1
Math 70 : Intermediate Algebra
Name : ____________________
Test 3 : System of linear equations, Polynomial and Exponents
Use the appropriate method to solve the problem.
Must show your work.
Circle your answers.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Points
5
5
5
6
12
6
10
5
5
5
5
5
5
5
6
5
5
5
5
Total
110
Your points
Comments
Your test score = _____________________________
Your current course grade = __________________________
1
Fall 2010
2
5 x  2 y  11
[5] 1. Use the substitution method to solve 
.
x

2
y


9

 x  4 y  8
[5] 2. Use addition method to solve 
.
3x  12 y  24
3
[5] 3. Flying with the wind, a plane flew 1000 miles in four hours. Against the wind, the
plane required 5 hours to fly the same distance. Find the rate of the plane in calm air and
the rate of the wind. [Use two variables and two equations to solve this problem.]
(i) Describe your variables.
The rate of the plane in calm air = __________.
The rate of the wind = __________.
(ii) Setup the equations. (Distance= rate • time)
(iii) Solve the equations and present your answers.
4
[6] 4. A coin bank contains only nickels, dimes and quarters. The value of the 19 coins in
the bank is $2. There are twice as many nickels as dimes. Find the number of each
type of coin in the bank.
(i) Describe your variables.
n = number of nickels in the bank.
d = number of dimes in the bank.
q = number of quarters in the bank.
(ii) Setup three equations.
(iii) Solve the equations and present your answers.
5
5. [4] (a) Simplify
2x y 5x
5
 2 1 x 2 y 3 
[5] (c) Simplify  2 5 
 4x y 
4
y 3 
2
[3] (b) Multiply ( 2x5) ( 3x+2 ) .
2
[6] 6. Divide by using synthetic division.
x
3
 x  2   x  1 . Present your answer.
6
x  y  4

[10] 7. Graph the solution set. 2 x  3 y  6
x  0

(a) Use a ruler.
(b) Write the equation next to the line.
(c) Find the point that the line x  y  4 and the line 2 x  3 y  6 intersect.
(d) Mark the point of intesection on your graph.
(e) Shade the area of the souliton set.
7
(8) [5] Divide by using the long division method.
(9) [5] Simplify (9 x y ) 2 x y
2
3

2 1
11. [5] Factor completely. x 2 y  2 x 2  y  2
8x
3
 9 2 x  3
 9ab2 
10. [5] Simplify  2 
 8a b 
3
8
12. [5] Factor 6x 2  17 x  10 . (Use grouping method)
a = ____, b =_____, c =_____
Find ac = ________
ac = (
)(
)
(
)+(
) = ______
Finish the problem.
13. [5] Factor 64 x 3  1 .
14. [5] Use the Remainder theorem to evaluate P (3) when P( x)  x 3  3x 2  3 .
[Use synthetic division, show your work clearly.]
9
15. [6] Find 3x 2  2 x  1 if x( x  6)  16 .
16. [5] The square of a number is 195 more than twice the number. Find the number.
17. [5] The length of a rectangle is (5x+3) ft. The width is (2x-7) ft. Find the area of the
rectangle in terms of the variable x.
18. [5] Solve for x, 3x(2 x  5)  0 .
19. [5] Given that 4 is in the range of the function defined by f ( x)  x 2  x  2 , find two
values of c for which f (c)  4.
10