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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2009
Module Title: Technological Mathematics 1
Module Code: MATH 6014
School: School of Engineering: Building and 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 – Year Bachelor of Engineering in Biomedical Engineering – Year Bachelor of Engineering in Building Services Engineering – Year Bachelor of Engineering (Honours) in Sustainable Energy – Year 1
Programme Code: CCIVL_7_Y1, EELXE_7_Y1, EELEC_7_Y1, EMARE_7_Y1, ESENT_8_Y1, EBSEN_7_Y1, EBIME_7_Y1, EMECH_7_Y1, SIMCT_6_Y
External Examiner: Dr. B. O’Regan Internal Examiner(s): Ms. M. Brennan, Dr. D. Cremin, Ms. H. Lordan, Dr. P. O’Connor, Mr. G. O’Driscoll, Dr. V. Morari, Dr S O Rourke
Instructions: Answer QUESTION 1 (worth 40 marks) and TWO other questions (worth 30 marks each)
Duration: 2 Hours Sitting: Autumn 2009
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 that a = 0.290, b = 14.86, c = 0.042, d = 31.8, e =0.
evaluate v in the formula: ab d v c e
(5 Marks)
(ii) Solve for x in the following equation: 10 e^2 x = 15 (5 Marks)
(iii) Express the following as the sum of two partial fractions:
x x x
(5 Marks)
(iv) Show that the following quadratic equation has no real solutions: 3 x^2 − 6 x + 15 = 0 (5 Marks)
(v) Use the data in the following table to find values for R 0 and α in the
relationship R = R 0 (1 + α t ).
(5 Marks)
(vi) A line passes through the point (500,7.08) and has a slope of −3.2 × 10 −^3. Find the value of x when y = 8.46. (5 Marks)
(vii) State the amplitude, periodic time, frequency and phase angle of the following function: f t ( ) = 75sin(200 π t − 0.54). (5 Marks)
(viii) Solve for x : 3sin( x − 30 )o^ =1.75 0 o^ ≤ x ≤ 360 o^ (5 Marks)
R 30 35
t 50 100
- (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) y = bax .…. a and b are constants
(ii) y = kxn ….. k and n are constants. (10 Marks)
(b) The following values of T and L are related by a law of the form T = kLn , where k and n are constants.
T 1 1.2 1.4 1.6 1.8 2
L 2.4 3.5 4.8 6.3 7.9 9.
By plotting a suitable linear graph, verify the law exists. Find approximate values for k and n and state the law. (20 Marks)
- Answers parts (a) and (b). Also answer part (c) or (d).
(a) Solve for x : 3cos(2 θ ) + sin θ= 1 0 o^ ≤ θ≤360 .o^ (8 Marks)
(b) In a triangle ABC , side a = 7 cm, b = 10 cm and side c = 11 cm. Find angles A B , and C. (8 Marks)
(c) The current flowing in a circuit at any time t (seconds) is given by i = 12sin(100 π t + 0.27)amperes. Find the
(i) value of the current when t = 0 seconds, (ii) value of the current when t = 0.002seconds, (iii) time when the current first reaches 5 amperes, and (iv) time when the current is first a maximum. (14 Marks)
(d) From a window 8.5 m above horizontal ground the angle of elevation of the top of a vertical tower is 38o^ and the angle of depression from the window of the bottom of the tower is 9.5o^. Calculate
(i) the distance of the tower from the window, and (ii) the angle of elevation of the top of the tower from ground level at a point perpendicularly below the window. (14 Marks)
