F4 Answer

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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


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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


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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


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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


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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


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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


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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


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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


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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


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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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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


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