Download ELEMENTARY ALGEBRA 10x y 7x y 10x y 7x y

ELEMENTARY ALGEBRA
This practice test measures your ability to perform basic algebraic operations and to solve problems that involve elementary algebraic concepts.
Directions: Solve each of the following problem in the space to the right of the question as provided and indicate you answer by circling it.
1.
3  x  7  
(A)
(B)
(C)
(D)
5.
If 15 – 4y = 12, then y =
(A) 
3x  21
3x  7
3x  10
3x  21
(B)
(C)
(D)
2.
 2x y 5x y  
4
(A)
(B)
(C)
(D)
27
4
3
4
4
3
27
4
3
10x7 y 2
6.
7x7 y 2
10x12 y 2
7x12 y 2
If a = 5 and b = -2, then
ab  6
=
3b 2
4
3
1
(B) 
3
1
(C)
3
4
(D)
3
(A) 
3. If, 6𝑥 = 5 − 9𝑥
then x =
5
3
1
(B) 
3
1
(C)
3
5
(D)
3
(A) 
4.
A
factored
7.
form
of
1  16a is
2
(A)
(B)
(C)
(D)
1  4a 1  4a 
1  4a 1  4a 
(1  4a) 1  4a 
1 16a 1  a 
The sum of two numbers
is 42. If one number is x,
then in terms of x, the
other number is
(A)
42  x
(B)
x  42
(C)
x
(D)
2x
GO ON TO THE NEXT PAGE
8. If 6x - 2 = 12x + 7,
then x =
(A)
(B)
−
13.
1
3
−
One of the solutions to
the equation
3x2 10 x  8  0 is
2
(A)
3
(C)
−1
(D)
2
3
1
(B)
2
(C)
(D)
9.  5x 4 3 
12
(A) 15x
(B) 125x
14.
7
12
(C) 125x
(D) 125𝑥 64
10.
 x  3y
=
(C)
x2  3 y 2
x2  9 y 2
x2  3xy  9 y 2
(D)
x2  6 xy  9 y 2
(A)
(B)
11. Which of the following is
a factor of
x 2  7 x  10 ?
(A)
(B)
(C)
(D)
9 36 3 3 
(A) 15
(B)
(C)
2
2
3
1
1
3
2

