Review Test
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Question 1 
Use the elimination method to solve the following system of equations:
y = 2x + 5
x + y = 2
A  y = 1 
B  x = 1 
C  x = 3 
D  x = 2 
E  y = 3 
Question 1 Explanation:
y = 2x + 5
x + y = 2
y  2x = 2x  2x + 5
x + y = 2
y  2x = 5
x + y = 2
y  2x = 5
y + x = 2
make on expression negative
y  2x = 5
(y + x = 2)
y  2x = 5
y  x = 2
add downwards
y + (y)  2x + (x) = 5 + (2)
3x = 3
3x/3 = 3/3
x = 1
plug in x = 1 into one of the equations
x + y = 2
(1) + y = 2
1 + 1 = y = 2 + 1
y = 3
Question 2 
Given the equation:
2x + 4  13x = 7x  2 + 14
solve for x.
A  4/11 
B  8/22 
C  7 
D  22 
E  7 
Question 2 Explanation:
2x + 4  13x = 7x  2 + 14
15x + 4 = 7x + 12
15x + 15x + 4 = 7x + 15x + 12
4 = 22x + 12
4  12 = 22x +12  12
8 = 22x
8/22 = 22x/22
8/22 = x or 4/11 = x
Question 3 
Divide, where 6a + 4b ≠ 0:
(36a²  16b²) / (6a + 4b)
A  6a  4b Hint: Factor the top first. 
B  6a + 4b Hint: Factor the top first. 
C  a + b Hint: Factor the top first. 
D  4a  6b Hint: Factor the top first. 
E  4a + 6b Hint: Factor the top first. 
Question 3 Explanation:
(36a^2  16b^2) / (6a + 4b)
If you can multiply the bottom expression and get the expression on top without the middle part of the expression then follow
ex
(6a + 4b) * (6a + 4b) = 36a^2 + 48ab + 16b^2
notice how the similar the bottom equation result is to the top
(36a^2  16b^2) / (36a^s + 48ab + 16b^2)
close but not quite the same
go back and the realize the factor of the top part is
(6a + 4b) * ( 6a  4b)
so that
((6a + 4b) * (6a  4b))/ (6a + 4b = 6a  4b
Question 4 
Evaluate 21  (6  2) / 2
A  11 
B  17 
C  19 
D  15 
E  16 
Question 4 Explanation:
21  (6  2) / 2
21  (4) / 2
21  [4 / 2]
21  2 = 19
Question 5 
Which of the following are prime numbers? 2, 5, 7, 9, 15, 21
A  2, 5, 7 Hint: Prime numbers are numbers that can be divide by 1 and itself.

B  2, 9, 21 Hint: Prime numbers are numbers that can be divide by 1 and itself.

C  7, 9, 15 Hint: Prime numbers are numbers that can be divide by 1 and itself.

D  9, 15, 21 Hint: Prime numbers are numbers that can be divide by 1 and itself.

E  2,15, 21 Hint: Prime numbers are numbers that can be divide by 1 and itself.

