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Cork Institute of Technology
Bachelor of Engineering in Biomedical Engineering –
Stage 2
(EBIME_7_Y2)
Summer 2009
Mathematics & Computing - Legacy
(Time: 3 Hours)
Instructions Answer FOUR questions from Section A and One Question from Section B.
Examiners: Ms. H. Lordan Ms. G. O’Callaghan Mr. M. Murphy Dr. G. McGuinness
Section A
1 (a) The parametric equations are given as
x = 3 t – 1 and y = t ( t - 1), determine
dy dx
in terms of t.
(6 marks)
(b) Determine
dy dx
: 2 y^3 − y + 3 x − 2 = 0
(6 marks)
(c) Sketch the function f ( ) x = 2 x^3 − 15 x + 3 from x = 0 to x = There is a root between x = 0 and x = 1 and again between x = 2 and x = 3. Use Newton’s method twice to get a closer approximation to one of these roots.
2 (a) Investigate the following function for maximum and minimum values:
f ( ) x^48 x^3 x
= +. Sketch the curve. What happens as x → 0?
(8 marks)
(b) Given z = 4 x y^2^3 − 2 x^3^ + 7 y^2 , find ,
z z x y
and
2 2
z x
(6 marks)
(c) The power P consumed in a resistor is given by
V^2
P
R
= watts. Determine
the approximate change in power when V increases by 5% and R decreases by 0.5% if the original values of V and R are 50volts and 12.5 ohms respectively. (6 marks)
3 Determine any THREE of the following:
(a)
2 2 4 1
x dx x x
(b) ∫ 5 x e^4 xdx
(c)
3 2 0
dx − x
(d)
x x dx x x x
6 (a) The mean height of 120 engineering students is 179cm with a standard
deviation of 5cm. Assuming that heights are normally distributed, calculate (i) the number of students who have heights greater than 184cm (ii) the number of students who have heights less than 169cm. (6 marks)
(b) The average number of employees absent from a firm each day is 4%. An office within the firm has seven employees. Determine the probabilities that (i) no employee and (ii) three employees will be absent on a particular day. (7 marks) (c) 0.5% of items produced are rejects. Using the Poisson probability distribution, for a production run of 400 items determine the probability of obtaining (i) no defective item (ii) more than two defective items.
Section B (Computing)
Answer either question 7 or question 8
7. The Department of Education is currently processing the results for the Leaving Certificate Geography examination. They are eager to do some statistical analysis on the results. All of the results for the Geography examination are held in an integer array called GeographyResults that holds up to 300 elements.
(a) Write the C++ code to declare the array and to read in the results into the array as they are entered by the user at the keyboard. (5 marks)
(b) Write a C++ function that receives the array and the size of the array as parameters and calculates the lowest result entered along with the highest result entered. You should also display your results to the screen. (9 marks)
(c) Write a C++ function that receives the array and the size of the array as parameters and calculates the average result achieved by all students. You should also display your results to the screen. (6 marks)
8. ABC Haulage Ltd are concerned with the mileage obtained by their trucks. They have asked one driver to keep track of all tanks of diesel used by recording miles driven and litres used for each tank full. Develop a C++ program that will input miles driven and litres used for each tank of diesel. The program should calculate and display the miles per litre obtained for each tank full of diesel. After processing all input information, the program should calculate and print the average miles per litre obtained for all tanks of diesel.
Sample Output: Enter the litres used (-1 to quit): 28. Enter the miles driven: 120 The miles/litres for this tank was 4.
Enter the litres used (-1 to quit): 40. Enter the miles driven: 300 The miles/litres for this tank was 7.
Enter the litres used (-1 to quit): - The overall average miles/litres was 5.
