Focus TG4 KSSM (Maths) Terbitan Penerbitan Pelangi Sdn Bhd

CONTENTS

Mathematical Formulae iv

1Chapter Quadratic Functions and Equations in One Variable 1

1.1 Quadratic Functions and Equations 2
SPM Practice 1 13

2Chapter Number Bases 16

2.1 Number Bases 17
SPM Practice 2 24

3Chapter Logical Reasoning 27

3.1 Statements 28
3.2 Argument 36
SPM Practice 3 44

4Chapter Operations on Sets 48

4.1 Intersection of Sets 49
4.2 Union of Sets 53
4.3 Combined Operation on Sets 59
SPM Practice 4 64

5Chapter Network in Graph Theory 69

5.1 Network 70
SPM Practice 5 80

6Chapter Linear Inequalities in Two Variables 84

6.1 Linear Inequalities in Two Variables 85
6.2 System of Linear Inequalities in Two Variables 90
SPM Practice 6 95

ii

7Chapter Graphs of Motion 99

7.1 Distance-Time Graphs 100
7.2 Speed-Time Graphs 104
SPM Practice 7 111

8Chapter Measures of Dispersion for Ungrouped Data 116

8.1 Dispersion 117
8.2 Measures of Dispersion 119
SPM Practice 8 133

9Chapter Probability of Combined Events 137

9.1 Combined Events 138
9.2 Dependent Events and Independent Events 139
9.3 Mutually Exclusive Events and Non-Mutually Exclusive Events 144
9.4 Application of Probability of Combined Events 149
SPM Practice 9 153

1 0Chapter Consumer Mathematics: Financial Management 156

10.1 Financial Planning and Management 157
SPM Practice 10 167

Pre-SPM Model Paper 170
Answers



iii

2Chapter Learning Area: Number and Operations

Number Bases

The length of this board 1 foot = 12 inch.
is two feet. 2 feet = 24 inches.
Oh, the length of the
board is 24 inches.

• Convert – Tukar Concept
• Digit value – Nilai digit map

• Number base – Asas nombor
• Place value – Nilai tempat
• Repeated division – Pembahagian berulang

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16

2.1 Number Bases Mathematics  Form 4  Bab 2  Number base 

A Representing and explaining numbers 8. In the number system in base m, we count
in various bases something by arranging them in group of m,
then group of (m × m) and so on.
1. The base for a number consists of base 2, 3 and Chapter 2
so on without limit. 9. Each digit in a number base has a certain value
according to the place value. The place value of
2. The number base shows the number of digits a number is mn where m is the base and n is the
used in the formation of the number system. power, n = 0, 1, 2, ….

3. The table below shows the examples of number 10. The value of a digit is the product of the digit
bases and digits used. with its place value.

Number base Digits used 11. The value of a number is the sum of all digit
Two 0, 1 values.
Three 0, 1, 2
Four 0, 1, 2, 3 12. Number 147 can be represented in blocks by
Five 0, 1, 2, 3, 4 grouping 10 blocks in a group, as shown in the
Six 0, 1, 2, 3, 4, 5 diagram below.
Seven 0, 1, 2, 3, 4, 5, 6
Eight 0, 1, 2, 3, 4, 5, 6, 7 1 group of 4 group of 7 ones
Nine 0, 1, 2, 3, 4, 5, 6, 7, 8 hundreds tens
Ten 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

(a) The place value for digits in the number
147 are as follows.

Place value 102 101 100
Digit 147

4. The number that we use daily is in base ten. The (b) The value of the digit 4 in the number 147
ten digits used in base ten numbers are 0, 1, 2, 3, = 4 × 101
4, 5, 6, 7, 8 and 9. For example, 147 is a number = 40
in base ten.
13. The number 378 can be represented in blocks by
5. Numbers in base eight use eight digits, which grouping 8 blocks in a group, as shown in the
are 0, 1, 2, 3, 4, 5, 6 and 7. For example, 378 is a diagram below.
number in base eight.

6. Numbers in base five use five digits, which are 3 groups of eights 7 ones
0, 1, 2, 3 and 4. For example, 2345 is a number in
base five. (a) The place value for digits in the number
378 are as follows.
7. Numbers in base two use only two digits, which
are 0 and 1. For example, 11012 is a number in Place value 81 80
base two.
Digit 37

SPM Tips (b) The value of the digit 7 in the number 378
= 7 × 80
2345 is read as “two three four base five”. =7

17

Chapter 2   Mathematics  Form 4  Bab 2  Number base 1
Represent the following numbers with blocks.
(c) The value of the number 378 (a) 2124
= (3 × 81) + (7 × 80) (b) 346
= 3110 (c) 11112
14. The number 2345 can be represented in blocks
by grouping 5 blocks in a group, as shown in the Solution
diagram below. (a)

2 groups of 3 groups of 4 ones (b)
twenty fives fives


(a) The place value for digits in the number (c)
2345 are as follows.

