Download Determine Angle - Technological Mathematics - Old Exam Paper and more Exams Mathematics in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2007/
Module Title: Technological Mathematics 1
Module Code: MATH 6014
School: School of Engineering: Building & Civil Engineering Electrical & Electronic Engineering Mechanical Engineering Biomedical Engineering National Marine College of Ireland
Programme Title: Bachelor of Engineering in Civil Engineering – Year 1 Bachelor of Engineering in Electronic Automation and Robotics – Year 1 Bachelor of Engineering in Applied Electronics Design – Year 1 Bachelor of Engineering in Communications Systems – Year 1 Bachelor of Engineering in Electrical Engineering – Stage 1 Bachelor of Engineering in Marine & Plant Engineering – Stage 1 Bachelor of Engineering in Mechanical Engineering – Stage 1 Bachelor of Engineering in Biomedical Engineering – Stage 1 Bachelor of Engineering in Building Services Engineering – Stage 1
Programme Code: CCIVL_7_Y1 EELXE_7_Y1 EELEC_7_Y1 EMARE_7_Y EMECH_7_Y1 EBIME_7_Y1 EBSEN_7_Y
External Examiner(s): Dr. P. Robinson Internal Examiner(s): Ms. M. Brennan, Dr. T. Creedon, Dr. D. Cremin, Ms. J. English, Ms. H. Lordan, Dr. P. O’Connor, Mr. D. O’Shea, Dr. S. O’Rourke
Instructions: Answer QUESTION 1 (worth 40 points) and TWO other questions (worth 30 points each)
Duration: 2 HOURS
Sitting: Autumn 2008
Requirements for this examination: Graph paper, Log Tables
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
- (i) Given the formula:
2
5
h x f t
π = (^) −
. Evaluate x when f = 2.1 10× −^3 ,
t = 3.2 × 106 and h = 6.7 ×10. 3 (5 marks)
(ii) Solve for x : 5 e^3 x = 90 (5 marks)
(iii) Express the following as the sum of two partial fractions:
3 7 ( 1)( 2)
x x x
(5 marks)
(iv) Show that the following quadratic equation has no real solutions: 3 x^2 + 4 x + 9 = 0 (5 marks)
(v) Use the data in the following table to find values for k and n in the relationship
n T
k H = +.
T 100 400
H 52 35
(5 marks)
(vi) A line passes through the point ( 10, −2.4 × 10 −^2 )and has a slope of 0.6.
Find the value of x when y = 84.6 × 10 −^2. (5 marks)
(vii) Draw a rough sketch of the function f ( ) x = 6sin(4 x − 20 )o^ , indicating the amplitude, period and the phase time. (5 marks)
(viii) Given the triangle ABC when A = 40 o^ , B = 63 o^ and a = 15 cm determine angle C and side c. (5 marks)
- (a) Express each of the following equations in linear form, indicating what you would plot on each axis and how each constant may be evaluated:
(i) 2 2
s = ut + at .…. u and a are constants
(ii) F = abT ….. a and b are constants. (12 marks)
(b) In an experiment carried out two variables x and y were found to have the following values:
x 40 60 90 115 140
y 1.92 4.32 9.72 15.87 23.
The relationship between x and y is thought to be of the form y = axb where a and b are constants.
(i) Write the given relationship in linear form. (ii) Show by plotting a graph of log y against log x that these results do in fact obey the given law. (iii) Use your graph to calculate the values of the constants a and b and hence state the law. (18 marks)
- (a) A triangle ABC has sides a = 20 mm, b = 36 mm and c = 42 mm. Determine its three angles. (9 marks)
(b) Given the function y t ( ) = 150sin(10 π t − 1.64)where t is measured in seconds, determine the
(i) value of y t ( ) when t = 0 (ii) value of y t ( ) when t = 15 ms (iii) time when y t ( ) is first a maximum (iv) time when y t ( ) first reaches 120 (14 marks)
(c) Find the values of A in the range 0 o^ ≤ A ≤ 360 o^ which satisfy the equation − sin 2 A + 2 cos A + 2 = 0. (7 marks)
