Download Large Batch - Mathematics - Exam and more Exams Mathematics in PDF only on Docsity!
Cork Institute of Technology
Higher Certificate in Engineering in Maintenance Technology – Stage 1
(National Certificate in Engineering in Maintenance Technology – Stage 1)
(NFQ – Level 6)
Summer 2005
Mathematics
(Time: 3 Hours)
Instructions Answer FIVE questions. Answer at least ONE from Section B.
All questions carry equal marks.
Examiners: Mr. S. O Leary Mr. R. Simpson Mr. J. Connolly
Section A
Q1. (a) (i) Solve the following simultaneous equations for x and y 2 x + y = 6 x –^2 y =^8 (ii) Illustrate your result by graphical means. (iii) Determine the slope and intercept for each of the lines given in (i) above. (9 Marks) (b) The data in the table below shows the force F Newtons which, when applied to a lifting machine, overcomes a corresponding load of L Newtons.
F(N) 19 35 50 93 125 147
L(N) 40 120 230 410 540 680
(11 Marks) Verify graphically that the equation relating F and L follows approximately a law of the form F = KL + C where K and C are constants. Calculate F when L = 100N.
Q2. (a) (i) Solve the following quadratic equation x 2 – 3 x – 28 = 0 (ii) Illustrate your answer graphically (8 Marks) (b) Determine the quadratic that has roots +3 and +4. (4 Marks) (c) A manufacturer wishes to make 5 litre cans by folding 600mm by 250mm sheets of tinplate around a rectangular former, butt jointing the seam and sealing the open ends. Neglecting any material needed to cover the open ends, calculate the width and depth of the former to the nearest mm. To allow for filling etc. allow a design capacity of 5. litres. (8 marks)
Q3. (a) Calculate the total surface area and volume of a hemisphere of radius 0.5m. (6 Marks) (b) In a roof truss, three members AB 4.5m, BC 6.2m, and AC 7.8m long form a triangle. Determine the angle formed between members AB and BC. (8 Marks) (c) Plot the graph of 12 Sin 2A for one complete cycle. (6 Marks)
Q4. 50 steel rods selected at random from a large batch of nominally identical rods were tested. The maximum stress that each rod could withstand is shown in the table below.
Stress in MN/m^2 174.4 173.2 153.1 162.2 166.2 165.7 157.4 179.9 164.8 153. 176.5 175.9 172.1 182.1 171.1 182.4 169.7 183.9 186.1 180. 168.9 163.0 178.9 176.1 177.2 158.9 153.7 180.3 176.2 174. 161.6 173.9 165.2 178.6 169.1 168.2 158.6 157.1 176.4 167. 159.4 167.7 163.6 176.4 162.3 165.3 181.3 174.8 170.6 186.
(i) Construct a frequency distribution table with class intervals beginning with 153 – 157 MN/m^2 (6 Marks) (ii) Draw a histogram using the table from (i) (6 Marks) (iii) Calculate the mean and standard deviation from the frequency distribution table in (i) above. What percentage of values lie in the range ( x + S )to ( x + S )where x is the mean and S = standard deviation