Question 5 Explanation:
Prime numbers are numbers that can be divide by 1 and itself.
2, 5, 7
Question 6 
Is the sentence 2 + 2 = 5 open or closed? Is it true or false?
A  Open and true Hint: Are there any unknown variables. such as a, x and etc. 
B  Open and false Hint: Are there any unknown variables. such as a, x and etc. 
C  Closed and false Hint: Are there any unknown variables. such as a, x and etc. 
D  I do not know Hint: Are there any unknown variables. such as a, x and etc. 
E  Closed and true Hint: Are there any unknown variables. such as a, x and etc. 
Question 6 Explanation:
It is closed because there are no variables.
The statement 2 + 2 = 5 is false.
Question 7 
²²What is the c set of x² <100?
A  X = 10 Hint: Solve for x. What you do to one side do to the other side. 
B  10 < X < 10 Hint: Solve for x. What you do to one side do to the other side. 
C  10 < X Hint: Solve for x. What you do to one side do to the other side. 
D  10 < X Hint: Solve for x. What you do to one side do to the other side. 
E  10 > X > 10 Hint: Solve for x. What you do to one side do to the other side. 
Question 7 Explanation:
x^2 < 100
(x^2)^(1/2) < (100)^(1/2)
x {10, 10}
10 < x < 10
Question 8 
Which of the following are integers? 3, 4, 1/2, 0, 1, 2
A  3, 4, 0 
B  0 
C  3, 4, 0, 1, 2 
D  1, 2 
E  3, 4 
Question 8 Explanation:
Integers are also known as whole numbers
Question 9 
Simplify √[(3X^2) / 4]
A  x (3/4)^(/1/2) 
B  (x/2) * (3)^(1/2) 
C  (3/4)(x^2) 
D  x^2 
E  (3/4)x 
Question 9 Explanation:
[(3x^2)/4]^(1/2)
Whatever i squared can be pulled out
x^2
&
2^2 = 4 so 2
x/2 * (3)^(1/2)
Question 10 
Find the slope (m) and yintercept (b): y  0.5x = 3.5
A  slope (m) = 3.5
yintercept (b) = 3 Hint: Put equation into Slopeintercept form. 
B  slope (m) = 3
yintercept (b) = 3.5 Hint: Put equation into Slopeintercept form. 
C  slope (m) = 0.5
yintercept (b) = 3.5 Hint: Put equation into Slopeintercept form. 
D  slope (m) = 1
yintercept = 2 Hint: Put equation into Slopeintercept form. 
E  slope (m) = 0.5
yintercept (b) = 3.5 Hint: Put equation into Slopeintercept form. 
Question 10 Explanation:
y  0.5x = 3.5
y  0.5x + 0.5x = 0.5x + 3.5
y = 0.5x + 3.5
slope (m) = 0.5
yintercept (b) = 3.5
Question 11 
5ab^{4}  ab^{4} =
A  ab^4 Hint: for like terms process is the same 
B  4ab^4 Hint: for like terms process is the same 
C  ab^{4} Hint: for like terms process is the same 
D  5 Hint: for like terms process is the same 
E  4 Hint: for like terms process is the same 
Question 11 Explanation:
5ab^4 ab^4 = 4ab^4
Question 12 
Evaluate the expression 12b + 3a when a = 3 and b = 2.
A  15 Hint: Plug in and solve. 
B  15 Hint: Plug in and solve. 
C  30 Hint: Plug in and solve. 
D  30 Hint: Plug in and solve. 
E  0 Hint: Plug in and solve. 
Question 12 Explanation:
12b + 3a; a = 3, b = 2
12 * (2) + 3 * (3)
24 + 9 = 15
Question 13 
What is the solution set of x²= 100?
A  10, 10 Hint: Solve for x. What you do to one side do to the other side. 
B  10 Hint: Solve for x. What you do to one side do to the other side. 
C  10 Hint: Solve for x. What you do to one side do to the other side. 
D  5 Hint: Solve for x. What you do to one side do to the other side. 
E  5 Hint: Solve for x. What you do to one side do to the other side. 
Question 13 Explanation:
x^2 = 100
(x^2)^(1/2) = (100)^(1/2)
x = {10,10}
Question 14 
Evaluate 5 + 6 * 2
A  13 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
B  22 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
C  11 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
D  16 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
E  17 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
Question 14 Explanation:
5 + 6 * 2
5 + [6 * 2]
5 + 12 = 17
Question 15 
Three times the sum of a number and 5 is equal to 27. What is the number?
A  5 Hint: Follow order of operations 
B  9 Hint: Follow order of operations 
C  1 Hint: Follow order of operations 
D  4 Hint: Follow order of operations 
E  3 Hint: Follow order of operations 
Question 15 Explanation:
3*(x + 5) = 27
divide by 3 on both sides
[3*(x + 5)]/3 = 27/3
x + 5 = 9
