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Cork Institute of Technology
Bachelor of Engineering in Biomedical Engineering-Stage 2
(EBIME_7_Y2)
Summer 2008
Mathematics & Computing
(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
Q1 (a) The parametric equations for a curve are
1 1 2 1 2 1
t t x y t t
Find the value of dy dx
when x = 1 and y = 1.
(8 marks)
(b) A function is described by the equation 2 x^3^ − y^3^ − 3 xy^2 = 6. Find
dy dx
for
the function at any point and in particular at the point (1, 3) (6 marks)
(c) Show that the equation f ( ) x = x^3 + 4 x − 1 has a root between x = 0 and
x = 1. Use Newton’s method twice to get a closer approximation to this root. (6 marks)
Q2 (a) Investigate the function V = 5 te −^2 t for its turning point and
sketch the curve. What is the initial value of V and what happens as t → ∞? (8 marks)
(b) Given z = 7 x^3^ + 4 xy^2 − 3 y^3 , find , z z x y
and
2 2
z x
(6 marks)
(c) An equation for heat H generated is given by
H = i Rt^2 (watts)
where variables i R t , , denote current, resistance and time respectively.
Determine the percentage error in the calculated value of H if the error made in measuring i is +4%, the error made in measuring R is -5% and the error made in measuring t is +7%. (6 marks)
Q3 Determine each of the following:
(a)
(^13 )
0
∫^2 te^ t − dt
(5 marks)
(b) ∫ 5 x e^4 xdx
(5 marks)
(c)
1 2 0
dx
∫ + x
(5 marks)
(d)
(^5 )
3
x x dx x x x
(5 marks)
Q6 (a) The mean height of 200 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 185cm (ii) the number of students who have heights less than 170cm (iii) the number of students who have heights between 170cm and 185cm. (7 marks)
(b) The probability that a new car needs a warranty repair in the first 90 days is 0.05. If a sample of 10 cars is selected, what is the probability that in the first 90 days (i) 2 need a warranty repair? (ii) at least one needs a warranty repair? (iii)three or more need a warranty repair? (7 marks)
(c) The number of accidents occurring in a certain factory follows a Poisson distribution with a mean of one accident per week. Calculate (i) the probability that exactly 2 accidents occur in a given week, (ii) more than two accidents occur in a given week. (6 marks)
Section B (Computing)
Answer either question 7 or question 8
Q7. The Department of Education is currently processing the results for the Leaving Certificate French examination. They are eager to do some statistical analysis on the results to find out the following figures. the lowest mark achieved the highest mark achieved the average mark achieved All of the results for the French examination are held in an integer array called FrenchResults that holds up to 200 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)
Q8.
ABC Ltd has two different types of employee. They have hourly workers, who receive a fixed hourly wage for up to the first forty^ hours they work and double their hourly rate for any overtime worked. They also have commission workers, who receive €400 plus 15% of their gross weekly sales. Each type of employee has its own pay code. Use a switch statement to compute each employee’s pay based on that employee’s pay code. You do not know the number of employees in advance and will therefore need to use a loop within your program.
You are required to write a C++ program to compute the weekly wage for each employee. (20 marks)
