WAYNE STATE UNIVERSITY MATH PROGRAM AT WESTERN INTERNATIONAL HIGH SCHOOL
HOMEWORK 73
ALGEBRA 2: TEST 1 WINTER 2010
Name:
Show all your work.
4 points
2 points
4 points
6 points:
3 points
each
8 points:
1 point
each
Date: _____________________
1) What is Algebra?
2) Explain, in English, what the following algebraic statement is saying:
11x  5x  6x
3) Evaluate 3a 2  ab  b 2 when a  2 and b  3
4) Determine if the following statement is “Not true” or if it “Might be true”.


a) x 3  8  x 2  2 x  4 x  2
b) x 2  1 
2x 2  1
2
5) Add, if possible. If not possible, write “NP”:
a) 4 yz 3  5 yz 3
b) 4 x 5  7 x 3
c) x 7  x 7
d)
e) 6 x 3  4
f)  7 x   3 x
g) 3.6 y 2  1.2 y 2
h)
1 2 3 2
a  a
3
5

1 OF 18
5 4

y y

6 points:
1 point
each
6) Subtract, if possible. If not possible, write “NP”
a) 9 x 2 y  6 x 2 y
b) 3 ab  5 ab
c) a 5  a 3
d)  3 y 3  7 y 3
e)
4 points
8 5

x x
f) 3x  1
7) Simplify completely, by adding or subtracting wherever possible:
 3xy 2  5 x  7 xy 2  x 3 y  7 x  x 3
4 points
8) Subtract and simplify completely:

2x 2  2x  9x 2  4x  5
6 points:
3 points
each
9) Multiply:

 
a) 4a 2 b 3 cd 3
b)
6 points:
3 points
each

z 3

w5 x y
10) Multiply and simplify completely:
a) x 5  x 7
 
b) x 4
3
2 OF 18
12
points:
3 points
each
11) Multiply and simplify completely:
a) 3x 5  6 y 2




b) 9a 4 b a 2 b 3
c) 5a 4 b
d)
12
points:
3 points
each

2
2x 7 y 3  7x 2 y 4
12) Multiply and simplify completely:
a) (5 x)( y 2  2)


b) 4 xy x 2  2 x  1

c)  7 x 2  3x  2

d)  3x 2 (4 x 5 y  2 y)
3 OF 18
12
points:
3 points
each
13) Multiply and simplify completely.
a) ( x  2)(3 x  1)
b) ( x  4)( x  y  z )
c) ( x  3) 2


d)  y  2 y 2  2 y  3
8 points:
4 points
each
6 points:
3 points
each
14) Divide and simplify completely:
a)
x3 y5
8z
 4 3
2
x y
b)
x x5

4
3
15) Factor completely:
a) 3 x 3 yz  7 y
b) x 4 y 3 z 3  x 7 yz 3  x 4 yz 5
4 OF 18
1. Multiply and simplify completely:
16 points
4 points
each
a) (3 x  2)( x  1)
b)
x2 x5

3
x
c) 3x 4 y 2 (2 x 5  x 2 y 8  y 7 )
d) ( x  4) 2
6 points
2. Divide and simplify completely:
2
x

x x3
3. Factor completely:
16 points
4 points
each
a) xyz 2  z 2 w3
b) 3ab  6
c) xy3  x
d) x 4 y 7  x 7 y  x 9 y 5
5 OF 18
6 points
4. Factor: x 2  9
5. Simplify completely:
8 points
4 points
each
x 2  3x
x 2  4x
a)
6 points
6. Simplify completely:
6 points
7. Add:
6 points
8. Subtract:
b)
5 xy  2 x
x
x7 y2
x2 y5
1
2

3
bc
a
3 5

x y2
9. Multiply and simplify completely:
8 points
4 points
each
6 points
each
a)
x 1 x

x  4 x 1
10. Divide and simplify completely:
b)
ab
c
d
c
6 OF 18
x5 1

y 1 x2
8 points
4 points
each
11. Simplify completely:


a) 7 x 2  2 x 2  5 x  1
b) 4 x  xx  3x  2
12. Simplify completely:
8 points
4 points
each
 x 
a) ( x  1)

 x 1
x

b) 5  3 
5

7 OF 18
4 points
30 points:
6 pts each
1) True or False? The number 3 is a solution of the equation 2 x 2  x  15 .
2) Solve:
a. 2x  3  8
b.
1
5
x 1 
3
3
c. 1.1x  .8x  1.5
d. 5x  2  2 x  17
e.
2 3

