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Algebra 1 Review

Total questions: 77

Worksheet time: 19hrs 15mins

Name
Class
Date
1.
Meg's teacher asked her to find the zero(s) of the equation below.  Meg decided to factor to find the zero(s). 
0= x2-4x +4

(x + ___) (x + ___)
a)
(x + -2)(x + 2)
b)
(x + -4)(x + 2)
c)
(x + -4)(x + 4)
d)
(x + -2)(x + -2)
2.
April wants to prove that she can solve the system of equations below using the substitution method.
3x + y = 8
y = 4x - 6

Which equation shows the first step in solving the system of equations using the substitution method?
a)
7x + 2y = 2
b)
-x +2y = 2
c)
3x + (4x-6) = 8
d)
3(4x-6) +y = 8
3.
Simplify
a)
9
b)
5√2 + 2
c)
10√2
d)
2√2 + 3√30
4.
Which of the following solutions fits the graph shown?
a)
-7 > x > -0.5
b)
-7 < x < -0.5
c)
-7 < x > -0.5
d)
-7 > x < -0.5
5.
Factor completely:
x² - 121
a)
(x + 11)(x - 11)
b)
(x + 11)(x +11)
c)
(x - 11)(x - 11)
d)
x(x - 121)
6.
Factor completely:
x³ - 4x² - 21x
a)
x(x - 3)(x + 7)
b)
x(x² - 4x - 21)
c)
x(x + 3)(x - 7)
d)
(x + 3)(x - 7)
7.
Which of the following solutions fits the graph shown?
a)
x < -2
b)
x > -2
c)
x ≤ -2
d)
x ≥ -2
8.
Write the number in standard notation
9x10⁴
a)
9,000
b)
90⁴
c)
90,000
d)
360
9.
Multiply the binomials.
(x + 5)(x + 3)
a)
x² + 8x + 15
b)
x² + 15x + 8
c)
2x² + 8x + 8
d)
2x² + 15x + 8
10.

Give the solution to the system
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
a hoppy hippo
11.
Simplify the exponential expression.
a)
2x6y12
b)
2x5y7
c)
8x6y12
d)
8x5y7
12.
a)
A
b)
B
c)
C
d)
D
13.
a)
A
b)
B
c)
C
d)
D
14.
Write the polynomial so the powers of x are in descending order.
 9x2 + 5x + 27 + 2x3
a)
27 + 5x + 9x2 + 2x3
b)
9x2 + 5x + 2x3 + 27
c)
9x2 + 5x + 27 + 2x3
d)
2x3 + 9x2 + 5x + 27
15.
(x +2)(x + 3)
a)
x2 + 5x + 6
b)
x2 + x + 6
c)
x2 + 5x + 5
d)
x2 + 6x + 6
16.
(x - 7)(x + 7)
a)
x2 + 7x - 49
b)
x2 - 7x + 49
c)
x2 - 49
d)
x2 + 49
17.

-5x6(3x2 - 12x + 30)

a)

-15x8 + 60x7 - 150x6

b)

15x8 - 60x7 - 150x6

c)

8x6 - 17x + 35

d)

-8x6 + 17x - 35x2

18.
(5c-2)(3c2-5c+4)
a)
15c3-31c4+30c2-8
b)
15c3-19c2+10c-8
c)
15c3-31c2+30c-8
d)
15c3-31c2+30c+8
19.

Which of the following graphs best represents the solution to the system of linear equations shown below?

a)

A

b)

B

c)

C

d)

D

20.

Which of the following is the solution for this system of linear equations?

a)

No Solution

b)

( -3, 4 )

c)

( 1, -2 )

d)

( 2, 1 )

21.

A coffee shop sells donuts for $2 and muffins for $3. On a very cold morning, the shop sold 10 more donuts than muffins and made $250. Which system of equations could be used to find the number of donuts, d, and muffins, m, that the shop sold that day?

a)

A

b)

B

c)

C

d)

D

22.

Which graph best represents the solution set of

−4x ≤ 6y − 54?

a)

A

b)

B

c)

C

d)

D

23.

