ceramah spm kelas tam cuti mei 2014
TRANSCRIPT
![Page 1: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/1.jpg)
MATHEMATICS
SPM 2014EN TAN CHUN NAM
![Page 2: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/2.jpg)
Format for SPM MathematicsMARKS: 40 marksNo. of Questions :40 questionsDuration: 75 minutes (1.8 minutes every question)INSTRUCTIONSAnswer all questionsScientific Calculator is allowed
![Page 3: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/3.jpg)
Format for SPM MathematicsMARKS: 100 marksNo. of Questions :Section A : 11 questionsSection B : 5 questionsINSTRUCTIONSAnswer all questionsScientific Calculator is allowed
![Page 4: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/4.jpg)
Format for SPM MathematicsINSTRUCTIONSSection A[52 marks - 78 minutes]11 questions, answer all questionSection B[48 marks - 72 minutes]Choose 4 questions out of 5.(18 minutes every question)
TOTAL =140 MARKS
![Page 5: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/5.jpg)
No Topic No. of questions
1 Polygon I & II 22 Transformations 1 & II 23 Algebraic Expressions I, II, III 14 Algebraic Formulae 15 Algebraic Fractions 16 Linear Equations I & II 1
![Page 6: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/6.jpg)
No Topic No. of questions
7 Trigonometry I 18 Indices 29 Linear Inequalities 110 Statistic I & II 3
![Page 7: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/7.jpg)
No Topic No. of questions
1 Standard Form 3 @ 42 Set 33 The Straight Line 24 Circles III 15 Trigonometry II 2 @ 36 Lines and Planes in 3-Dimensions 17 Angle of Elevation and Depressions 1 @ 2
![Page 8: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/8.jpg)
No Topic No. of questions
1 Number Bases 22 Matrices 1 @ 23 Variations 2 @ 34 Probability I & II 2 @ 35 Bearing 16 Earth as a Sphere 1 @ 27 Graph of Functions 1
![Page 9: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/9.jpg)
No Topic MarksSPM 2013
1 Set 32 Simultaneous Linear
Equations4
3 Quadratic Equations 34 Lines and Planes in 3
Dimensions3
SPM kertas 2
![Page 10: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/10.jpg)
No Topic MarksSPM 2013
5 Straight Lines 56 Circles 67 Mathematical
Reosening6
8 Probability 5
SPM kertas 2
![Page 11: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/11.jpg)
No Topic MarksSPM 2013
9 Matrices 610 Gradient and Area
under a Graph6
11 Solid Geometry 5
SPM
![Page 12: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/12.jpg)
No Topic Marks2011 2012 SPM
201312 Graph Functions kubic kuad kub1213 Planes and Elevasion 1214 Earth as a sphere 1215 Transformations 1216 Statistic. HISTOG
12P.KE
12PKE12
SPM
![Page 13: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/13.jpg)
![Page 14: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/14.jpg)
QUADRATIC EQUATION
REARRANGE TO GENERAL FORM OF QUADRATIC EQUATION
02 cbxax
Factorise 0
State the values of x
![Page 15: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/15.jpg)
7,31
0713
n
nn
07203
014763)21(7632
22
nn
nnnnnn
Solve the quadratic equation nnn 21763 2
Factors must be given by using the
whole number
![Page 16: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/16.jpg)
Solve the quadratic equation 22 5 33
k k
K1
K1
N1 N1
![Page 17: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/17.jpg)
Solve the quadratic equation 22 5 33
k k
K1
K0
N0 N0
![Page 18: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/18.jpg)
Solve the quadratic equation 22 5 33
k k
K1
K0
N0 N0
![Page 19: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/19.jpg)
101
10
![Page 20: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/20.jpg)
K1
K1
N1 N1
![Page 21: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/21.jpg)
![Page 22: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/22.jpg)
Elimination method
SIMULTANEOUS LINEAR EQUATIONS
Substitution method
Matrix method
4 MARKS
![Page 23: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/23.jpg)
Substitution method
qpqp 627276
965 qp1
2
49630135
96)627(5
qqqqq
3)4(627
pp
1 2substitute into
Correct operation
276 qp965 qp
K1
K1
N1 N1
![Page 24: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/24.jpg)
101
10
![Page 25: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/25.jpg)
K1
N1
5 8 38 3
5
x yyx
8 3 1 55 2
y y
16 6 5 5011 66
66 611
y yy
y
8 3(6) 10 25 5
x
K1 N1
Substitution method
![Page 26: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/26.jpg)
![Page 27: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/27.jpg)
