Additional Mathematics Form 5 KSSM TB

(b) y 2. (a) 30x + 25y < 3 000, x > 20, y > x + 10
(b) y
80 y = 4x
70 (16, 64) y – x = 10 120
60
100 x = 20
50 80 y = x + 10
60
40 R x + y = 80 40 R
30 20 30x + 25y = 3 000

20 0 20 40 60 80 100 x

KEMENTERIAN PENDIDIKAN MALAYSIA10

0 10 20 30 40 50 60 70 80 x (c) RM1 350
3. (a) x + y < 7 000, y < 2x, y > 1 000
(c) (i) 30 < y < 60 (ii) RM5 440
2. (a) 40x + 20y < 2 000 or its equivalent, (b) y

30x + 60y > 1 800 or its equivalent, 7 000 x + y = 7 000
y < 3x or its equivalent 6 000 y = 2x

(b) y

100 40x + 20y = 2 000 5 000
90
4 000

80 3 000
70 y = 3x 2 000 R
60 (20, 60)
1 000
50 y = 1 000

0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 x

40 (c) (i) 5 000 litres (ii) RM330 000
30 R
Summative Exercise

20 1. (a) 3x + 5y > 60, 2x + 3y < 60, x > 5, y > 5
(b) y
10 30x + 60y = 1 800
0 10 20 30 40 50 60 70 x x=5

(c) (i) 15 (ii) RM21 000 20 (5, 17)
15
Formative Exercise 7.2
10 R 2x + 3y = 60
5 y=5

1. (a) 4x + 5y > 1 000 or its equivalent, 3x + 5y = 60
0.4x + 0.3y < 300 or its equivalent, 0 5 10 15 20 25 30 35 x
y – x < 200 or its equivalent
(b) y (c) (i) x = 5, y = 17 (ii) RM1 560
2. (a) 5x + 6y > 60, 3x + 4y < 60, x < 2y
900 0.4x + 0.3y = 300
(b) y

800 y – x = 200 16
700 14
12
600 (342, 542) 10 3x + 4y = 60 x = 2y
500 8 R
6
400 4
2
300 R
02
200 4x + 5y = 1 000 x (c) RM324 5x + 6y = 60
100 4 6 8 10 12 14 16 18 20 x

0 100 200 300 400 500 600 700 291

(c) (i) 500 (ii) RM2 497.80

3. (a) 12x + 5y < 60, y < 3x, y > 2 2. (a) –8 ms–1 (b) 1 s and 7 s (c) 1 , t , 7
(b) y 3. (a) –8 ms–2 (b) 2 s (c) t , 2

12 12x + 5y = 60 y = 3x Self-Exercise 8.2 (b) 111 m
10
1. (a) 68 m (ii) 45 m (b) 7 m
2. (a) (i) 8 m

8 Formative Exercise 8.1

6 1. (a) t (s)
s (m)
4R (b) s (m) 12 3 4 5
2 y=2 –3 – 4 –3 0 5
0 1234567 x 5
s = t2 – 4t (c) 4 s

(c) (i) 1 < y < 4 KEMENTERIAN PENDIDIKAN MALAYSIA1(ii) RM800
x 3
4. (a) x + y < 80, y > or y < 3x, 100x + 120y > 5 000 t (s)
(b) y 2 45
0

80 y = 3x –4

70 2. (a) 2 (b) (i) 14 m (ii) 35 m

3. 0, 320 m 4. 9 ms–1, 23 ms–1
5. (a) 4 ms–2 (b) t . 2
60
6. (a) 21 m (b) 55 m
50
7. (a) Time, t (s) 012345 6
40
30 100x + 120yR= 5 000 x + y = 80 Displacement, s (m) 9 6 5 6 9 14 21
20 (b) s (m) (c) 20 m
10
21 s = (t – 2)2 + 5

0 10 20 30 40 50 60 70 80 x 9
5
(c) (i) 33 (ii) RM2 300 t (s)
5. (a) 2x + 5y < 30, 3x + 2y < 24, x < 2y 02 6

