DT004/1 8776 OMAT 1010 DUBLIN INSTITUTE OF TECHNOLOGY BOLTON STREET, DUBLIN 1 Bachelor of Engineering Technology in Civil Engineering FIRST YEAR: SEMESTER ONE 2017-18 ENGINEERING MATHEMATICS & COMPUTING 1 John Turner, BE, MEngSc, MIEI Edmund Nevin Monday 11th December 2017 9.30am - 11.30am Answer all of the following four questions All Questions carry equal marks Exam Duration: 2 Hours Given: Mathematical Tables Graph Paper
DT004/1 8776 OMAT 1010 M+VM2+T 1. a) Transpose the formula B = 2 to make M the subject. Hence calculate M when B = 12.87 and T = 9.76. (8 marks) b) Simplify the following expression 3xy2(3xy)2 and hence write in the form axmy" where a, m and n are constants. c) Solve the following equation for x: 3x(1 + 2x) - 4 = 4x2 (3 marks) (4 marks) d) In a triangle AABC, the length of the sides are: | AB| = 17cm, |BC] = 9cm and |AC| = 15cm. Find the value of the internal angles. (10 marks) Total marks for Question 1: 25 marks 2. a) Given the function y = f (x) = x2 + 6x + 8 carry out the following: i) Use the discriminant to determine how many roots the function has. (3 marks) ii) Determine the point on the x-axis through which the symmetry line passes. iii) Factorise the given equation and hence find its roots. (4 marks) iv) Draw a sketch of the given function. (5 marks) b) Solve the following equation for x: (5 marks) 2 log2 (x + 2) - log2 (x2 + 2x + 1) = 4 c) From a window 8m above horizontal ground the angle of elevation to the top of a higher building across the road is 20° and, from the same window, the angle of depression to the foot of the building is 30°. Find the width of the road and the height of the building. (5 marks) (3 marks) Total marks for Question 2: 25 marks 3. a) Solve the following inequality for t: (10 marks) b) Simplify each of the following expression (3 marks) c) Solve the following equation for x: (6 marks) t+ 1 3t - 6 0 xv16x2 y3 and hence write in the form axmy" where a, m and n are constants. 4x 3 - x d) Solve the following equation for x: - 24-2 - 44 3 - ln 4x + 1 x - 2 (6 marks) = 2.14 Total marks for Question 3: 25 marks 1 C DIT 2017
DT004/1 8776 OMAT 1010 4. a) Solve the following inequality for z: (2z + 1)2 > 9 b) Determine, using Pascal's triangle method, the expansion of (2p - 3q)3. c) Plot a graph of y = 2x2 over the range -3 ? x ? 3 and hence solve the following equations: 2×2 - 8 = 0 (3 marks) i) ii) 2×2 - x - 3 = 0 d) A storage hopper is illustrated in Figure Q4.1. Determine its lateral surface area given that it consists