ExampleExample
Shade the setShade the setI
VIVIII IVII
C
B
A
CBA )(
1. Label each part.
![Page 28: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/28.jpg)
2. Identify the shaded region2. Identify the shaded region
(A B) U C(A B) U C
I
VIVIII IVII
C
B
A
III, IV U IV, V
U
III, IV, V
![Page 29: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/29.jpg)
3. Shade the region mark with3. Shade the region mark with III, IV, VIII, IV, V
(A B) U C
U
![Page 30: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/30.jpg)
101
10
![Page 31: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/31.jpg)
1
2 3 4
P’ = 1,3,4Q = 1,2,3P’∩ Q = 1,3
1
2 3 4
P = 2 Q’ = 4P ∪Q’= 2,4R = 3,4(P∪Q’)∩R= 4
1
2 3P1
P2
![Page 32: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/32.jpg)
![Page 33: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/33.jpg)
C
A D
CB
6
G
H
F
E 6
6
LINES AND PLANES IN 3 DIMENSION
Name the angle between the line CE and the plane EFGH
C E
E F G H
E GTan θ= 6 √72
θ= 35.26°
K 2
N1
P1
![Page 34: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/34.jpg)
Find the angle between the plane JFE and the plane DEF.L
E
DF
J
M5
513
5
Answer : JMD
![Page 35: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/35.jpg)
22 513
5
Tan JMD
JMD'3722
62.22o
o
atau
L
E
DF
J
M5
513
5
![Page 36: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/36.jpg)
![Page 37: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/37.jpg)
8
12
![Page 38: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/38.jpg)
![Page 39: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/39.jpg)
THE STRAIGHT LINE – 6 MARKSREMEMBER :
1. Gradient
2. Equation of a line21
21
xxyym
cmxy
![Page 40: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/40.jpg)
REMEMBER :
3. Parallel lines , same gradient 21 mm
THE STRAIGHT LINE
![Page 41: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/41.jpg)
REMEMBER :
5. x-intercept , substitute
6. y-intercept , substitute
0y
0x
THE STRAIGHT LINE
![Page 42: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/42.jpg)
![Page 43: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/43.jpg)
21
m
21
m
P1
![Page 44: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/44.jpg)
1
![Page 45: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/45.jpg)
![Page 46: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/46.jpg)
Solid Geometry & Volume
Combination of two solid geometry
1. Determine the two solids involved
2.Choose the operations + or -
3.Write the correct formulae
4.Substitute the values of r, h, d
Use 722
![Page 47: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/47.jpg)
Example 1 A hemisphere PQR has taken out from the cylinder.
Find the volume of the remaining solid.
32
32 rhr
555722
32855
722
P
Q
R
10 cm
8 cm
Cylinder - hemisphere
32366
![Page 48: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/48.jpg)
The diagram shows a solid cone with radius 9 cmand height 14 cm. A cylinder with radius 3 cm and height 7 cm is taken out of the solid.
Calculate the volume,in cm3 , of theremaining solid.
Use 722
Example 2Example 2
![Page 49: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/49.jpg)
Diagram 3 shows a solid cone with radius 9 cm andheight 14 cm. A cylinder with radius 3 cm and height 7cm is taken out of the solid.
14 cm
9 cm
7 cm
3 cmhrhrV 22
31
73722149
722
31 22
9901981188 V
![Page 50: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/50.jpg)
![Page 51: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/51.jpg)
![Page 52: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/52.jpg)
![Page 53: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/53.jpg)
CIRCLES : Perimeter and Area
722
1. Use the correct formulae
2. Substitute with the correct values.
rP 2 rP 2360
2rA 2
360rA
![Page 54: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/54.jpg)
V
S
P
R6 cm
T
6 cm
9 cm
30O
7 cm
6 cmU
Q
W
a) Find the perimeter of the shaded region
b) Calculate the area of the shaded region
![Page 55: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/55.jpg)
(a).
Perimeter = PU + UV + VQ + ( PQ – ST ) + SWT
7218
7131@ 14.31@
27
7222
3601807966
7222
360309
7218
V
SP
R6 cm
T
6 cm
9 cm
30O
7 cm6 cm
U
Q
W
![Page 56: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/56.jpg)
(b).
2
2
6722
36030
27
722
360180912
21
28709
28925@ 32.25@
V
SP
R6 cm
T
6 cm
9 cm
30O
7 cm6 cm
U
Q
W
Area = area of triangle – area of semicircle – area of the sector
![Page 57: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/57.jpg)
![Page 58: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/58.jpg)
K1 1
![Page 59: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/59.jpg)
120 22 180 22 60 227 7 3.5 3.5 3.5 3.5360 7 360 7 360 7
A
K1 K1
N1
![Page 60: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/60.jpg)
![Page 61: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/61.jpg)
MATHEMATICAL REASONING
9229
Is the following sentence a statement ? Give your reason.
Statement Not acceptedyes
A statement.It is a false statement.
answer
![Page 62: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/62.jpg)
Make a conclusion for the number sequence below
712
312
112
012
3
2
1
0
...,3,2,1,0,12 nn
3 dots
2 MARKS
![Page 63: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/63.jpg)
-1 marks
2n ─ 1
2n ─ 1 , n = 0 , 1 , 2 , 3 , ..