(b) y

Self-Exercise 8.3

12 1. (a) v = 4 − 8t + 3t 2 (b) v = 16 – 2t

11 (c) v = 6t 2 – 8t + 2 (d) v = 27t 2 + 24t 3 + 5t 4

10 (e) v = 6t 2 – 18t – 5 (f) v = t 2 – 6t + 5

2. (a) a = 2t – 1 (b) a = 6t – 10

9 (c) a = –12t (d) a = 18t – 30
8 3x + 2y = 24 1 (f) a = 18t 2 + t8 3
(e) a = 6t + t 2

7 3. (a) v = 2 – 2t, a = –2 (b) s/v/a
6 x = 2y
98

5 2 4a = –2 t
4 (5, 4) –20 1 2

3R 2x + 5y = 30 –6 v = 2 – 2t
2

1 Self-Exercise 8.4
0 2 4 6 8 10 12 14 x
1. (a) (i) –2 ms–1 (ii) 5 ms–1 (iii) 21 ms–1
2. (((cba))) 80(i)m< st–121, se23coonrdt .(b()1i i)32 s2ecsoencodn, d1ss eco(iniid) 3 seconds
(c) (i) 4 (ii) RM2 000

CHAPTER 8 KINEMATICS OF LINEAR
MOTION

Self-Exercise 8.1 Self-Exercise 8.5

1. (a) (i) –3 m (ii) 4 s (ii) –5 m 1. (a) 8 ms–2 (b) –8 ms–2 (c) 4 seconds
(b) (i) 3 s (c) t . 3 2. (a) 1 second (b) t , 1

292

Formative Exercise 8.2 2. (a) –7 m (b) –12 ms–1 (c) 6 ms–2

1. (a) –2 ms–1 (b) 3 seconds (c) 4 m 3. (a) (i) 12 mmin–1 (ii) 12 mmin–1

(d) 10 m (e) t . 1 (iii) 6 mmin–2 (iv) 149 m
(ii) 0 ms–1
2. (a) h = 1 , k = 1 (b) v (ms–1)
2
(b) (i) 1 ms–1 (iii) –1.5 ms–1 36 v = 6t2 – 18t + 12

3. (a) v = 3t 2 – 10t – 8, a = 6t – 10

(b) –11 ms–1, 8 ms–2 (c) 4 s
(d) 1 s, 6 s (e) 84 m
12
Self-Exercise 8.6 (b) 2 ms–1 0 1.5 t (s)
1. (a) 10 ms–1 (b) –2 ms–1 4
2. (a) –13 ms–1 (b) –12 ms–1 –1.5 1 2
3. (a) 2 , t , 6 (c) 1.5 s
4. (a) 32 cms–1 (b) 36 cms–1 4. (a) v = 10t, s = 5t2
KEMENTERIAN PENDIDIKAN MALAYSIA
(d) 9 s (b) The particle is at point X after 0.5 second with a velocity

of 5 ms–1.

Self-Exercise 8.7 5. (a) 8 ms–1 (b) –10 m
6. (a) t = 1 s, 3 s (b) 69 13 m
1. (a) 27 21 m (b) 14 m 5
2. (a) –10 m (b) –16 m 7. (a) m = 5, n = –20 (b) s = 6  t 3 – 10t 2 + 30t
3. (a) 48 m (b) 8 m
=km43 (c) 6 seconds (d) 35 m
4. (a) s t3 + 3t2 – 18t, v = 4t 2 – 6t – 18 6
(c) 9 8. (a) –10 ms–1 (b) 14 ms–2
113
Formative Exercise 8.3 9. (a) t = 4 (b) 6 m

1. (a) 42 ms–1 (b) 35 m on the right O (c) The car reverses for 4 seconds and then moves forward.
2. (a) 24 ms–2 10. (b) – 43 m
(b) 2 s (c) 6 s 11. (a) v = (3t 2 – 3) ms–1, a = 6t ms–2