subtract 5 from both sides
x + 5  5 = 9  5
x = 4
Question 16 
Solve for x:x² + 4x = 12 x
A  3, 4 Hint: Rearrange the equation. 
B  2, 6 Hint: Rearrange the equation. 
C  2, 6 Hint: Rearrange the equation. 
D  4, 4 Hint: Rearrange the equation. 
E  4, 3 Hint: Rearrange the equation. 
Question 16 Explanation:
x^2 + 4x = 12
x^2 + 4x 12 = 12  12
x^2 + 4x  12 = 0
use quadratic formula or factor out 12
factors of 12: 1, 2, 3, 4, 6, 12
2 + 6 = 4
2 * 6 = 12
x^2 + 4x  12 = (x  2)(x + 6)
Question 17 
Divide, where x ≠ 11:
(x²  x  110) / (x  11)
A  x  10  x  11 
B  x  10 
C  x + 10 
D  x + 11 
E  x  11 
Question 17 Explanation:
(x^2  x  110) / (x  11)
factor the top expression
(x^2  x  110) = (x + 10) (x  11)
place back into equation
[(x + 10) (x  11)] / (x  11)
cancel like terms
[(x + 10) (x  11)] / (x  11) = x + 10
x + 10
Question 18 
If Raven travels at 65 miles per hour (mph) for 3.5 hours, how far does she travel? Use the formula D = rt. r = rate, t = time.
A  2275 miles Hint: plug in and solve 
B  75 miles Hint: plug in and solve 
C  22.5 miles Hint: plug in and solve 
D  25 miles Hint: plug in and solve 
E  227.5 miles Hint: plug in and solve 
Question 18 Explanation:
D = rt
D = r * t
D = 65 * 3.5 = 227.5 miles
Question 19 
Simplify √(12xy)/(√x)
A  12xy 
B  12 
C  2(3y)^0.5 
D  12y^0.5 
E  x^0.5 
Question 19 Explanation:
[(12xy)^(1/2)] / (x)^(1/2)
same as
(12^0.5 * x^0.5 * y^0.5) / (x^0.5)
cancel like terms
factor 12 = 2 * 2 * 3
pull out the 2
2*(3y)^0.5
Question 20 
Divide, where x ≠ 2:
(3x  6)/(x  2)
A  3 Hint: Pull out the common factor 
B  2 Hint: Pull out the common factor 
C  1 Hint: Pull out the common factor 
D  3 Hint: Pull out the common factor 
E  0 Hint: Pull out the common factor 
Question 20 Explanation:
(3x  6) / (x  2)
Pull 3 out from the top part of the equation
3 * (x  2) / (x  2)
where (x  2)/(x  2) = 1
3 * 1 = 3
Question 21 
Given the equation:
6(x + 6) = 3(4x + 3)
Solve for x.
A  8/5 Hint: Distribute and then solve for x. 
B  8/5 Hint: Distribute and then solve for x. 
C  12/6 Hint: Distribute and then solve for x. 
D  45/6 Hint: Distribute and then solve for x. 
E  9/2 Hint: Distribute and then solve for x. 
Question 21 Explanation:
6(x + 6) = 3(4x + 3)
6x  36 = 12x  9
6x  36 + 36 = 12x  9 + 36
6x = 12x + 27
6x + 12x = 12x + 12x + 27
6x = 27
6x/6 = 27/6
x = 27/6 or x = 9/2
Question 22 
What is the solution set of 3x + 4x = 7x +1?
A  3 Hint: Solve for x. What you do to one side do to the other side. 
B  1 Hint: Solve for x. What you do to one side do to the other side. 
C  0 Hint: Solve for x. What you do to one side do to the other side. 
D  2 Hint: Solve for x. What you do to one side do to the other side. 
E  Empty {} Hint: Solve for x. What you do to one side do to the other side. 
Question 22 Explanation:
3x + 4x = 7x + 1
7x = 7x + 1
7x  7x = 7x  7x + 1
0 = 1, Statement is false.
Set is empty {}.
Question 23 
What expression is equivalent to "ten more than three times a number?
A  10 + 3 * 10 Hint: The word "more" means adding.
The word "times" means multiplying. 
B  10 * 3* x Hint: The word "more" means adding.
The word "times" means multiplying. 
C  3 * (x +10) Hint: The word "more" means adding.
The word "times" means multiplying. 
D  3x + 10 Hint: The word "more" means adding.
The word "times" means multiplying 
E  10 * (3+x) Hint: The word "more" means adding.
The word "times" means multiplying. 
Question 23 Explanation:
3x + 10
Question 24 
Evaluate 12  3 + 4
A  19 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
B  16 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
C  5 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
D  11 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
E  13 Hint: Order of Operations
P.E.M.D.A.S. = P(), E^, [M* D/], [A+ S]
[M* D/] order is from left to right
[A+ S] order is from left to right 
Question 24 Explanation:
12  3 + 4
[12  3] + 4
9 + 4 = 13
Question 25 
Factor the polynomial 4x² + 4x.
A  4x(x +1) 
B  x + 1 
C  x  1 
D  1 
E  4x 
Question 25 Explanation:
4x^2 + 4x
4x is common in both parts
4x(x + 1)
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