2n ─ 1 , n = 0 , 1 , 2 , 3 ,
2n ─ 1 , n = 0 , 1 , 2 ,
![Page 64: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/64.jpg)
12553 pjikahanyadanjikap
Write two implication
Jika , maka p = 125
Jika p = 125 ,maka
53 p
53 p2 marks
, maka p = 125
jika p = 125 ,
53 p
53 pno mark
![Page 65: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/65.jpg)
Premise1 : All A are BPremise 2 : C is AConclusion : C is B
PQRST has a hexagon
![Page 66: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/66.jpg)
Complete the following argument
164 x
Premise1 : If 4x = 16 , then x = 4Premise 2 : Conclusion :
4x
Premise1 : If A , then BPremise 2 : A trueConclusion : B true
![Page 67: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/67.jpg)
Complete the following argument
Premise1 : If 4x = 16 , then x = 4Premise 2 : Conclusion :
Premise1 : If A , then BPremise 2 : A FalseConclusion : B False
4x164 x
![Page 68: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/68.jpg)
![Page 69: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/69.jpg)
A Statement
R P then P R P IfP R P then R P If
P1
P1
P1
![Page 70: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/70.jpg)
P1 P1
![Page 71: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/71.jpg)
![Page 72: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/72.jpg)
KEBARANGKALIAN
)()()(
SnAnAP
![Page 73: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/73.jpg)
10. Diagram 9 shows two boxes , P and Q . Box P contains four cards labeled with letters and box Q
contains three cards labeled with numbers.
TSEB 764
Two cards are picked at random, a card from box P and another card from box Q .a)List the sample space and the outcomes of the events . b) Hence , find the probability that(i)a card labeled with letter E and a card labelled with an even number are picked (ii)(ii) a card lebelled with letter E or a card labelled with an even number are picked
P Q
![Page 74: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/74.jpg)
a) {(B, 4), (B, 6), (B, 7), (E, 4), (E, 6), (E, 7), (S, 4), (S, 6), (S, 7), (T, 4), (T, 6), (T, 7)}
Notes : 1. Accept 8 correct listings for 1 mark
b) i) {(E, 4), (E, 6)}
ii) {(E, 4), (E, 6), (E, 7), (B, 4), (B, 6), (S, 4), (S, 6), (T, 4), T,6)}
61@
122
43@
129
![Page 75: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/75.jpg)
11
1
11
![Page 76: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/76.jpg)
1
1
1
1
1
![Page 77: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/77.jpg)
![Page 78: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/78.jpg)
![Page 79: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/79.jpg)
35
241012
1
![Page 80: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/80.jpg)
![Page 81: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/81.jpg)
![Page 82: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/82.jpg)
52
13215
1
171
m 1n
![Page 83: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/83.jpg)
![Page 84: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/84.jpg)
621193
yx
yx
69
21131
yx
![Page 85: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/85.jpg)
69
21131
yx
69
11132
)3(11)2(11
yx
![Page 86: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/86.jpg)
69
11132
)3(11)2(11
yx
30
930
311
6991818
311
yx
![Page 87: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/87.jpg)
30
930
311
6991818
311
yx
3,0 yx
![Page 88: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/88.jpg)
36
4231
nm
23,
23
36
1234
101
nm
nm
P1
K1
N1 N1
![Page 89: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/89.jpg)
36
4231
nm
23,
23
1234
36
101
nm
nm
P0
K0
N0 N0
![Page 90: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/90.jpg)
36
4231
nm
23,
23
1234
36
101
nm
nm
P1
K0
N0 N0
![Page 91: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/91.jpg)
![Page 92: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/92.jpg)
K1 K1
![Page 93: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/93.jpg)
![Page 94: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/94.jpg)
![Page 95: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/95.jpg)
P1
![Page 96: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/96.jpg)
P1
![Page 97: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/97.jpg)
K1
![Page 98: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/98.jpg)
![Page 99: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/99.jpg)
![Page 100: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/100.jpg)
![Page 101: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/101.jpg)
gcmpb
![Page 102: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/102.jpg)
gcmpb
![Page 103: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/103.jpg)
gcmpb
![Page 104: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/104.jpg)
gcmpb
![Page 105: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/105.jpg)
gcmpb
![Page 106: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/106.jpg)
gcmpb
![Page 107: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/107.jpg)
gcmpb
![Page 108: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/108.jpg)
gcmpb
![Page 109: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/109.jpg)
![Page 110: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/110.jpg)
P1
![Page 111: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/111.jpg)
