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Applied Mathematics Final Examination, Fall 2009, Dawson College, Exams of Applied Mathematics

Punjab Engineering CollegeApplied Mathematics

A final examination for the applied mathematics course at dawson college, department of mathematics, fall 2009 semester. The exam consists of 19 questions worth a total of 100 marks and covers various topics in mathematics such as algebra, trigonometry, calculus, and vectors. Students are required to answer all questions directly on the examination paper and are permitted to use non-programmable calculators.

Typology: Exams

2012/2013

Uploaded on 02/12/2013

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Dawson College
Department of Mathematics
Final Examination
Fall 2009
Applied Mathematics (201-921-DW)
Date: December 11, 2009 Time: 3 hours
Examiner: J. Requeima
Last Name: _________________________________________________
First Name: _________________________________________________
Student I.D.: ________________________________________________
•Print your name and student ID number in the space provided above.
•All questions are to be answered directly on the examination paper in the provided space.
•Non-programmable calculators are permitted.
This examination consists of 19 questions worth a total of 100 marks. Please ensure that you
have a complete examination before starting. This exam must be returned intact.
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Dawson College

Department of Mathematics

Final Examination

Fall 2009

Applied Mathematics (201-921-DW)

Date: December 11, 2009 Time: 3 hours

Examiner: J. Requeima

Last Name: _________________________________________________

First Name: _________________________________________________

Student I.D.: ________________________________________________

  • Print your name and student ID number in the space provided above.
  • All questions are to be answered directly on the examination paper in the provided space.
  • Non-programmable calculators are permitted. This examination consists of 19 questions worth a total of 100 marks. Please ensure that you have a complete examination before starting. This exam must be returned intact.
  1. (3 marks) Simplify, expressing your final answer using positive exponents only:

( 3 a^2 b−^3 )−^2 a^1 /^2 (

9 a^2 b)^2

  1. (3 marks) Solve for F. Express your answer as a single fraction:

Q = Fm(x + 1 )−^1 /^2 −

(x + 1 )^1 /^2 p

  1. (5 marks) Given the vectors ~A and ~B with A = 426 .1, θA = 126. 23 ◦^ and B = 891 .2, θB = 231. 5 ◦ find ~A +~B.
  1. (10 marks) Given the following system of equations:

2 y + z = 0 x + y + z = − 2 x + z = 1

(a) Solve the system of equations using Cramer’s rule:

  1. (5 marks) Given
A =
[
]
B =
 C =
[
]

compute the following if possible. If not possible explain why.

a) AC−^1

b) B(C − A)

c) A^2 − AC

  1. (6 marks) Find x in the following diagram:

x

1100mm

770mm

610mm

670mm

  1. (5 marks) What is the floor area (the shaded area) in the figure. The inside and outside of the hallway are circular arcs:
  1. (10marks) Prove the following trigonometric identities:

(a) cot x − tan x =

cos 2x sin x cos x

(b)

sin x(csc x − sin x) 1 + sin x

= 1 − sin x

  1. (4 marks) Find tan 2x, given sin x = 21 /75 and x is in the second quadrant (express your answer as a fraction, do not use decimals).
  2. (3 marks) Evaluate 3276^145. Express your answer with 4 significant digits. Clearly show your work.
  1. (5 marks) Solve for the following trigonometric equation for x with 0 ≤ x ≤ 2 π :

sin^2 x − cos^2 x + sin x + 1 = 0

  1. (3 marks) Rationalize the denominator and simplify: √ 6 +
  1. (5 marks) An elements decays according the the equation y = y 0 ekt^ where y 0 is the initial amount in grams and t is in years. (a) If it takes 17.2 years for 10.3g of the element to decay to 6.62g find k. (b) Find the half life of this element.
  1. (4 marks) 0 .210mol of ideal gas occupies 11.5L at 745torr. What is the temperature of the gas in ◦C?
  2. (4 marks) What temperature must 45.0L of gas at 23. 0 ◦C of gas be cooled at constant pressure so that the volume of the gas is reduced to 39.0L