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Simon Fraser University
Math 100
Final Exam Date: December 12, 2007
Time: 15:30 - 18:
Last Name (print): First Name
Signature: SFU Email ID:
Instructions:
- Do not open this exam until instructed to do so.
- No calculators, notes or books are allowed.
- When presenting a final answer for your solution, calculator-ready expressions will be given full credit.
- Show all your work. No credit will be given for an answer without the correct accompanying work.
- Answer the questions in the space provided. Continue on the back of the pre- vious page if necessary.
- There are 80 possible points in this examination.
- During the examination, communicating with, or deliberately expos- ing written papers to the view of, other examinees is forbidden.
Question 1 2 3 4 5 6 7 8 9 10 11 Total
Mark
Maximum 2 5 9 13 11 5 7 6 7 6 9 80
[2 pts] 1. Find the solution to the system of linear equations:
4 x − 3 y = 5 2 x − y = 4
[5 pts] 2. Find the coordinates of the center and the radius of the circle with equation x^2 + y^2 + 6x − 4 y = 5.
- Find all solutions to the following:
[6 pts] (a) log 2 (x − 6) + log 2 (x − 4) − log 2 x = 2
[4 pts] (b) 3 sin^4 x − 6 sin^2 x + 3 = 0
(c) x
(^3) − 16 x [3 pts] 2 x + 8 = 0
- Evaluate the following expressions.
[2 pts] (a) log 3 (log 2 8)
[2 pts] (b) cos(sin−^1 (−^12 ))
(c)
∑^4
i=
[2 pts] i^2
(d) cos−^1
cos 54 π
[2 pts]
[3 pts] (e) p(−3), where p(x) = x^4 − 3 x^2 + 8x − 2, using the remainder theorem.
- Consider the function p(t) = x
(^3) − 9 x 4 x(x + 3)(2x − 7).
[2 pts] (a) Find the domain of p(t)
[3 pts] (b) Determine all asymptotes of p(t).
[2 pts] (c) Find the x and y-intercepts of the graph of p(t), if they exist.
- Andy and Beth are standing 8m apart from each other, trying to read a sign which is some distance away from both of them. The angle formed by Andy’s line of vision to the sign and his line of vision to Beth is π/3. The angle formed by Beth’s line of vision to the sign and her line of vision to Andy is π/6.
[4 pts] (a) Find the distance between Andy and the sign.
[2 pts] (b) Using the Pythagorean identity, find the distance between Beth and the sign.
- Recall that the half-life of Carbon-14 (C-14) is 5730 years.
[3 pts] (a) Give the radioactive decay model for the amount of C-14 that remains after t years.
[3 pts] (b) If you found today an old bone containing 70% of its original amount of C-14, how old would that bone be?
- This question is based on the following diagram:
1 ! 3
Q
2 P
1
2
[3 pts] (a) Find the coordinates of the point Q.
[4 pts] (b) Find the equation of the line through P and Q.
[2 pts] (c) Find the coordinates of P.
