DT004/1 OMAT1010 TE D.I.T ISNI . DUBLIN LO ATHA CLIATH . XE NE CHT DUBLIN INSTITUTE OF TECHNOLOGY DT004 - Bachelor of Technology in Civil Engineering Stage 1 WINTER EXAMINATIONS 2018/19 Engineering Mathematics & Computing 1 [OMAT1010] Mr Edmund Nevin Mr John Turner 2 Hours Special Instructions: Answer all four questions. All questions carry equal marks. Given: Graph paper, Mathematical tables
DT004/1 8776 OMAT 1010 1. a) Transpose the following formula to make I the subject: n = E - Ir IR b) Solve the following equation: 5x - (7x - 4) - 2 = 5 - (3x + 2) Include a check with your solution. c) Find the measure of the angle 0 (rounded to the nearest degree) if sin 0 = - 0.6293 and the terminal side of 0 (in standard position) lies in quadrant III, where 0° ? 0 ? 360°. d) If the total surface area of a solid cone is 486.2cm2 and its slant height is 15.3cm, determine its base diameter. (5 marks) (5 marks) (5 marks) (10 marks) Total marks for Question 1: 25 marks 2. a) Solve the following inequality for x: (5 marks) Also, graph your solution. |3x-2| ? 0 b) Solve the following equation for x: (5 marks) log (2x - 3) = log_(x) + log_(x-2) c) Use Pascal's triangle to determine the binomial expansion of: (5 marks) (2x + 4)4 d) Solve the triangle whose side lengths are a = 8, b = 6, and c = 7. (10 marks) Total marks for Question 2: 25 marks 3. a) Solve the following equation for x: 5x-2 = 33x+2 (5 marks) b) Simplify the following expression and hence write in the form axn where a and n are constants: (5 marks) ( 2 X ) 4 c) Plot a graph of y = 2x2 over the range -3 ? x ? 3 and hence solve the following equation: (5 marks) 2× 2 - x - 3 = 0 d) 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. (10 marks) Total marks for Question 3: 25 marks C DIT 2018 1
DT004/1 8776 OMAT 1010 4. 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) Find the real roots, if any, of the given equation. iv) Draw a sketch of the given function. (3 marks) (2 marks) (2 marks) b) Solve the following equations graphically: (5 marks) 1.20x + y = 1.80 x - 5.0y = 8.50 c) The building illustrated in Figure Q4.1 is 4.0m long and 2.0m wide. A concrete