3. (a) m = –10, n = 4 (b) –24.5 ms–1 (c) 189 m (b) The particle moves to the left with initial velocity of
4. (a) – 227 m 5
5. (a) 18 ms–1 (b) t , 4 (c) 63 m –3 ms–1 and zero acceleration. For t = 2, the particle

(b) t = 0 s, 6 s (c) 40 m moves to the right with velocity of 9 ms–1 and
3 experiences acceleration of 12 ms–2.
25 75 ms–1 (c) 6285 m
6. (a) 2 s (b) 16 (c) t . 1

Self-Exercise 8.8 12. (a) h = 3, k = –9 (b) 4.5 s
(c) 18 ms–2 (d) 14.5 m
13. (a) 2 ms–1 (b) 3 seconds
1. (a) 2 seconds (b) s = 20t – 5t2 16
(c) (i) 20 m (ii) 4 seconds (c) (ms–1) (d) 3 m
v
2. (a) 8 ms–1
(b) (i) v (ms–1) 2 v = 8t – 2t2 – 6
(ii) 18 m

8 (c) 17 m t (s)

6 v = 6 + 4t – 2t2 01 23

0 1 3 t (s) –6 (ii) 1 , t , 6 (iii) t. 7
3. (a) m = 12.5, n = –12.5 (b) –3.125 kmh–1 2
14. (a) (i) 6 cms–1
(b) v (ms–1)

(c) 125 km 6
12 v = t2 – 7t + 6
4. (a) 20 ms–2 (b) 9 m

Formative Exercise 8.4 0 1 3 —21 6 t (s)
–6 —41
1. (a) 56 ms–1 (b) 104 m (c) 20 m
2. (a) 8 ms–1 (b) 40 ms–1 4
3. (a) t , 2 (b) No 3

(d) s (m) 15. (a) –1 ms–1 (b) m
12 (c) t . 3
v (ms–1)
0 4 6 t (s)
15

4. (a) 47 m (b) –  4 ms–1 v = t2 – 6t + 8
3
2 86 8
(c) 3 , t , 2 (d) 27 m

Summative Exercise 0 2 3 4 7 t (s)
–1
1. (a) 208 m (b) 48 ms–1 (c) –12 ms–2 (d) t = 3 s, 5 s

293

Glossary

Acceleration (Pecutan) Rate of change of velocity.KEMENTERIAN PENDIDIKAN MALAYSIAIndefinite integral (Kamiran tak tentu) Integration
without limits.
Arc of a circle (Lengkok bulatan) Arc is part of the
circumference of the circle. Instantaneous acceleration (Pecutan seketika) Rate of
change in velocity at a particular time.
Binomial distribution (Taburan binomial) The
probability distribution involving n Bernoulli trials Integration (Kamiran) A concept in calculus which is
which are similar or identical where the possibility of the inverse of differentiation.
‘success’ is constant in every trial and every trial is
independent of each other. Kinematic of linear motion (Kinematik gerakan linear)
Kinematic means the movement of an object represented
Binomial experiment (Eksperimen binomial) Composed by a straight line in words, diagrams, numbers, graphs
of n Bernoulli trials which are independent but similar. and equations.
Each trial has only two outcomes, which are ‘success’
and ‘failure’. Limit (Had) The value of a function when a variable
approaches a certain value.
Chord (Perentas) A straight line connecting any two
points on the circumference of the circle. Maximum displacement (Sesaran maksimum) Distance
between the end point and the starting point in a straight
Circumference of a circle (Lilitan bulatan) Perimeter line when the velocity is zero.
for a circle.
Negative angle (Sudut negatif) The angle formed by
Combination (Gabungan) A selection of all or part rotating a straight line at an origin clockwise from the
of a set of objects, regardless of their orders of the positive x-axis.
selected objects.
Normal (Normal) A perpendicular straight line to its
Complementary angle (Sudut pelengkap) Angle A is tangent line.
the complementary angle of angle B if A + B = 90°.
Normal distribution (Taburan normal) A continuous
Composite function (Fungsi gubahan) A function that random variable and is one of the most important
combines two or more functions. distributions in statistics because it represents many
natural phenomena. The distribution graph is
Constant velocity (Halaju malar) The velocity of linear bell-shaped.
motion of an object that is not changing.
Objective function (Fungsi objektif) A function used to
Constraint (Kekangan) Limitations within a situation determine the optimal value.
like a lack of raw materials, capital, operating time and
so on. Positive angle (Sudut positif ) An angle formed by
rotating a straight line at an origin anticlockwise from
Definite integral (Kamiran tentu) An integration whose the positive x-axis.
value is fixed by a certain range of values.
Radian (Radian) The unit used to measure the size of
Event (Peristiwa) Set of possible outcomes for an an angle in circular measure.
experiment. An event is a subset of sample space.
Radius (Jejari) A straight line from the centre of the
Factorial (Faktorial) n objects can be arranged in circle to any point on the circumference of the circle.
n(n – 1)(n – 2)…(3)(2)(1) ways. This product can be
represented by the symbol n! which is called a Random variables (Pemboleh ubah rawak) A random
n factorial. variable is a variable whose value is numeric and from a
random phenomenon.
Feasible region (Rantau tersaur) A region that satisfies
all the mathematical model requirements for a situation. Segment (Tembereng) Region that is bounded by a
curve and a chord.
Generated volume (Isi padu janaan) The volume of an
object formed when a shaded region rotates on an axis, Standard normal distribution (Taburan normal
which can be the x-axis or the y-axis. piawai) A normal distribution with a mean of 0 and a
standard deviation of 1.
Gradient of tangent (Kecerunan tangen) Gradient of a
straight line that touches a curve at only one point.