Place value 52 51 50 2

Digit 234 State the place value of the underlined digit for each
of the following numbers.
(b) The value of the digit 2 in the number 2345 (a) 213
= 2 × 52 (b) 4067
= 50 (c) 53249
(d) 345
(c) The value of the number 2345
= (2 × 52) + (3 × 51) + (4 × 50) Solution Place value 31 30
= 6910 (a) 31
15. The number 11012 can be represented in blocks (b) 71 Digit 21
by grouping 2 blocks in a group, as shown in the (c) 92
diagram below. (d) 50

1 group of 1 group of 0 group of 1 ones 3
fours twos Find the value of the underlined digit in each of the
eights following numbers.
(a) 3578
(a) The place value for digits in the number (b) 110112
11012 are as follows. (c) 4125
(d) 60127
Place value 23 22 21 20
Solution
Digit 1101 (a) 5 × 81 = 40
(b) 1 × 24 = 16
(b) The value of the underlined digit in the (c) 2 × 50 = 2
number 11012 (d) 0 × 72 = 0

= 1 × 22 4
=4 Find the value for each of the following numbers.
(a) 2113
(c) The value of the number 11012 (b) 4056
= (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20) (c) 101012
= 1310 (d) 10234

18

  Matematik  Tingkatan 4  Jawapan

ANSWERS

1Chapter Quadratic Functions and Equations in (e) f(x) (f) f(x)
one variable x

0
–4 4

Try This! 1.1

1. (a) Yes, this expression only has one variable, x, and the x
highest power of x is 2. –2 0

(b) Yes, this expression only has one variable, u, and the 14. x = 7
highest power of u is 2.
15. 2 hours.
(c) Not, because the highest power of variable x is 1. 16. The product of two consecutive odd number is 323. x = 17
(d) Not, because the highest power of variable x is 3.
(e) Yes, this expression only has one variable, x, and the 17. RM 24

highest power of x is 2. 18. (a) Not
(f) Not, because the highest power of variable x is 1. (b) Yes
(c) Not
2. (a) Parabolic shape opens up with a minimum point.
(b) parabolic shape opens up with a minimum point.
(c) Parabolic shape opens down with a maximum point.
(d) Parabolic shape opens down with a maximum point.

3. (a) The shape of the graph is and the width decreased. SPM Practice 1
and is on the right of the
(b) The shape of the graph is PAPER 1 2. A 3. D 4. B 5. A
y-axis. and moves downward 7. B 8. D 9. C 10. A
1. C
(c) The shape of the graph is 6. C
vertically.

4. The graph moves 12 units upwards vertically. PAPER 2
5. f(x) = 2x2 + 16x
6. f(x) = 12x2 + 31x + 9 1. x = 2, –9
7. (a) f(x) = 10x2 – 33x – 28
2. x = 3 ,  –2
(b) 10x2 – 33x – 86 = 0 5
8. (a) f(x) = 7x2 + 26x – 6
3. 30
(b) 7x2 +26x – 126 = 0

9. (a) Not   (b) Yes   (c) Yes   (d) Not 4. 0.2 m
5. P(–1, 0) and Q(4, 0)
10. (a) Yes    (b) Not    (c) Yes   (d) Not

11. (a) 0, 8 (b) 0, –  52 (c) 0, 3   6. f(x)
(d) –6, 6 (e) –  25 ,  52 2

(f)  –   3 ,  32 x
2 –8 0 2

12. (a) –3, –5 (b) 3, –8 (c) 4, –  72

(d) 5 , –   2 (e) 6, 2 (f)  –   9 , 3
2 3 3 2 2

13. (a) f(x) (b) f(x) –8
10 12
7. f(x) = –  74 x2 – 28x + 112
02 5 x 8. x = 4
(c) f(x) 9. 304 m2
–3 0 x 10. Bus A is 90 km and bus B is 120 km away from the bus station.
4 11. 6 seconds
12. x = 60 m, h = 45 m
(d) f(x) 13. They have to sell 32 slices of cheese cake with the price of

3 RM5 per slice or sell 40 slices of cheese cake with the price
of RM4 per slice.
– –31 0 x –1 0 –43 x 14. The measurement of the photo is 15 cm × 12 cm
–2 2

188