bothInter-qu le range (IQR) = 56.3 48
= 8.3
(ii) The third qu le means that
..... 30 students in the class weigh not more (less) than 56.3 kg. OR
2
1
1
1
1
1
1
1
1
Frequency
Cumu ve F
Upper boundary
Point (35.5, 0)
8 points connected
Smooth curve
Uniform axes
35.5 40.5 45.5 50.5 55.5 60.5 65.5 70.5
..... 10 students in the class weigh not less (more) than 56.3 kg 2 12
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15 a)
B i)
B ii)
3
4
5
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16 (a) 1430
B
(b) 900
- 7060
5400
200
N
(c) (i) 180 x60 xcos 70 3693.8 n.m
(ii) { 180 (70+70) } x 60
2400
(d)
522.45
1 1
1
1
1
1
1
1
1
1
1
1
12
22
5400)7060180(60)}7070(180{ +++ kos
END OF MARKING SCHEME
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