MATH 32 FALL 2012
MIDTERM 1 - SOLUTIONS
(1) (6 points) Find all values of x satisfying the inequality
x+2
<2
x1
Solution: Well multiply both sides by x 1.
Case 1: x 1 0. This happens when x 1. Then we have
x + 2 < 2(x 1)
x < 2x 2 2
x < 4
x>4
Case 2: x 1 <
MATH 32 MIDTERM 1 REVIEW
This is just a list of the main concepts and skills weve explored so far this semester.
Its purpose is to help you organize your studying for the midterm exam. Of course, not
everything on the exam will correspond exactly to an it
MATH 32 FALL 2012
FINAL EXAM - PRACTICE EXAM SOLUTIONS
(1) You cut a slice from a circular pizza (centered at the origin) with radius 6 along radii at
angles and with the positive horizontal axis.
4
3
(a) (3 points) What is the area of your slice?
Solutio
MATH 32 FALL 2012
MIDTERM 1 - PRACTICE EXAM SOLUTIONS
(1) Find all values of x satisfying the inequality
1
5
x
Solution: Case 1:
1
x
0. This happens when x > 0. Then
1
5
x
Case 2:
1
x
1
5
x
x
1
x
1
= x.
1 5x
1
= x.
1 5x
1
5
< 0. This happens when x < 0.
MATH 32 SPRING 2013
FINAL EXAM SOLUTIONS
(1) (10 points) Suppose you put $100 in a bank account which gives 6% interest compounded
monthly. If you dont add or remove money from the account, after how many years will
you have $500 in the account?
You may e
MATH 32 SPRING 2013
FINAL EXAM SOLUTIONS
(1) (9 points) Fill in the following table:
Solution:
/6
5/4
sin
cos
1/
3
2
/2
2/2 2/2
2 2
2
/8
2+ 2
2
tan
1/ 3 = 3/3
1
22 = 2 1
2+ 2
/6 is one of our special angles - we know its sine and cosine. If you dont ha
MATH 32 FALL 2013
MIDTERM 1 - SOLUTIONS
1
.
x
(a) Is f (x) an even function, an odd function, or neither? Explain.
(1) (12 points) For this problem, let f (x) =
Solution: f (x) =
1
1
= = f (x), so f (x) is an odd function.
x
x
(b) Give a formula for a fun
MATH 32 SPRING 2013
MIDTERM 1 SOLUTIONS
(1) Suppose that the motion of a ball through the air is described by the equation h(t) =
t2 + 4t + 4, where h represents the height of the ball (in feet) after it has been in the air
for t seconds.
(a) (6 points) W
MATH 32 FALL 2012
FINAL EXAM - PRACTICE EXAM SOLUTIONS
(1) (6 points) Solve the equation |x 1| = 3.
Solution: Since |x 1| = 3, x 1 = 3 or x 1 = 3. Solving for x, x = 4 or x = 2.
(2) In the triangle below, let a = 4, b = 2, and c =
22.
(a) (3 points) Find