What is the solution set for −4x + 10 ≥ 5x + 55?

a)

F

b)

G

c)

H

d)

J

24.

A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.

Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?

a)

F

b)

G

c)

H

d)

J

25.

Which graph best represents the solution set of

y≤ - 4x ?

a)

A

b)

B

c)

C

d)

D

26.
-4x + 14 ≤ 54
a)
x ≥ - 10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
27.
-4x-7≥21
a)
x≥7
b)
x≥-7
c)
x≤8
d)
x≤-7
28.
What are the two equations used when setting up this system:
The Lawn and Garden Shop sold 40 bags of lawn seed one week for a total of $263. Large bags of lawn seed sell for $8.50 and smaller bags for $5.75 each. How many bags of each size were sold?
a)
8.5L + 5.75S = 263
L + S = 40
b)
8.5L + 5.75S = 40
L + S = 263
c)
8.5L = 5.75S
L + S = 303
d)
8.5L + 5.75S = 263
8.5L + 5.75S = 40
29.
Factor completely:
x² - 121
a)
(x + 11)(x - 11)
b)
(x + 11)(x +11)
c)
(x - 11)(x - 11)
d)
x(x - 121)
30.
Simplify the expression
(k²)⁴
a)
k⁶
b)
2k⁸
c)
k⁸
d)
k¹⁶
31.
Simplify the expression 
k⁹/k³
a)
k³
b)
1³
c)
k⁶
d)
1/k⁶
32.
Write the number in standard notation
9x10⁴
a)
9,000
b)
90⁴
c)
90,000
d)
360
33.
Which of the following expressions is equivalent to  
x² - 8x + 16
a)
(x+4)²
b)
(x+4)(x - 4)
c)
(x+8)(x+2)
d)
(x - 4)²
34.
What is the solution to this system of equations?
y = 2x - 10
y = 10 - 2x
a)
(5, 0)
b)
(1, -8)
c)
(0, 0)
d)
(2, 6)
35.
Which inequality is represented by the number line shown?
a)
x < 0
b)
x > 0
c)
x ≤ 0
d)
x ≥ 0
36.
Which compound inequality is represented by the number line shown?
a)
-6 < x < 0
b)
-6 < x ≤ 0
c)
-6 ≤ x ≤ 0
d)
-6 ≤ x < 0
37.
Multiply the binomials.
(x + 5)(x + 3)
a)
x² + 8x + 15
b)
x² + 15x + 8
c)
2x² + 8x + 8
d)
2x² + 15x + 8
38.
Which inequality is pictured?
a)
y ≤ 4/3x - 4
b)
y ≥ 4/3x - 4
c)
y > 4/3x - 4
d)
y < 4/3x - 4
39.
Which inequality is pictured?
a)
y < -4
b)
y > -4
c)
x < -4 
d)
x > -4
40.
What is the correct inequality for the graph shown on the number line?
a)

∣x + 1∣ < 3
b)
∣x + 1∣ > 3
41.
Which number from top to bottom shows
∣x∣ ≤ 2 ?
a)
1
b)
2
c)
3
d)
4
42.
Which of the following equations match the given graph?
a)
y ≤ -3/4 x + 3
b)
y ≥ -3/4 x + 3
c)
y < -3/4 x + 3
d)
y > -3/4 x + 3
43.
What kind of boundary line does this graph have?
a)
Dotted
b)
Solid
44.
-3 < x + 6 ≤ 5
a)
-9< x  or   x≤ -1
b)
All Real numbers
c)
-9< x   and   x≤ -1
d)
-10< x   and   x≤ -7
45.
Match:
You must be at least 48 inches tall to ride the bumper cars.
a)
h < 48
b)
h > 48
c)
h ≤ 48
d)
h ≥ 48
46.
What is the opposite of squaring a number?
a)
divide
b)
multiply 
c)
fractions
d)
square root
47.

Find the length of the missing side. (Calculators are allowed)

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

48.

Find the missing side. (Calculators are allowed)

a)

9

b)

41

c)

6.4

d)

3

49.