P1
![Page 112: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/112.jpg)
![Page 113: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/113.jpg)
P3
![Page 114: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/114.jpg)
![Page 115: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/115.jpg)
object of Area Image of Area 2 k
K1
K1
N1
![Page 116: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/116.jpg)
![Page 117: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/117.jpg)
2014 ???2013 POLIGON KEKERAPAN2012 POLIGON KEKERAPAN2011 HISTORAM2010 OGIF2009 HISTOGRAM2008 POLIGON KEKERAPAN 2007 OGIF2006 POLIGON KEKERAPAN2005 HISTOGRAM2004 HISTOGRAM2003 OGIF
![Page 118: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/118.jpg)
![Page 119: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/119.jpg)
Marks Midpoint Frequency20 – 24 22 525 - 29 27 730 - 34 32 835 - 39 37 1040 - 44 42 645 - 49 47 450 - 54 52 2
962524476421037832727522
84.10696
10257
![Page 120: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/120.jpg)
![Page 121: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/121.jpg)
Marks Midpoint Frequency20 – 24 22 525 - 29 27 730 - 34 32 835 - 39 37 1040 - 44 42 645 - 49 47 450 - 54 52 2
![Page 122: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/122.jpg)
![Page 123: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/123.jpg)
OGIF
020406080
100120
SEMPADAN ATAS
KEK
ERA
PAN
LO
NG
GO
KA
N
Upper boundary
Cumulative frequency Full marks
![Page 124: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/124.jpg)
OGIF
020406080
100120
SEMPADAN ATAS
KEK
ERA
PAN
LO
NG
GO
KA
N
Upper boundary
Cumulative frequency
less marks
![Page 125: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/125.jpg)
OGIF
0102030405060708090
100110
MARKAH
KEK
ERA
PAN
LO
NG
GO
KA
N
limit
Cumulative frequency
No mark
Upper boundary
![Page 126: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/126.jpg)
![Page 127: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/127.jpg)
![Page 128: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/128.jpg)
TABLE FOR HISTOGRAM
CLASSfrequency
fmidpoint x
Upper boundary
36 – 40 41 – 4546 – 5051 – 55 56 – 60 61 – 65 66 – 70 71 – 75
JUMLAH 50
0461210558
3843485358636873
40.545.550.555.560.565.570.575.5
![Page 129: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/129.jpg)
Full mark
![Page 130: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/130.jpg)
40.5 45.5 50.5 55.5 60.5 65.5 70.5 75.5
Full mark
![Page 131: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/131.jpg)
41 -
45
46 -
50
51 -
55
56 -
60
61 -
65
61 -
70
71 -
75
Full mark
![Page 132: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/132.jpg)
-1 mark
Should have gap
![Page 133: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/133.jpg)
41 - 45 46 - 50 51 - 5556 - 60
61 - 6561 - 70 71 - 75
no mark
![Page 134: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/134.jpg)
![Page 135: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/135.jpg)
![Page 136: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/136.jpg)
30 – 3435 – 3940 – 4445 – 4950 - 54
273237424752
578
10642
![Page 137: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/137.jpg)
22 5 25 7 32 8 37 10 42 6 47 4 52 242
1469 34.9842
![Page 138: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/138.jpg)
![Page 139: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/139.jpg)
P1 P1 P1 P1
![Page 140: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/140.jpg)
![Page 141: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/141.jpg)
K1
K1
K2 N1
![Page 142: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/142.jpg)
K1
K1
N1
![Page 143: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/143.jpg)
![Page 144: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/144.jpg)
![Page 145: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/145.jpg)
![Page 146: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/146.jpg)
6
5
3 K1 K1 K1 N1
![Page 147: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/147.jpg)
![Page 148: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/148.jpg)
7
7
8
8
![Page 149: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/149.jpg)
7
8
52
5
5
K1 K1 N2
![Page 150: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/150.jpg)
8
6
8
6
![Page 151: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/151.jpg)
8
6
3 3
5
33
3
3 K1 K1 N2
![Page 152: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/152.jpg)
![Page 153: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/153.jpg)
63125W
0 180 E180 W 125 W180
?
55 E63
30
![Page 154: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/154.jpg)
63125W 55 E63
30
25 E
P2P1
![Page 155: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/155.jpg)
63125W 55 E63
30
25 E
6354
N1K1 K1
![Page 156: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/156.jpg)
63125W 55 E63
30
25 E
N1K1K1
![Page 157: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/157.jpg)
63125W 55 E63
30
25 E
63
![Page 158: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/158.jpg)
63125W 55 E63
30
25 E
63 SpeedceDisTime
TimeceDisSpeed
tan
tan
43.16510
18.8377
N1K1
K1
![Page 159: CERAMAH SPM Kelas Tam Cuti Mei 2014](https://reader037.vdocuments.site/reader037/viewer/2022102703/577cc57c1a28aba7119c8dad/html5/thumbnails/159.jpg)