AM025/1
Mathematics 2
Paper 1
Semester II
Session 2019/2020
1 ½ hours
AM025/1
Matematik 2
Kertas 1
Semester II
Sesi 2019/2020
1 ½ Jam
KOLEJ MATRIKULASI MELAKA
KEMENTERIAN PENDIDIKAN MALAYSIA
SET 2
AM025/1
INSTRUCTIONS TO CANDIDATE :
PART QUESTION MARKS
This question paper consists of 7
questions.
1
Answer all questions.
2
The full marks for each question or section
are shown in the bracket at the end of the
questions or section.
A
3
4
All steps must be shown clearly.
5
Only non-programmable scientific
calculators can be used.
Numerical answers can be given in the
form of π, e, surd, fractions or up to three
significant figures, where appropriate,
unless stated otherwise in the question.
1
B
2
TOTAL
70
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO
Kolej Matrikulasi Melaka
AM025 (PAPER 1)_SET 2
AM025/1
Mathematics 2
Paper 1
Semester II
Session 2019/2020
1 ½ hours
AM025/1
Matematik 2
Kertas 1
Semester II
Sesi 2019/2020
1 ½ Jam
LIST OF MATHEMATICAL FORMULAE
SENARAI RUMUS MATEMATIK
Differentiation and Integration
Pembezaan dan Pengamiran
d u  x  v  x u ' x  u  x v ' x


2
dx  v  x  
v  x  
1
eaxb dx  eaxb  c
a
d
u  x  v  x    u  x  v '  x   v  x  u '  x 
dx 
 f  x e
f  x
 f  x
f ( x)


dx  e f ( x )  c
dx  ln
f  x  c
n 1

 f  x  
f  x   f  x   dx  
n 1
n
'
1
1
dx  ln ax  b  c
ax  b
a
c
Application of Definite Integral
Penggunaan Kamiran Tentu
Consumers’ surplus =

x0
0
x0
D( x)dx  x0 y0 , Producers’ surplus =  x0 y0   D( x)dx
0
Lebihan pengguna
Lebihan pengeluar
Partial Differentiation
Pembezaan Separa
D( x, y)  f xx  f yy   f xy 
2
Mathematics of Finance
Matematik Kewangan
I  Prt
D  Sdt
d
r
1  dt
 (1  i) n  1 
Sn  R 

i


S  P(1  rt )
Proceed = S (1  dt)
S  P 1  i 
n
1  (1  i)  n 
An  R 

i


re  1  i   1
m
Kolej Matrikulasi Melaka
AM025 (PAPER 1)_SET 2
AM025/1
Mathematics 2
Paper 1
Semester II
Session 2019/2020
1 ½ hours
AM025/1
Matematik 2
Kertas 1
Semester II
Sesi 2019/2020
1 ½ Jam
PART A [45 marks]
1.
2.
RM 65,000 is invested for 6 years 9 months. If the investment is offered 5%
compounded semi-annually for the first 2 years, 6% compounded monthly for the
next 18 months and 7% compounded daily for the rest of the period, find the future
value of this investment. (Assuming 360 days per year).
[5 marks]
The demand fuction and supply function of a product are D  x   ax 2  23 and
S  x   x  b respectively, where a and b are constants. Given the market
equilibrium point is  3,5  .
(a)
(b)
(c)
3.
Show that the values of a  2 and b  2 .
[3 marks]
Hence, sketch and label on the same graph, the region for the consumer’s
surplus and the producer’s surplus.
[4 marks]
Determine the consumer’s surplus.
[3 marks]
(a)
A distribution farm has to transport minimum of 1200 packages using large
vans which can take 200 packages each and small van which can take 80
packages each. The cost of running each large van is RM 40 and each small
van is RM 20. Not more than RM 300 is to be spend on the job. The number of
large vans must not exceed the number of small vans. By using x and y
represents the number of large and small vans respectively, formulate the
objective function and determine the constraints.
[4 marks]
(b)
State the inequalities that define the shaded region in the diagram below.
y
2x  y  4  0
12
8
3
2
12
x
[5 marks]
Kolej Matrikulasi Melaka
AM025 (PAPER 1)_SET 2
AM025/1
Mathematics 2
Paper 1
Semester II
Session 2019/2020
1 ½ hours
4.
AM025/1
Matematik 2
Kertas 1
Semester II
Sesi 2019/2020
1 ½ Jam
By using the Lagrange multiplier method, find the minimum value of the function
[11 marks]
f  x, y   9 x3  y 3 subject to the constraint x  y  8  0 .
2
5.
(a)
(b)
3

Find    x  dx
x

3
1
Given that  f  x  dx  5 , find
3
0
[3 marks]
3
 f  x  dx . Hence, find
0
0
(i)
the value of
 f  x  dx .
[3 marks]
3
3
(ii)
the value of k if
  f  x   k  dx  12
[4 marks]
0
PART B [25 marks]
4 x
dx .
1 2 x
4
1.
2.
(a)
Evaluate 
(b)
Given f ( x, y )  ln y 4  2 x 4 . Show that
(a)
Find the area bounded by the curve y   x 2  8 x  12 , the straight line x  7
and the x  axis .
[6 marks]
(b)
The management of a company determines that the marginal revenue and the
marginal cost functions from the production and sales of x units of a product
are
R '  x    x 2  300
C '  x   x  60
The fixed cost is RM 1 000. Find
(i)
the price function
(ii)
the cost function
Kolej Matrikulasi Melaka
[4 marks]
xf x
2
 fy  .
y
y
[8 marks]
[4 marks]
[3 marks]
AM025 (PAPER 1)_SET 2
AM025/1
Mathematics 2
Paper 1
Semester II
Session 2019/2020
1 ½ hours
AM025/1
Matematik 2
Kertas 1
Semester II
Sesi 2019/2020
1 ½ Jam
ANSWERS
PART A
RM 98534.96
1.
2.
(a)
(b)
Shown
y
D  x   2 x 2  23
23
S  x  x  2
CS
5
2
PS
x
3
3.
(c)
Consumer’s surplus  RM36
(a)
Objective function, Z  40 x  20 y
Constraints:
200 x  80 y  1200  5x  2 y  30
40 x  20 y  300  2 x  y  15
x y
y  2x  4
x  y  12
2 x  3 y  24
y3
x2
(b)
4.
The minimum value is 288
5.
(a)
PART B
1.
(a)
2.
9
x2
  12 x   c
x
2
(b)
(i)
-15
(ii)
k 1
(i)
p  x  
(ii)
C  x 
5.5
(b)
Shown
(a)
7
@ 2.33 unit 2
3
Kolej Matrikulasi Melaka
(b)
x2
 300
3
x2
 60 x  1000
2
AM025 (PAPER 1)_SET 2