x 5
8 OF 18
6 points
6 points:
3 pts each
3) Solve for t :
at  b 3  cd
4) Let x = the cost of a movie ticket. Translate each of the following into an algebraic expression.
a. Two less than five times the cost of the movie ticket.
b. The total of the cost of the movie ticket and 13% of the cost of the movie ticket.
6 points
6 points
6 points
12 points:
6 pts each
5) Three times a number is seven more than twice the number. What’s the number?
6) The number of miles that Jose ran in the morning, which was 7 miles, is two miles more than four
times the number of miles he ran that night. How many miles did he run that night?
7) Factor completely: 3x 2  10 x  7
8) Solve:
a.
x 2  5x  6  0
b. x 2  3x  10
9 OF 18
6 points
6 points
6 points
 3x  2  8
9) Solve and graph the solution on a number line:
10) True or False? The ordered pair 3,  1 is a solution of the equation 2 x  y 2  4 .
11) Graph x  2 y  6
y
x
10 OF 18
6 points
12) Graph the equation x  1 :
y
x
1) Evaluate:  3 x 2  8 x  2 when x  2 .
2) Say whether the following algebraic statement “might be true” or is “ not true”:
x2  4  x  2
3) Add, if possible. If not possible, write “NP”:
6 points:
3 each
a)
2 x 3 y 2  5x 3 y 2
b)
4) Subtract, if possible. If not possible, write “NP”:
6 points:
3 each
a)
7x3  9x3
b)
11 OF 18
x5  x2 :
x4  x4
5) Simplify by adding or subtracting wherever possible:  2 x 2 y  4 x  8 x 2 y  7 x

6) Subtract and simplify completely: 8x 2  3x  5x 2  2 x  4

 
7) Multiply and simplify completely: 3x 5 y 4 xy3
2
6 points
8) Multiply
2x 7 y 8 x 4 y

9) Multiply and simplify completely: 3x  1 x 2  2 x  2
6 points
10) Multiply and simplify completely:  x  4 
11) Divide and simplify completely:
2
2a c

b3 d 2
12) Factor completely: xy5  3x 4 y 2  x 5 y 7
13) Factor completely: x 2  25
12 OF 18


14) Simplify completely:
x 2  2x
xyz 3
15) Simplify completely:
x5 y 4
x2 y9
16) Add:
6 points
3 5

x2 y
17) Multiply, writing your answer in simplest terms:
x
x2

x  2 x 1
18) Simplify completely: 2 x  3(5 x  2( x  1))
6 points
19) Solve: 4( x  1)  x  6
6 points
20) Solve:
2
7
x 1 
3
3
21) Solve:
x6
3
x
6 points
6 points
13 OF 18
22) Solve for t: a 2 t  b  cd 3
23) Let x= the weight of a car. Translate each of the following into an algebraic expression.
6 points
a) Three less than twice the weight of the car.
b) Seventeen percent of the weight of the car.
14 OF 18
24) The number of adult tickets sold at a movie theatre which was 32 was two more than half of the
number of children’s tickets sold. How many children’s tickets were sold?
6 points
25) Factor: x 2  x  20
26) Solve: x 2  7 x  10  0
6 points
27) Solve: x 2  4 x  5
6 points
28) Solve the inequality  2x  1  7 and graph the solutions on the given number line.
-4
5
-3
-2
-1
0
1
2
3
29) Circle all of the following that are linear equations:
A) y  3x  5
B) y  2 x 3  1
C) 2 x  y  1
15 OF 18
D) y  x
4
30) Graph y  2 x  3 .
y
x
31) Graph x  3 .
y
x
16 OF 18
32) Given the line y  3x  6 , find
6 points:
3 each
a)
:
the y-intercept
b) the x- intercept
33) Estimate the slope, if it exists, of each of the following lines. If the line doesn’t have a slope, write
“No Slope”.
6 points:
3 each
a) m ≈ ________
b) m ≈ ________
y
y
x
x
34) Graph the line that goes through 1,2 and has slope
3
.
4
y
x
17 OF 18
35) What is the slope of each of following lines the line:
a)
6 points,
2 each
y  2x  1
b)
y2
c)  3 x  4 y  7
36) Find the slope of the line that goes through the points 2,3 and 5,1 .
x  3 y  5
37) True or False? The pair 2,1 is a solution of the system 
2 x  y  7
2 x  y  9
38) Solve the system: 
x  3 y  1
6 points
6 points,
2 each 39) An
6 points
airline has coach seats and first class seats available for a flight to Chicago. The number of coach
seats is three more than two times the number of first class seats. The total number of coach seats
and first class seats is 219. How many coach seats and how many first class seats are available?
40) Given the quadratic eauqtion y  2 x 2  4 x  3 :
a)
Does the parabola open “upwards” or “downwards”?
b)
Find the vertex of the parabola.
c)
Graph the equation, labeling the vertex.
18 OF 18