294

KEMENTERIAN PENDIDIKAN MALAYSIAReferences

Barret, R. (2008). NCEA Level 2 Mathematics Year 12. New Zealand: ESA Publications (NZ) Ltd.

Chow, W. K. (2013). Discovering Mathematics (2nd ed.). Singapore: Star Publishing Pte Ltd.

Deborah, B. (2012). Complete Mathematics for Cambridge Secondary 1. UK: Oxford University Press.

Greenwood, D., Robertson, D., Woolley, S., Goodman, J. & Vaughan, J. (2017). Essential Mathematics
for the Australian Curriculum Year 10. Australia: Cambridge University Press.

Ho, S. T., Khor, N. H. & Yan, K. C. (2013). Additional Mathematics 360. Marshall Cavendish Education.

Ho, S. T. & Khor, N. H. (2007). Additional Mathematics. Singapore: Panpac Education.

Dewan Bahasa dan Pustaka. Istilah Matematik untuk Sekolah-sekolah Malaysia (2003). Kuala Lumpur.
Malaysia: Dewan Bahasa dan Pustaka.

Lim, L. N. (2007). GCE O Level Additional Mathematics Key Points Exam Guide. Singapore: Redpost
Publications Pte Ltd.

Patrick, T. (2004). Mathematics Standard Level (3rd ed.). Australia: IBID Press.

Pemberton, S. (2016). Cambridge IGCSE and O Level Additional Mathematics Coursebook.
UK: Cambridge University Press.

Robert, H., Sandra, H., Michael, H., Matjut, M. & Mark, H. (2012). Mathematics for the International
Student: Mathematics SL (3rd ed.). Australia: Haese Mathematics.

Rondie, P. L., Kemp, E., Buchanan, L., Fensom, J. & Steve, J. (2012). Oxford IB Diploma Programme:
Mathematics Standard Level Course Companion. UK: Oxford University Press.

Teh, K. S & Looi, C. K. (2006). New Syllabus- Additional Mathematics (7th ed.). Singapore: Shinglee
Publishers Pte. Ltd.

Thomas, E. J. & Brunsting, J. R. (2010). Styles and Strategies for Teaching Middle School Mathematics.
USA: Corwin Press.

Val, H. & Jeanette, P. (2018). Cambridge IGSCE ® and O Level Additional Mathematics.
UK: Hodder Education.

Wong, M. K., Chen, C. W., Tan, P. L. & Nor A’idah Johari (2012). Matematik Tambahan Tingkatan 5.
Malaysia: Percetakan Rina Sdn. Bhd.

