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CHAPTER 2 : QUADRATIC EXPRESSIONS
EXERCISE 1
1. x2 – 5x – 24
2. x2 – 9
3. mx + my – x – y
4. 2x2 + 5x – 3
5. – x2 – x – 8
6. 2x2 – 18x
7. 2x2 – 11x – 40
8. 3u2 – 5us + 2s2
9. 5x – 5x2
10. –u2 + u + 15
EXERCISE 2
1. 3p2 – 3pq + q2
2. 2q2 – 2pq
3. 6f2 – fg – 2g2
4. 3hk – 17h2
5. 6x2 + 2x + 1
6. – 3p2 – q2
7. – 16x + 16
8. 9x2 – 11x – 4
9. a2 – 56a + 16
10. 3m2 + 5k2 – 4mk
DIAGNOSTIC TEST
1. B
2. D
3. B
4. A
5. B
6. A
7. C
8. D
9. C
10. B
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CHAPTER 2 : QUADRATIC EXPRESSIONS AND EQUATIONS
EXERCISE 1
1. p(p – 2)
2. (2x-9)(2x+9)
3. (r – 6)(r + 2)
4. k= 2 , 10
5. Area = 12x2 + 3x
EXERCISE 2
−4 1
1. b = ,
3 2
2. ( 3 + 2x ) ( 2 – 7x )
1
3. w = - , w=3
2
4. m=4, m=-2
5. Johan’s age is 6 years old
DIAGNOSTIC TEST
1
1. y = 0 ,
3
2
2. y = - , y=1
3
3
3. y = -1 ,
2
5
4. x = 2,
3
5. (a) (2x)2 + 92 = (x + 9)2
(b) AC = 12 cm
Panitia Matematik Daerah Seremban 2006
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CHAPTER 3 : SETS
EXERCISE 1
1. 5
2. {E,R,N}
3. 9
4. { 3 , 7 , 9 , 12 }
5. 18
6. { 11 , 13 , 14 , 16 , 17 , 19 }
7.
K
L M
8. 10
9. IV
10. 25
DIAGNOSTIC TEST
1. D 2. C 3. A 4. C 5. B
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CHAPTER 3: SETS
EXERCISE 1.
1. . a. A∪ B b.
A
AC C
B B
DIAGRAM 1 DIAGRAM 2
2. a. . P ∩ Q ∩ R’ b. P ∪ Q ∩ R '
P
P Q R Q
R
DIAGRAM 3 DIAGRAM 4
3. a b.
E E
F
G
G F
DIAGRAM 5 DIAGRAM 6
c. DIAGRAM 7
E
c.
G
F
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4. a) i. 3 5. a) 11
ii. 2 b) 3
b) i. 5 c) 13
ii. 6
EXERCISE 2
1. (a) B = {20, 30} C = {20, 21, 30, 31, 32}
(b) 4
(c) 2
2.
(a) T
S •7
•3 •8 •12
•1 R •2 •4
•6 •0
(b) {2, 3, 4, 5, 6}
(c) 7
3.
(a) P∩Q (b) P'∩Q∩R
P Q P Q
R R
DIAGRAM 1 DIAGRAM 2
4. (a) P = {21, 24, 27, 30}
(b) Q= {20, 25}
(c) 2
Panitia Matematik Daerah Seremban 2006
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5.
Q P Q
(a)
R
P R
R
DIAGRAM 3 DIAGRAM 4
DIAGNOSTICS TEST
1.
(a) ξ (b) ξ
P P
Q R Q
R
DIAGRAM 1 DIAGRAM 2
2.
(a) K (b)
J L J K L
DIAGRAM 3 DIAGRAM 4
3. (a) (b) P R
P R
S S
DIAGRAM 5 DIAGRAM 6
Panitia Matematik Daerah Seremban 2006
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4. A
(a) (b) A
B B C
C
DIAGRAM 7 DIAGRAM 8
(c) A
B C
DIAGRAM 9
5.
ξ
J K
L
DIAGRAM 10
Panitia Matematik Daerah Seremban 2006
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CHAPTER 4 : MATHEMATICAL REASONING
EXERCISE 1
1(a) true
(b) Implication 1: If x is a multiple of 3 , then it is divisible by 3.
Implication 2: If x is divisible by 3 , then it is a multiple of 3.
(c) Premise 2 : y is less than zero.
2 (a) Statement.
(b) Conclusion: The side of cube p is not 4 cm.
(c) 10 m x 10 n = 10 m+n
3 (a) 52 = 10 or 1 = 0.25
4
(b) Premise 2 : x is an angle in a semicircle.
(c) some
4 (a) Some even numbers are divisible by 4.
(b) (i) false
(ii) true
(c) Conclusion : m > 0
5 (a) statement . It’s a false statement.
(b) ‘2 is multiple of 4…or...... x + 2x = 3x’
(C) Premise 1 : All quadrilaterals have 4 sides.
