Math

2007/2008 SEMESTER 1 – COMMON TEST Course : Diploma in Molecular Biotechnology Diploma in Food Science Diploma in Pharmaceutical Sciences Module : CL1104–Mathematics for Life Sciences

Jun 2007

Time Allowed: 1 hr

INSTRUCTIONS TO CANDIDATES

1 2 3 4 5

This test paper consists of TEN (10) pages including this page. There are SEVEN (7) questions. Attempt ANY SIX (6) questions; show all workings. Answer all questions in the space provided below each question. Formulae list is on the last two pages. Group: CL1104 -

Admin no:

Question 1 2 3 4 5 6 7 Total

Marks

Common Test / CL1104 / Page 2

Question 1 (a) The number of milligrams of a radioactive substance present after t years is given by Q  125e0.375t . (i) How many milligrams were present at the beginning? (ii) How many milligrams were present after 1 year? (iii) How many milligrams were present after 16 years? (3 marks) The loudness in decibels  of a noise is given by the formula   10 log
I , I0

(b)

where I 0  1012 W/m2, and I is the intensity of the noise in W/m2. At takeoff, a certain jet plane has a noise level of 105 decibels. What is the intensity of the sound wave produced by this airplane? (4 marks) (c) Solve 3x  5 Solution 1(ai) 125 mg 1(aii) (3 marks)

Q  125e0.375  85.0mg
1(aiii)

Q  125e0.37516  0.310mg
1(b)

  10 log
105  10 log

I I0

I 1012 I 10.5  log 12 10 I 1010.5  12 10 I  0.0316 W / m 2
1(b)

ln 3 x  ln 5 x ln 3  ln 5 ln 5 x  1.465 ln 3

Common Test / CL1104 / Page 3

Question 2 (a) Given the functions f x   5x  7 and (i) (ii) fg (x) gf (0)
3  2 x  7  5x .

g ( x) 

2 x , determine the following: x2  2

(7 marks) (3 marks)

(b) Solve the inequality Solution 2(ai)

 2 x  fg ( x)  5  2 7  x  2  10  5 x  7 x 2  14  x2  2 7 x2  5x  4  x2  2
2(aii)

gf ( x) 

5 x  7   2 2  0  7 gf (0)  2 0  7  2
2

2  5 x  7 



9 47

2(b)
7  5x  3  2 x  0 4 