This document contains sample answers and solutions to exercises in a math textbook. It includes: 1) Answers to standard form exercises and diagnostic tests in Chapter 1. 2) Answers to quadratic expressions exercises and diagnostic tests in Chapter 2. 3) Answers to sets exercises and diagnostic tests in Chapter 3. 4) Sample exercises and answers on mathematical reasoning in Chapter 4. 5) Sample exercises and answers on straight lines in Chapter 5. The document provides concise worked out solutions to math problems across multiple chapters in a standardized format for student practice and review.

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ANSWERS
CHAPTER 1 : STANDARD FORM
EXERCISE 1 EXERCISE 2
1. (a) 43000 (b) 1800 1. (a) 2960 (b) 51900
2. (a) 68.7 (b) 70 2. (a) 71⋅ 7 (b) 70
3. (a) 0.00305 3. (a) 0 ⋅ 0605
(b) 0.0030 (b) 0 ⋅ 061
(c) 0.003 (c) 0 ⋅ 06
4. (a) 5.6 × 101 4. (a) 4 ⋅ 8 × 10 4
(b) 7.241 × 10 2 (b) 9 ⋅ 20005 × 10 3
(c) 9.3 × 10 −1 (c) 2 ⋅ 6 × 10 −2
(d) 2.81 × 10 −3 (d) 3 ⋅ 8 × 10 −7
5. (a) 346000 (b) 0.00297 5. (a) 2190 (b) 0 ⋅ 00082
6. (a) 5.68 × 10 −3 (b) 4.06 × 10 7 6. (a) 1 ⋅ 85 × 10 7 (b) 1 ⋅ 1141 × 101
7. (a) 5.61 × 10 −4 (b) 4.79 × 10 8 7. (a) 8 ⋅ 33 × 10 5 (b) 4 ⋅ 205 × 10 −2
8. (a) 8.667 × 10 −8 (b) 3.1598 × 1012 8. (a) 3 ⋅ 36 × 10 3 (b) 1 ⋅ 885 × 10 −4
9. (a) 9 × 10 7 (b) 6 × 10 5 9. (a) 1 ⋅ 458 × 10 0 (b) 2 ⋅ 4 × 10 −3
DIAGNOSTIC TEST
1. D 6. D
2. C 7. D
3. A 8. A
4. A 9. D
5. C 10.D
Panitia Matematik Daerah Seremban 2006

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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
Panitia Matematik Daerah Seremban 2006

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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
Panitia Matematik Daerah Seremban 2006

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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
Panitia Matematik Daerah Seremban 2006

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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.
Panitia Matematik Daerah Seremban 2006

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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
Panitia Matematik Daerah Seremban 2006

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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
Panitia Matematik Daerah Seremban 2006

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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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CHAPTER 6 : STATISTICS
Exercise 1
1. 13.5
2. 5
3. 15.65
4. 1–5
5. 6.5
6. 6
7. 2.59
8. 24
9 29-34
10 31.5
Exercise 2:
1(a) 4 (b) 8
2(a) 3 (b) 3 (c) 3.433
3(a) 2, 5,8,11,14 (b) 8.107
4(a) 11 (b) 17
5(a)14 (b)11
6(a) 13 (b) 19
7 (a) 40 (b) 140 (c ) 190
8(a) 680 (b)1400
9(a) 19.75 (b) 18
10(a) 20-29 (b) 24.5
DIAGNOSTIC TEST:
1. A
2. C
3. C
4 B
5 B
6. B
7C
8B
9B
10C
Panitia Matematik Daerah Seremban 2006

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CHAPTER 6 : STATISTICS
EXERCISE 1
1.
Mark Frequency
10 – 16 5
17 – 23 6
24 – 30 6
31 – 37 11
38 – 44 2
2.
Lower Upper Lower Upper
Class Class size
limit limit boundary boundary
55 – 60 55 60 54.5 60.5 6
61 – 66 61 66 60.5 66.5 6
67 – 72 67 72 66.5 72.5 6
73 - 78 73 78 72.5 78.5 6
TABLE 1
3. a)
Mass of Class
Frequency
fruits (kg) midpoint
36 – 43 3 39.5
44 – 51 7 47.5
52 – 59 8 55.5
60 – 67 4 63.5
68 – 75 5 71.5
76 – 83 3 79.5
(b) (52 – 59) kg
(39.5 × 3) + (47.5 × 7) + (55.5 × 8) + (63.5 × 4) + (71.5 × 5) + (79.5 × 3)
(c) Mean =
3+7+8+ 4+5+3
= 58.17 kg
Panitia Matematik Daerah Seremban 2006

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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
Panitia Matematik Daerah Seremban 2006

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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˚
Panitia Matematik Daerah Seremban 2006

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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
Panitia Matematik Daerah Seremban 2006

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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’
Panitia Matematik Daerah Seremban 2006

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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°
Panitia Matematik Daerah Seremban 2006

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CHAPTER 11 : LINES AND PLANES IN 3-DIMENSION
EXERCISE 1
1. (a) LN = 4 cm
(b) ∠ MLN
(c) ∠ KNL = 36º 52´
2. ∠ VCN = 17 o 6′
3. (a) EG = 10 cm
(b) ∠ DGE = 16º 42´
4. (a) ∠ VPT = 45º
(b) ∠ VQT = 51° 20´
5. (a) BT = 17 cm
(b) ∠ ACT = 56° 19´
6. ∠ MQS = 38° 40´
7. ∠ DQC = 29º 7´
8. (a) ∠ DAM
(b) ∠ MBN = 24.78º
9. (a) ∠ BGF = 53.13º
(b) ∠ HBD = 25.09º
10. (a) ∠ RTS
(b ∠ RPT = 35.75º
EXERCISE 2
1.. (a) 13 cm.
(b) ∠ ACB
(c) 31º 36´
2. (a) ∠ PRM = 26.57º
(b) ∠ POM
3. (a) ∠ BGF
(b) ∠ BHC = 35.26º
4. (a) ∠ TSN = 33.56º
(b) ∠ MTN
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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