Mat575 2009-1
Mat575 2009-1
Mat575 2009-1
CS/APR 2009/MAT400/575
COURSE
COURSE CODE
MAT400/575
EXAMINATION
APRIL 2009
TIME
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.
2.
Answer ALL questions in the Answer Booklet. Start each answer on a new page.
3.
Do not bring any material into the examination room unless permission is given by the
invigilator.
4.
Please check to make sure that this examination pack consists of:
i)
ii)
CONFIDENTIAL
CONFIDENTIAL
CS/APR 2009/MAT400/575
QUESTION 1
a)
ii)
By using the bisection method, determine the approximate root of f after four
iterations. Give your answer correct to four decimal places.
(6 marks)
iii)
b)
Show that the Newton-Raphson iteration formula of calculating the root of the
given function is written as
r
5^
P*+i -
6P* + -J ; , /c=0,1,2,....
kJ
(4 marks)
ii)
(6 marks)
CONFIDENTIAL
CS/APR 2009/MAT400/575
CONFIDENTIAL
QUESTION 2
Given the following table of data:
/
*,
n*,)
a)
b)
c)
0
1.5
1
1
2.5
2
3.5
3
4.5
10
25
55
i)
ii)
By using your result in a)i) above, calculate the approximation of f(4.0). Give
your answer correct to four decimal places.
(2 marks)
i)
ii)
By using your result in b)i) above, calculate the approximation of f(4.0). Give
your answer correct to four decimal places.
(2 marks)
(2 marks)
CONFIDENTIAL
CONFIDENTIAL
CS/APR 2009/MAT400/575
QUESTION 3
a)
Find a least squares line to approximate the continuous function y = 2e x_1 - 1 on the
interval [0,2].
(10 marks)
b)
The table below gives the continuous assessment marks and the final-examination
marks for 20 numerical methods students. Obtain the least squares line equation for
the given data.
i
Assignment
Marks/50, x,
Final-examination
Marks/50, y.
Assignment
Marks/50, x}
Final-examination
Marks/50, y,
1
2
3
4
5
6
7
8
9
10
35
45
20
23
28
43
20
35
45
30
45
46
30
36
34
44
30
45
43
34
11
12
13
14
15
16
17
18
19
20
45
27
15
10
15
48
14
33
14
47
48
40
35
29
28
50
12
29
26
35
Hence, use the least squares line obtained to determine the final-examination marks
given the assignment marks are 45 and 20.
(10 marks)
QUESTION 4
A motorist test drives his racing car on a race track for 70 seconds. The speed in m/s of the
car is recorded for every 5-second interval starting from the beginning of the drive. The table
below records the data collected.
/
Time
Speed
a)
0
0
120
1
5
130
2
10
140
3
15
155
4
20
165
5
25
160
6
30
152
7
35
148
8
40
140
9
45
138
10
50
130
11
55
125
12
60
120
13
65
110
ii)
b)
CONFIDENTIAL
14
70
100
CONFIDENTIAL
CS/APR
QUESTION 5
<ty = yx
.~2 with y(0) = 2.0.
Given an initial value problem
dx
a)
ii)
iii)
iv)
b)
CONFIDENTIAL