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EXERCISE 2
1(a) Implication 1: If x – g > y – g , then x > y
Implication 2: If x > y, then x – g > y – g
(b) i) Some
ii) All
2 (a) i) k < 3
ii) 2 is a factor of 4
(b) or
3 (a) The numerical sequence is represented by n 2 − 1 where n = 1, 2, 3, 4,…
(b) All angles less than 90º are acute angles
4 (a) If tan α =1, then α = 45º
If α = 45º, then tan α = 1
(b) If –1 x a > 0, then a < 0.
(c) True
5 (a) n is not an even integer
(b) All isosceles triangles have two sides of equal length.
(c) It is a statement because it can be determined as a true statement.
DIAGNOSTIC TEST
1(a) (i) non statement
(ii) statement
(b) (i) >
(ii) >
(c) All
(d) 5 has only two factors.
2(a) (i) true
(ii) false
(b) Implication 1: If mn = 0 , then m = 0 or n = 0
Implication 2: If m = 0 or n = 0, then mn = 0
(c) Premise 2: The circumference of circle P is not 10п
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3 (a) Some odd numbers are prime numbers.
(b) 3 + (- 2) = 5 or 16 is a perfect square.
(c) Premise 1 : If the sum of interior angles of a polygon is 540° , then it is a
pentagon.
4(a) Antecedent : a triangle has two equal sides.
Consequent : it is an isosceles triangle.
(b) (i) If x < 6, then x < 4 , false
(ii) If A ⊂ B , then A ∩ B = A , true
(c) 2 + 7 n where n = 0,1,2,3,…….
(d) Premise 1 : If M is a subset of N then M ∩ N = M
5.(a) (i) true
(ii) false
(b) some
(c) Premise 1 : All natural numbers are grater than zero .
(d) n2 is an odd number if and only if n is an odd number
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CHAPTER 5 : THE STRAIGHT INE
EXERCISE 1 EXERCISE 2
1 a) 1 b) -2 1 6
2 a) 3 b) y =3x +3 1
2 a) k = -1 b) -
1 6
3 -
4 3 a) 2 b) y = 2x -11
4 6 4 a) y = -3 x + 6 b) R(0,-6)
1 5 a )k = 6 b) y = -x + 6
5 - 2
2 6 a) -6 b) -
1 3
6 − 19
3 7 a) 4 b)
7 3 2
1 8 a) (6,9) b) 3
8 − 5
4 9 a) − b) y = 3x -1
9 y=x+4 3
10 a) M(0 ,4 ) b) x = 6 10 ( 6,0)
DIAGNOSTIC TEST
1. C
2. C
3. D
4. D
5. A
6. C
7. B
8. D
9. A
10. B
Panitia Matematik Daerah Seremban 2006
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CHAPTER 5 : THE STRAIGHT LINE
EXERCISE 1
1 a) 2 b) y = 2x-3 c) 1.5
2 a) -3 b) y = -3x + 15 c) 15
3 a) 10 b) y = 2x – 4 c) (0,4)
4 a) (5,0) b) -20 c) y = 4x - 20
5 a) 6 b) 2 c) 2y = -x + 4
EXERCISE 2
5
1 a) y = 10 b) -8 c) y = x + 10
4
1 1
2. a) - b) y = − x + 8 c) 16
2 2
3. a) -7 b ) 24 c ) y = -4x + 24
3
4. a ) ( 0 , 5 ) b)y= x+5
2
5. a ) 3 b ) y = 3x – 9 c ) -9
DIAGNOSTIC TEST
1 1
1. a)- b) (0, 3) c) y=- x+8
2 2
12 12
2. a) 9 b) y= x–5 c) y= x+9
5 5
2 2
3. a) (0, 8) b) c) y= x +8
3 3
4. a) k = 5 b) y = -x + 2 c) (2, 0)
5. a) h = 8, k = 6 b) 7y = -3x + 33
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4.
(a) Based on the data in Diagram 3 and by using a class interval of 5, complete Table
2.
Class interval Frequency Midpoint
20 – 24 4 22
25 – 29 8 27
30 – 34 10 32
35 – 39 5 37
40 – 44 2 42
45 – 49 1 47
(22 × 4) + (27 × 8) + (32 × 10) + (37 × 5) + (42 × 2) + (47 × 1)
(b) Mean =
4 + 8 + 10 + 5 + 2 + 1
= 31.33
5.