Find the missing side. (Calculators are allowed)

a)

48

b)

108

c)

83.6

d)

72

50.
Find h
a)
35.60
b)
35.00
c)
35.71
d)
61.03
51.

How would you write 5.6 x 10-3 in standard form?

a)

56,000

b)

5,600

c)

0.00056

d)

0.0056

52.
How do you write
8.317 x 106
in standard form?
a)
8, 371, 000
b)
83, 170, 000
c)
837, 100
d)
8, 317, 000
53.
Which of the following is correct scientific notation?
a)
20.35 x 104
b)
.2035 x 104
c)
2035 4
d)
2.035 x104
54.
Express the following in scientific notation:
.000457
a)
457 x 106
b)
457 x 10-6
c)
4.57 x104
d)
4.57 x 10-4
55.
Convert to scientific notation:
520,000,000  
a)
52 x 107
b)
5.2 x 107
c)
5.2 x 108
d)
0.52 x 109
56.
(2m4)(5m2)
a)
10m6
b)
10m8
c)
7m6
d)
7m8
57.
1.)  Simplify
 (2a2b4z)(6a3b2z5)
a)
8a5b6z6
b)
12a6b8z5
c)
12a5b6z6
d)
8a6b8z5
58.
a)
A
b)
B
c)
C
d)
D
59.
Write each product using an exponent. 
4 x 4 x 4 x 4 x 4 
a)
45
b)
54
c)
46
d)
46
60.
Simplify the following expression: 
xy-7
a)
xy7
b)
x/y7
c)
x7/y
d)
x7y
61.

0 < x + 7 < 9

a)

-7< x <2

b)

-7< x or x<2

c)

2 < x < -7

d)

-7>x or x>2

62.
Solve:  -3 ≤ 2x - 1 ≤ 5
a)
-1 ≤ x ≤ 3
b)
-1 < x < 3
c)
1 < x < 3
d)
1 ≤ x ≤ 3
63.
3x-4< -13 or 7x+1> 22
a)
All Real numbers
b)
  x>3   and x>-9
c)
The answer is not listed
d)
x<-3   or x>3
64.
a)

x > -3 or x > 1

b)

x < -3 or x < 1

c)

x ≥ 3 and x ≤ 1

d)

x > -3 and x < 1

65.
a)

x ≤ 3 and x > -2

b)

x < -2 or x ≥ 3

c)

x > -2 or x < 3

d)

x < 3 and x ≥ -2

66.
Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-3,-8)
b)
(-8,-3)
c)
(3,-8)
d)
(8,3)
67.
Solve for x and y
2x − 3y = −1
 y = x − 1
a)
(-2,-3)
b)
(0,-1)
c)
(3,4)
d)
(4,3)
68.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
69.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
70.
Solve:
y = 2x -11
-3y = -6x -15
a)
(-1.5,-4)
b)
(1.5,4)
c)
No solution (parallel lines)
d)
Infinitely many solutions
71.
5x + 4y = −30
3x − 9y = −18
a)
(-6, 0)
b)
(-6, -15)
c)
(0, -6)
d)
(2, -10)
72.
Answer.
a)
A
b)
B
c)
C
d)
D
73.
Which point below is NOT part of the solution set?
a)
(3, 4)
b)
(0, 4)
c)
(-2, 6)
d)
(6, 2)
74.
Which of the following inequalities matches the graph?
a)
y < -4x - 1
b)
y > -4x - 1
c)
y ≤ -4x - 1
d)
y ≥ -4x - 1
75.
Which of the following inequalities matches the graph?
a)
y ≤ 3/4x + 5
b)
y ≥ 3/4x + 5
c)
y < 3/4x + 5
d)
y > 3/4x + 5
76.
Which of the following inequalities matches the graph?
a)
y > 2x - 2
b)
y < 2x - 2
c)
y ≥ 2x - 2
d)
y ≤ 2x - 2
77.
Which of the following inequalities matches the graph?
a)
x ≤ -4
b)
x ≥ -4
c)
y ≤ -4
d)
y ≥ -4

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