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Cork Institute of Technology
Bachelor of Engineering in Biomedical Engineering โ Stage 1
(NFQ Level 7)
Summer 2007
Mathematics & Computing
(Time: 3 Hours)
Instructions Answer FIVE questions. Answer at least ONE question from Section B. Question 8 in Section C is compulsory. Use a separate answer book for Section C. All questions carry equal marks.
Examiners: Mr. D. O'Shea Mr. A. McGibney Mr. M. Murphy Prof. P. McHugh
SECTION A
Q1 (a) Using the laws of indices simplify the following, giving your final answers with positive indices.
(i)
7 3 4 5 4
a b c ab c
โ .
(ii)
3 4 4 2 2 3 2
x x x x
(6 marks)
(b) Solve for x : (i) log 8 4 = x
(ii). log 3 ( 25 x โ 14 ) โ log 3 ( 2 x + 7 )= 2
(iii) 52 x^ +^3 = 6 x โ^1. (8 marks)
(c) (i) Transpose the formula
t x y w t
to make t the subject.
(ii) Calculate the value of y when: t = 2.25 ร 10 โ^3 , x = 5, w = 1.3 ร 10 โ^1. (6 marks)
Q2 (a) The table below shows values of x and y that are believed to be related by
the law y = axb , where a and b are constants. y 50 112 310 800 1,510 2, x 1 1.5 2.5 4 5.5 7
Verify the law is as stated. Determine the approximate values of a and b and hence state the law. (10 marks)
(b) The population, P, of a region is given by the formula P = Aekt , where t is the time in years and A is the population at time t = 0. If the initial population is 5,000, find: (i) The value of A. (ii) The value of k if the population after 5 years is 7,500. (iii) How many years it will take the population to reach 12,000. (iv) The population after 16 years. (10 marks)
Q3 (a) Solve for a, b and c:
3 2 4 13 4 7 5 48 2 6
a b c a b c a b c
(9 marks)
(b) Expand (^4)
(1 + 2 ) x
as far as the term in x^4.
(8 marks)
(c) Convert: 285ยบ to radians and 3.24 radians to degrees. (3 marks)
SECTION B
Q6 (a) Differentiate each of the following:
(i) (^43)
y x x x x
(ii) y = e^5^ x โ^2 cos( x^2 โ4)
(iii) y = ln( x^3^ โ 2 x^2 +10)
(iv) y = 5 x^2 โ 8 x + 12 (12 marks)
(b) Draw a rough sketch of the function: y = x^3 โ 10 x^2 + 17 x + 28 , showing all the critical points. (8 marks)
Q7 (a) Determine each of the following integrals:
(i) (^54)
x dx x x
โซ^ +^ +^ +
(ii) โซ(8 x โ5)^4 dx
(iii)
1
1
cos(5 x 3) dx โ
(iv)
(^328)
1
โซ (2^ x^ โ8)(^ e^ x^ โ x ) dx (14 marks)
(b) Find the area enclosed by the curve y = 2 x^2 โ x + 3 , the x-axis and the ordinates
x = - 2 and x = 4. (6 marks)
SECTION C
Use a SEPARATE ANSWER BOOK for Question 8
8 (a) Study the following program:
void main() { int num1 = 1;
for(int count = 1; count <= 3; count++) { num1 = num1 * count; num1 = num1 + num1; }
cout << "The Result is: "<< num1 << endl; }
What will the output of this program be; explain your reason step by step. (5 marks)
8 (b) Write a program that displays the 4 options listed below. Allow the user select an option until Quit is selected. Program must report on an invalid selection.
- Sing
- Dance
- Clap
- Quit For each option display what operation that can be done. (10 marks)
8 (c) Look at the following program:
#include using namespace std;
void main() { int x = 4; int y = 7; int z = 2 ; int ans = y+x / z ; cout << "The Answer is : "<<endl ; cout<< ans + y <<endl; }
Explain each line of the code individually, and indicate what would be output to the screen for cout statements. (5 marks)