(a) 30 cm
(b)
Upper
Height (cm) Frequency Midpoint
boundary
10 – 16 5 13 16.5
17 – 23 6 20 23.5
24 – 30 7 27 30.5
31 – 37 10 34 37.5
38 – 44 2 41 44.5
TABLE 3
(c)
i) (31 – 37) cm
(13 × 5) + (20 × 6) + (27 × 7) + (34 × 10) + (41 × 2)
ii) Mean =
5 + 6 + 7 + 10 + 2
= 26.53 cm
Panitia Matematik Daerah Seremban 2006
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CHAPTER 7 : PROBABILITY 1
Exercise 1
1. (a) {1,3,5}
(b) {3, 6}
2. (a) P = { N, E, R}
(b) Q = { N, R, 3, 9 }
3. 11
4. (a) HH, TT
(b) HT, TH
5. 28
6. 146
1
7. (a)
6
2
(b)
3
8. 90
1
9.
3
10. (a) 135
(b) 30
Exercise 2
1. 9
2. O, A, I, I
3. HHT , HTH , THH
1
4.
3
5. 7
6. 110
7. 6
8. 30
9. 80
7
10.
30
Diagnostic Test
1. A 6. A
2. B 7. C
3. A 8. B
4. D 9. C
5. B 10. B
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CHAPTER 8: CIRCLES III
EXERCISE 1
DIAGNOSTIC TEST
Answers:
1. a) 35˚ b) 35˚ 1. B 70˚ 6. A 76˚
2. a) 70˚ b) 70˚ 2. D 70˚ 7. B 132˚
3. a) 80˚ b) 30˚ 3. A 30˚ 8. D 40˚
4. a) 115˚ b) 30˚ 4. A 40˚ 9. B 80˚
5. a) 56˚ b) 24˚ 5. C 30˚ 10 C 96˚
6. 65˚
7. 41˚
8. 6˚
9. 64˚
10. 70˚
EXERCISE 2
1a) 60˚ b) 60˚ c) 30˚
2a) 24˚ b) 24˚ c) 156˚
3a) 66˚ b) 33˚ c) 57˚
4a) 40˚ b) 70˚ c) 20˚
5a) 56˚ b) 22˚
6. 40˚
7. 28˚
8. 14˚
9. 105˚
10. 130˚
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CHAPTER 9: TRIGONOMETRY II
EXERCISE 1: EXERCISE 2:
3 8
1. sin x = (1)
5 17
− 12
2. cos y = (2) 4.8 cm
13
3. 5
(3) 216 o 26' or 216.4 o
4. y = sin x
(4) – 0.75
o
5. 20
5
6. 0.4743 (5) −
13
7. 0.8944
(6) 240 o
8. BC = 15 cm
8
(7) −
9. BC = 16 cm 17
10. AB = 12 cm (8) 9 cm
15
(9) −
17
4
(10)
5
DIAGNOSTIC TEST:
(1) C
(2) B
(3) A
(4) D
(5) C
(6) A
(7) A
(8) D
(9) B
(10) B
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CHAPTER 10 : ANGLES OF ELEVATION AND DEPRESSION
EXERCISE 1
1. ∠RPQ
2. 61.44m
3. 5.2m
4. 14.69m
5. 12.29m
6. 20o
7. 7.4m
8. 58o
9. 50o 54’
10. 30o
EXERCISE 2 DIAGNOSTIC TEST
1. 14m 1. D
2. 84m 2. A
3. 15m 3. C
4. 69.28m 4. C
5. 23m 5. B
6. 58.32 m 6. C
7. a) 458 m 7. D
b) 56° 46’ 8. B
8. a) 40° 9. B
b) 22° 10. A
c) 43.07m
9. a) 6.882 m
b) 16° 12’
10. a) CD- 14.66
EF- 0.671
b) 7.1° 4’
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CHAPTER 11 : LINES AND PLANES IN 3-DIMENSION
EXERCISE 1 (paper 1)
1. a) ∠DBH b) ∠AHB c) ∠EBA
2. a) ∠CHG b) ∠AGE
3. a) ∠QRP b) ∠VRU
4. a) ∠GRF b) ∠CED c) ∠GQP
5. a) ∠AZM b) ∠AYM c) ∠NBX
EXERCISE 2
1. a) ∠EDH b) ∠CHG c) ∠GDH
2. ∠PEM = 33° 41 '
3. ∠TRS = 28° 18 '
4. a) ∠DXS b) i) 9.17 cm b) ii) 23° 35 '
5. a) 60° b) 26° 34 ' c) ∠SAT
DIAGNOSTIC TEST
1. a) ∠EDF or ∠ACB
b) 19° 26 ' or 19.44°
2. a) ∠PRQ
b) 49° 41 ' or 49.68°
3. 32°
4. 24° 47 ' or 24.8°
5. 36° 52 ' or 36.9°
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5. ∠ QTU = 26º 34´
6. ∠ HUS = 36º 52´
7. ∠ PZQ
8. ∠ WHT
9. ∠ VSM = 24º 47´
10. ∠ LRQ = 32°
DIAGNOSTIC TEST
1. B
2. B
3. C
4. C
5. D
6. B
7. B
8. C
9. D
10. C
Panitia Matematik Daerah Seremban 2006