Math Placement Exam, 1
Name _
MATH PLACEMENT EXAM
NO CALCULATORS
PLEASE CIRCLE YOUR ANSWERS AND WRITE YOUR NAME ON EVERY
PAGE!
Part I: Algebra, Geometry and Logic
1. Evaluate or simplify each of the following:
i. ( x 2 x 3 ) 8
ii.
3
( x 2 25)
3
iii.
(k!3
9 qy8 h Q7EySl3ay
pn RPH j ya Dd|R g
gB P i B D BHD B Y p DH D Ya h D gB ga i PH n R PH j ya Dd | R g
[email protected]# WyQm8 h QiEySl3ay
gB P i B D BHD B Y DH D Ya h D gB ga 9 o DH D i D Va B Y R P
eySpPiSwQ% ywyfwaGEyfRQ`P'[email protected]
o
Calculus Placement Exam
Harris School of Public Policy
September 21, 2009
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
Calculus Placement Exam
Harris School of Public Policy
September 22, 2008
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
Calculus Placement Exam
Harris School of Public Policy
September 17, 2007
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
Calculus Placement Exam
Harris School of Public Policy
September 24, 2007
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
Part I Algebra (adapted from previous years exams)
Solve the following:
1. (x2x1)5
2.
1 / (x 2- 25) + 6 / (5 + x)
3. 27-2/3
4. -21/x2 + 4/x + 1
5. 3x2 - 4x + 1 = 0
6. Given the parabola:
y = x2 + 6x + 13
a. Find the vertex (x and y coordinates)
b. Does th
Part II. Calculus
1. Consider the function
y = (5 x)1/3
a. What is the domain of the function?
b. What is the image of the function?
c. What is f(x) at x = 13?
d. What is f(x)?
e. What is f(x) at x = 4?
f. Find the slope and the equation of the tangent li
Calculus Placement Exam
Harris School of Public Policy
September 23, 2013
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
Calculus Placement Exam
Harris School of Public Policy
September 24, 2012
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
Calculus Placement Exam
Harris School of Public Policy
September 19, 2011
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
Calculus Placement Exam
Harris School of Public Policy
September 20, 2010
You have ninety minutes for this exam. No books, notes, calculators, or other aids are allowed. Please
answer in the blue books provided, and please make sure to include your name a
h
6 W S 3 U 6 g 3 t F 3 g cfw_ a
QQ#&BE
6 W S
p
s H l P s 46 g4 S
wrVH #`7e8
8 4 8
[email protected]
3 W 3 g 4 F 3 g cfw_ a H 4 6 g 4 t 3 G F 3 C A 3 4 F 3 X W 3 U F S G 6 3 P
eB`dBE#ee(eeBETEDBe8 [email protected]|t(VH 5o"0 ty
4 3 1
a
p `"TQeTQVQT~hn #BBETEDBeEe4
H
rCguUS ChAuYSQIXhuwhf`
6 c c v` S v V Dv r6 ~ F` F S H q v D
[email protected]@[email protected]'UdEH1C9CaIvCIwUYSdFU
Bv v F Ht x t D@ v V ` F@ D B 6 ~ p 6 ~ p t @ v
rTC YSQUIuq AUGwIHFEHjvUISI@[email protected]
6 c F` F S H v D ` B v v F H t x t D @ v 8 8
D` [email protected]
H qHhWA8 EAW YHAw 6 Y wH Wd Wd H WH5 W
pGXrpiSgSIDpiFTE aA `Dxw ISA xI%Y6 i g8 f72w D
~ ~ fr
rr
~ ~ ~ ~ ~ i ~
Di ~ n i B m rr m rr (D ~ Fl n m n i
E E A
E E Y R 6 q A H E W H H RD G5 A GHSEE H $cfw_Uh6W H 5
p Pi G5DTHU67UrGHr7s5rrg8U6SA %V7s52f7%
Econ 421
Autumn 2015
Leverage
Margin buying
Margin buying refers to the buying of securities with cash borrowed from a broker, using other
securities as collateral. This has the effect of magnifying any profit or lo