Yeo, J., Keng, S. T., Cheng, Y. L. & Chow, I. (2013). New Syllabus Additional Mathematics. (9th ed.).
Singapore: Shinglee Pte Ltd.

295

Index

Acceleration 256, 257, 260, 262,KEMENTERIAN PENDIDIKAN MALAYSIAFirst order differentiation 49, 63Radian 2, 3, 4, 6, 9, 13, 20, 23

264, 265, 267, 269 Generated volume 106, 107, 111, 114 Radius of a circle 2, 3

Acceleration functions 267, 269 Gradient of tangent 34, 35, 36, 51, Random variables 142, 143, 144,
52, 70 145, 148, 152, 153, 155, 156,
Approximation 30, 70, 71, 73, 76 158, 161, 166, 170, 171, 172,
Indefinite integral 85, 86, 92, 114 173, 184, 185
Area of a sector 12, 13, 15, 17, 18,
20, 23 Instant acceleration 256, 257 Random variations 169, 170

Area under the curve 95, 96 Integral 83, 85, 86, 87, 92, 93, 94, Rate of change 60, 65, 66, 67, 68, 76
97, 98, 99, 114, 117
Bernoulli trial 152, 153, 154, 161, Reference angle 197, 222, 228
Integration 82, 83, 85, 86, 87, 90, 92,
184 111, 114 Secant 193, 196

Binomial experiment 152, 153, 155 Kinematics of linear motion 275 Sector of a circle 2, 18
Limits 30, 31, 34, 35, 42, 76
Binomial random variables 153, 155 Second derivative 49
Linear programming 234, 240, 246
Chain rule 42, 46, 65, 66, 67, 76, 77 Second order differentiation 60
Maximum point 57, 58, 59, 60, 62
Chord 7 Segment 23
Minimum point 57, 58, 59, 61, 62
Circular measure 2, 20, 23 Small changes 70, 71, 76
Multiplication rule 120, 121, 122,
Circumference 5, 6, 12 124, 128, 135, 137 Standard deviation 162, 167, 169,
170, 171, 172, 184
Combination 132, 133, 135, 137, Negative angles 190, 191, 198, 228
138, 139 Standard normal distribution 170,
Normal 53, 76 172, 173, 174
Complementary angles 194, 228
Normal distribution 166, 167, 168, Stationary point 57, 58, 76
Constraints 234, 235, 237, 240, 246 170, 171, 172, 173, 174, 184,
185 Tangent 34, 35, 36, 38, 51, 52, 53,
Continuous random variables 143,
144, 166, 173, 184 Objective functions 234, 240, 242, 55, 57, 58, 59, 60, 62, 70, 76

Cosecant 193, 196 246 Trigonometric ratio 193, 196, 197,
198, 199, 212, 213, 215, 216,
Cotangent 193, 196 Optimal value ​237, 246 222, 228

Definite integral 92, 93, 94, 97, 114 Outcomes 142, 144, 145, 152, 153, Turning point 57, 58, 59, 60, 61, 76,
155, 156, 166, 169, 170 77
Differentiation 260, 272
Permutation 121, 122, 123, 124, 125, Variance 162, 184
Discrete random variables 143, 144,
145, 148, 161, 184 126, 127, 132, 134, 137, 138, Velocity 254, 255, 256, 257, 260,
139 262, 264, 265, 267, 269, 275
Displacement 252, 253, 254, 255,
260, 262, 269, 275 Point of inflection 57, 58, 62, 76 Velocity at an instant 254, 256

Events 120, 121, 137 Positive angles 190, 191, 228 Velocity function 267, 269
Factorial 122
Probability 145, 148, 152, 153, 155, z score 171
Feasible region 240 156, 157, 158, 161, 166, 167,
168, 169, 173, 174, 175, 184
First derivative 35, 36, 38, 39, 40,
43, 44, 49

296

KEMENTERIAN PENDIDIKAN MALAYSIA

RM 10.50

ISBN 978-983-2914-68-6

9 789832 914686

FT435002