Monday April 26, 2010
Math 40 - Quiz 12 Solutions
1. Find all solutions to:
1
2
and u =
sin 3 =
1
Solution: sin u has the value 2 at u =
So the solutions are given by:
3 =
and
3 =
7
6
11
.
6
7
7 2
+ 2k = =
+
k
6
18
3
11
11 2
+ 2k = =
+
k
6
18
3
for k = 0
Wednesday April 21st, 2010
Math 40 - Quiz 11 Solutions
1. Suppose (3, 4) is on the terminal side of an angle in standard position. Find the
six corresponding trig functions.
(3)2 + (4)2 =
In this case r =
4
sin = ,
5
5
csc = ,
4
9 + 16 = 25 = 5. So we hav
Monday April 5, 2010
Math 40 - Quiz 9 Solutions
1. Let f (x) =
1
x+3
2
and g (x) = x . Find the domain of f g .
Solution:
(f g )(x) = f (g (x)
So x = 0 and g (x) = 3. So the domain of the composition is:
x = 0,
2
3
2. Solve 2x = 16.
Solution:
2x = 16 = 2x
Thursday March 30, 2010
Quiz 8 Solutions
1. Sketch the graph of f (x) = (x + 3)(x 2)2 (x 1)3 .
The graph will have x-intercepts at x = 3, 2, 1. At x = 3 and x = 1 the graph
crosses the x-axis since they are zeros of odd multiplicity. At x = 2 the graph to
Thursday March 25, 2010
Quiz 7 Solutions
1. Find the equilibrium price if supply is given by S (p) = 20p 1000 and demand is
given by D(p) = 10p + 800?
The equilibrium price is the price for which S (p) = D(p). We have:
S (p) = D(p) = 20p 1000 = 10p + 800
Monday March 15, 2010
Math 40 - Quiz 6 Solutions
1. A piecewise dened function is dened as:
:x<0
x 2
3
:x=0
f (x) =
2
x
:0<x<2
(a) What is the domain of f ?
Solution: Putting these domains together, you see the domain is all real
numbers less than 2.
(b)
Wednesday March 3, 2010
Math 40 - Quiz 5 Solutions
1. Let f (x) =
2x1
.
x 2
(a) What is the domain of f ?
Solution: All real numbers except 2.
(b) List the x-intercepts of the graph of f .
Solution:
1
2x 1
= 0 = 2x 1 = 0 = x = .
x2
2
(c) List the y -inter
Monday February 22nd, 2010
Math 40 - Quiz 4 Solutions
1. Find the distance between (4, 3) and (6, 2).
Solution:
d = (4 6)2 + (3 2)2 = 100 + 25 = 125 = 5 5
2. Find the x and y intercepts of 9y 2 + 4x = 36.
Solution: To nd the x-intercepts, set y = 0. Then
Tuesday April 6, 2010
Math 40 - Exam 3 Solutions
1. You launch an anvil directly upward at 64 feet per second. The height of the anvil t
seconds after being launched is given by h(t) = 16t2 + 64t where t is in seconds.
(a) How high will the anvil go?
Solu
Tuesday March 16, 2010
Math 40 - Exam 2 Solutions
1. Find the distance from the center of the circle 2(x + 1)2 + 2(y 1)2 = 32 to the point
(4, 3). Is this point inside or outside the circle?
Solution: The center of this circle is (1, 1). So the distance b
Tuesday February 9, 2010
Exam 1 Solutions
This test is worth 36 points. No notes or calculators are allowed. Please put a box around
your nal answer in each problem. For full credit, show all work. Good luck!
1. Completely simplify the following expressio
Thursday Dec. 21, 2010
Name:
Math 40 - Quiz 1
1. Is x2 2x5 + 55
2. Simplify
3. Simplify
3
3
3x a polynomial? If so, what is its degree?
(41 )3
x2 7x8
.
x2 64
Thursday April 29, 2010
Name:
Practice Final Exam
This practice test contains 9 pages with 11 total problems. Please check to make sure you
have all pages. It is worth 72 points. No notes or calculators are allowed. Please put a box
around your nal answer
Math 40 - Exam 3 Practice Problems
1. The cost C , in dollars, of renting a moving truck for a day is given by the function
C (x) = 1 x + 40, where x is the number of miles driven.
4
(a) What is the cost if you drive the truck 80 miles?
(b) How far can yo
Math 40 - Exam 2 Practice Problems
1. Find all the points on the x-axis that are 5 units from the point (4, 3).
2. What is the slope and y-intecept of the line: x + 2y = 4.
1
3. Find an equation for the line perpendicular to the line y = 2 x + 4 containin
Wednesday April 21st, 2010
Math 40 - Quiz 11 Solutions
1. Suppose (3, 4) is on the terminal side of an angle in standard position. Find the
six corresponding trig functions.
(3)2 + (4)2 =
In this case r =
4
sin = ,
5
5
csc = ,
4
9 + 16 = 25 = 5. So we hav
Monday April 5, 2010
Math 40 - Quiz 9 Solutions
1. Let f (x) =
1
x+3
2
and g (x) = x . Find the domain of f g .
Solution:
(f g )(x) = f (g (x)
So x = 0 and g (x) = 3. So the domain of the composition is:
x = 0,
2
3
2. Solve 2x = 16.
Solution:
2x = 16 = 2x
Thursday March 30, 2010
Quiz 8 Solutions
1. Sketch the graph of f (x) = (x + 3)(x 2)2 (x 1)3 .
The graph will have x-intercepts at x = 3, 2, 1. At x = 3 and x = 1 the graph
crosses the x-axis since they are zeros of odd multiplicity. At x = 2 the graph to
Thursday March 25, 2010
Quiz 7 Solutions
1. Find the equilibrium price if supply is given by S (p) = 20p 1000 and demand is
given by D(p) = 10p + 800?
The equilibrium price is the price for which S (p) = D(p). We have:
S (p) = D(p) = 20p 1000 = 10p + 800
Monday March 15, 2010
Math 40 - Quiz 6 Solutions
1. A piecewise dened function is dened as:
:x<0
x 2
3
:x=0
f (x) =
2
x
:0<x<2
(a) What is the domain of f ?
Solution: Putting these domains together, you see the domain is all real
numbers less than 2.
(b)
Tuesday April 6, 2010
Math 40 - Exam 3 Solutions
1. You launch an anvil directly upward at 64 feet per second. The height of the anvil t
seconds after being launched is given by h(t) = 16t2 + 64t where t is in seconds.
(a) How high will the anvil go?
Solu
Tuesday March 16, 2010
Math 40 - Exam 2 Solutions
1. Find the distance from the center of the circle 2(x + 1)2 + 2(y 1)2 = 32 to the point
(4, 3). Is this point inside or outside the circle?
Solution: The center of this circle is (1, 1). So the distance b