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Lecture

# Mock-Ma129-Fin-s11.pdf

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Wilfrid Laurier University

Mathematics

MA129

Shane Bauman

Winter

Description

MA129 Mock Final
Name:
Time Allowed: 120 minutes
Total Value: 85 marks
Number of Pages: 9
Instructions:
Cheat Sheet: One 8:5" ▯ 11" page of study notes (both sides) is allowed as a reference
while completing the mock test. Please note, that the cheat sheet is permitted
for the mock test only!
Non-programmable, non-graphing calculators are permitted. No other aids allowed.
Check that your test paper has no missing, blank, or illegible pages. Note that test questions appear
on both sides of the paper.
Answer in the spaces provided.
Show all your work. Insu¢ cient justi
cation will result in a loss of marks.
1. [2 marks] Solve the equation for x: 43x+1 = 16 2x▯5
2. [5 marks] Solve the equation for x: log2(x ▯ 4) = 3 ▯ log2(x ▯ 2)
1 ▯ 2 ▯
ln x ▯ 4
3. [3 marks] Determine the domain of the function f (x) = x + 5 . Express your answer using
interval notation.
2
4. [4 marks] Determine the equation of the line tangent to the curve y = f (x) = lnx + x at x = 1.
Express your answer in the form y = mx + b.
5. [2 marks] Determine the derivative of the function: g (x) = x log (3 ▯ x)
4
00 2x+1 ▯ 3 ▯1=3
6. [4 marks] Determine y given: y = 3 + 2x ▯ 1
2 7. [6 marks] Suppose you own an apartment building containing 100 uniIf you charge $400 per
month for each unit, then all units can be rentedFor every $20 increase in monthly rent, you
will lose one customer. What monthly rent should you charge to maximize your revenue? Show that
the corresponding revenue is an absolute maximum.
8. [3 marks] Given the following matrices,
2 3
" # " # 2 1
3 ▯1 2 1 0 1 4 5
A = 0 1 4 B = 0 1 1 C = 0 ▯1 ,
1 0
determine (A ▯ 2B)C.
3 2 2
x 0 x ▯ 4x 00 8
9. [9 marks] Let f (x) = x ▯ 2 . Then f (x) = 2 and f (x) = 3.
(x ▯ 2) (x ▯ 2)
(a) State the intervals on which f is increasing and those on which f is decreasing.
(b) Determine the coordinates of all relative maximum points and relative minimum points.
(c) State the intervals on which the graph of f is concave up and those on which it is concave down.
4 Z 4 2
x + 3x ▯ 4
10. [2 marks] Evaluate the integral: x2 dx
Z ▯ ▯
1 x e x e+1
11. [2 marks] Evaluate the integral: + ▯ x + e ▯ 2 dx
x e
R p
12. [4 marks] Evaluate the de
nite integral: x2 3x + 1 dx
0
Z

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