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 125e0.375t . (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 1012 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 125e0.375 85.0mg
1(aiii)
Q 125e0.37516 0.310mg
1(b)
10 log
105 10 log
I I0
I 1012 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
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 125e0.375t . (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 1012 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 125e0.375 85.0mg
1(aiii)
Q 125e0.37516 0.310mg
1(b)
10 log
105 10 log
I I0
I 1012 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