Download TAKE-HOME EXAM 3

MATH 101
INTERM. ALGEBRA
NAME:
ID#:
TAKE-HOME EXAM 3
(Chapter 9)
Solve the following problems showing all your work for full credit.
1. Evaluate each expression without a calculator.
81
a) (3 pts.) 4
16
1
b) (2 pts.) 32 5
c) (2 pts.) 10000
1
4
2
 8 3
d) (4 pts.)  
 27 
e) (4 pts.) 64
 2
− 
 3
2. Express each expression in simple radical form.
a) (3 pts.) 48
b) (3 pts.)
3 5
1
2
3
3
c) (4 pts.)  
2
d) (3 pts.) 25
1
4
2
− 
3
3. Perform the operations and express your answer in simple radical form.
a) (4 pts.) 12 + 27
b) (4 pts.)
50 − 45
c) (4 pts.)
6 12
d) (4 pts.)
8
48
4. Solve each quadratic equation. Give roots as exact numbers in simple radical form.
a) (4 pts.) x 2 + 1 = 55
b) (4 pts.) x 2 + 4 x − 14 = 0
c) (4 pts.) 3x 2 − 13 = 12 x
5. (4 pts.) Show that the functions y1 =
other.
6. Find the variation constant a .
a) (3 pts.) y = ax , y = 2 when x = 6
b) (3 pts.) y = ax 2 , y = 45 when x = 3
1
c) (3 pts.) y = ax 3 , y = 0.4 when x = 8
1
d) (3 pts.) y = ax 2 , y = 100 when x = 10
1
x − 4 and y 2 = 3 x + 12 are inverses of each
3
7. (5 pts.) The height of an equilateral triangle varies directly as the length of its sides.
The height of an equilateral triangle is 3 cm when the sides are 2 cm each. What is
the height, if the sides are
3
cm each?
2
8. Use algebra to solve each equation. Note any extraneous solutions.
a) (4 pts.) 2 x 6 = 98
b) (4 pts.) ( x − 2) − 5 = 22
3
c) (2 pts.) x 4 = −30
1
1
d) (4 pts.) x 2 = −2
8
1
3
e) (4 pts.) − 5 x − 4 = 1
9. (5 pts.) Sketch the graph of the inverse function of the function, which graph is given
below. Find the coordinates of the point corresponding to the point (1,0 ) .
1
0.5
0
-2
-1
-0.5 0
-1
-1.5
-2
-2.5
1
2
3
4