Partial Fractions - Mathematics - Exam, Exams of Engineering Mathematics

Download Partial Fractions - Mathematics - Exam and more Exams Engineering Mathematics in PDF only on Docsity! Cork Institute of Technology Higher Certificate in Engineering in Building Services Engineering -Stage 1 (NFQ - Level 6) Autumn 2006 Mathematics (Time: 3 Hours) Instructions Answer FIVE questions. All questions carry equal marks. Examiners: Ms.H.Lordan Dr.N.J.Hewitt Mr.Declan Leonard Q1 (a) Using the laws of indices: (i) Solve for x : 2 1 2 34 8 32x x x+ − −× = . (ii) Simplify: 2 8 4 2 2 16 ( ) x y x y − − − . (8 marks) (b) Solve for x using the laws of logarithms: (i) 27 21xe = (ii) 53 12x+ = . (6 marks) (c) For the formula 1 1 2 f LCπ = (i) Make C the subject. (ii) Find the value of f if 62.66, 4 10L C −= = × . (6 marks) Q2 (a) Solve for 1R and 2R , given 1 2 14R R+ = 1 2 1 1 7 20R R + = . (8 marks) (b) Sketch the curve 25 xy e−= for values of x from 0x = to 2x = using intervals of 0.4. From the graph, or otherwise, find the value of x for which 1y = .5. (6 marks) (c) Resolve into its partial fractions 7 12 ( 2)( 3) x x x + + + . (6 marks) Q3 (a) Write each of the following in the form y mx c= + . In all cases a and b are constants. (i) 2v a bt t t = + (ii) 2 10s at bt= + − (iii) btp ae= . (6 marks) (b) x 2.5 3.7 4.5 6.3 7.0 y 1.525 35.125 168.151 2481.558 5764.801 Show that the values of x and y are connected by the law by ax= by plotting the graph of log y against log x . Solve for constants a and b . (14 marks)