Mathematical Methods (MATS2108)
Biological Science - BS
Semester: First Semester
Level: 200
Year: 2013
UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE
CONTINOUS ASSEMENT
DEPARTMENT: Mathematics COURSE INSTRUCTOR: Fomboh nee NFORBA M
MONTH: December COURSE CODE & NUMBER: MATS2108
YEAR: 2013 COURSE TITLE: Mathematical methods
DATE: 18-12-2013 CREDIT VALUE: Six credits
TIME ALLOWED: 1.5 hours.
SECTION A(Write down only the letter corresponding to the correct answer)
1. The value of k for which the
is
A: 0 B: 6 C: -6 D: ∞
2. A spherical cell of radius r has volume V=
and surface area S= 4π
. V expressed as a function of S is
A: V(s) =
π B: V(s) =
C: V(s) =
r A: V(s) =
π
An environmental study of a certain community suggests that the average daily level of carbon monoxide in the air
will be C’(p)=0.4p+1 parts per million which the population is p thousand. If t years from now the population of the
community is p(t)= S + 0.2t2 thousand where t is time in years.
3. The level of carbon monoxide in the air expressed as a function of time is
A. C(t)=0.4t + 1 B. C(t)= 0.4(8 + 0.2t2) + 1 C: p(t)= 8 + 0.2t2 D : p(t)=0.4p + 1
4. The carbon monoxide level two years from now will be
A: C(2)=1.8 B: C(2)=4.52 C: p(2)=8.8 D: p(2)= 1.8
5. Public health records indicate that x weeks after the outbreak of an epidermic in a community, the number of
inhabitants who have contracted the disease is given by P(x) = 12x
. After 16 weeks, the number of inhabitants who
contract the disease is
A: 24 B: 3 C: 48 D: 6
6. The domain of the function f:x
is
A: (-4, 4) B: (-∞, -4) U (4, ∞) C:
D: (-∞, -4) U (4, ∞)
7. Which of the following statements is true
A: ln(
) =
lnx + 2lny B: ln
= lnx + lny C:
= 5
D: ln(
) =3lnx +2lny
8. The domain of the function f where f(x) =
A:
B:
C:
D:
9. The number of bacteria in a certain culture grows according to the equation r(t)= 640
. Where t is the time in
hours. The number of bacteria after 12hours is
A. 3840 B. 5120 C. 80 D. 20
10. f(x) =
expressed as partial fraction has the general form
A:
+
B:
+
+
C:
D:
+
Given the following f: xf(x), x
o
D
f
and the following condition:
i)
exists (ii)
(iii)
(iv) L= f(x
o)
11. f is said to have a limit at x
o
if:
A: only (i) holds B: only (i) and (ii) hold C: only (iii) holds D: only if (i) , (ii) and (iv) holds.
12. f is said to be continuous at x
o
if
A: only (iii) and (iv) hold. B. only (i) and (ii) hold C: only (iii) holds D: only (i), (ii) and (iv) holds
13. The gradient of the tangent to the curve f(x) =
+ 3
- 2x -3 at the point (1, 0) is A;
B: 10 C: 10 D:
14. Which of the following is true about the functions f and g where f(x) =x + 1and g(x)=
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A: (fg)(x) =
+
B: (fog)(x) =
+
C: (fof)(x) =
D: (gof)(x) =
+1
SECTION B: Answer all the questions. All necessary work must be shown and must be nealtly and orderly presented.
1. a) Evaluate
∞
b) Given that
f(x) =
find (i) f(2) (ii) f(5)
(iii) find
and
and determine whether or not
exists. (5 marks)
c) differentiate the function k(x) =
by definition .
d) Given the function :x
,show that
= (
4
(
3
3 marks
2a) Define (i) Half-life of a substance (ii) The doubling time of a population (2marks)
b) The population of bacteria in a certain culture grows according to the law N(t) = N
o
where N(t) is the number of
bacteria present at time t and k> 0. Suppose initially, there were 50 bacteria in the culture and after 12 hours, the
number grew to 400. Find the number present after 16 hours.
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