3
1
1
3
(D)
14 3
15 3
15 6  3
1
1
𝑥
2
15. If + 3 =
(A)
5
3
(B)
−5
(C)
−3
(D)
−2
, then x =
2
2
3
x2
x2
x  10
x5
12. Arty downloaded 45 apps
per hour for t hours. In
terms of t, what number
of apps did he download?
(A)
(B)
45
t
t
45
(C) 45t
(D)
45+t
GO ON TO THE NEXT PAGE
16.
x 3x
 =
8 7
(A) 56
10 x
(B)
23
31x
(C)
56
4x
(D)
15
20. Which of the following could
represent the graph
3x = y ?
(A)
(C)
y
y
x
(B)
x
(D)
y
y
17. The length of a rectangle
x
is 7 inches greater than its
width. Which of the following
expressions represents its area
in terms of its width, w ?
(A)
2w  w  7 
(B)
2  2w  7 
(C)
2  w  7
(A)
(D)
w w  7
(B)
3 4b  =
2
21.
(C)
(D)
6 4b
12 b
18b
36b
18. If x 2  9 x  25 is
divided by x  4 , the
remainder is
(A) 0
(B) 5
(C) 20
(D) 25
x  3y  6
2 x  5 y  10
22. In the solution of the system
of equations above, what is the
value of y ?
(A)
19. If
5
3
x6  x,
2
5
x
2
11
(B) -1
then x =
(A) 7
(B)
2
5
3
5
(C) 
60
(D) 19
(C)
2
5
(D) 5
5
11
7
5
GO ON TO THE NEXT PAGE
23.
If
𝑥+3
2
=
3𝑥−4
3
26.
,
(A) 5𝑏 3 + 5𝑏 2 − 4
then x =
(A)
(B)
(C)
5𝑏 3 + 3𝑏 2 − (2𝑏 2 − 4)
(B) 5𝑏 3 + 5𝑏 2 + 4
17
3
(C) 5𝑏 3 − 𝑏 2 − 4
1
(D) 5𝑏 3 + 𝑏 2 + 4
2
17
9
27.
1
(D) 3
1
𝑥
1
− =
𝑦
(A) 0
(B)
If 𝑎𝑥 − 𝑏 = 𝑐𝑥 − ⅇ,
𝑡ℎⅇ𝑛 𝑥 =
24.
(A)
(B)
(C)
(D)
25.
𝑥−𝑦
𝑦−x
𝑥𝑦
−𝑥𝑦
𝑥𝑦
𝑎𝑐
𝑏+ⅇ
𝑎+𝑐
𝑏−ⅇ
𝑎−𝑐
𝑏−ⅇ
𝑎𝑐
=
𝑎−𝑎2
(A) −
(C)
(D)
𝑏−ⅇ
𝑎
(B)
(C)
1
1
𝑎2
1
1−𝑎
1
1−𝑎2
(D) 1 −
1
𝑎2
STOP!
ELEMENTARY ALGEBRA
This practice test measures your ability to perform basic algebraic operations and to solve problems that involve elementary algebraic concepts.
Directions: Solve each of the following problem in the space to the right of the question as provided and indicate you answer by circling it.
1.
3  x  7  
(E)
(F)
(G)
(H)
5.
3x  21
3x  7
3x  10
3x  21
If 15 – 4y = 12, then y =
(E) 
Apply the distributive law of
multiplication & watch your
“signs”.
(F)
3x  21
(G)
(H)
2.
 2x y 5x y  
4
(E)
(F)
(G)
(H)
Multiply: remember that
exponents add when you
multiply this.
10x7 y 2
7x7 y 2
10x12 y 2
7x12 y 2
(F)
(G)
(H)
y
4
3
1
(F) 
3
1
(G)
3
4
(H)
3
+ 9x
3
4
 5 2  6
ab  6   
=
2
3b 2
3  2 
10  6 16

3 4
12

4
3
15x  5
5
x
15
x
form
1
3
of
1  16a 2 is
(E)
4 y  3
3
y
4
If a = 5 and b = -2, then
ab  6
=
3b 2
(E) 
6x  5  9x
+ 9x
5
3
1
(F) 
3
1
(G)
3
5
(H)
3
factored
6.
10x7 y 2
(E) 
A
15  4 y  12
-15
-15
3
3. If, 6𝑥 = 5 − 9𝑥
then x =
4.
27
4
3
4
4
3
27
4
1  4a 1  4a 
1  4a 1  4a 
(1  4a) 1  4a 
1 16a 1  a 
Thinking of the Reverse
FOIL method (factoring),
you’ll need the “Outside &
Inside” multiplicands to
“cancel out” for this result:
1  4a 1  4a  =
1  4a  4a  16a 2 =
1  16a 2
7.
The sum of two numbers
is 42. If one number is x,
then in terms of x, the
other number is
To make it easier for you, let
the unknown number or
“other number” be
represented by “y”.
(E)
42  x
(F)
x  42
Therefore:
(G)
x
x  y  42
(H)
2x
Now solve for y:
y  42  x
GO ON TO THE NEXT PAGE
8. If 6x - 2 = 12x + 7,
then x =
(E)
−
1
3
−
(F)
2
3
(G)
−1
(H)
2
3
1
2
13.
6𝑥 − 2 = 12𝑥 + 7
- 6x
- 6x
−2 = 6𝑥 + 7
-7
-7
−9 = 6𝑥
1
𝑥 = −1 2
(F)
Multiply it 3 times:
 5x 
3
4
(F) 125x
7
12
(G) 125x
(H) 125𝑥 64
(H)

5x 5x 5x  
4
(E) 15x12
 x  3y
(E)
(G)
9.  5x 4 3 
10.
One of the solutions to
the equation
3x2  10 x  8  0 is
4
3x  2 x  4  0
Solve each factor for x:
3x  2  0
3x  2
2
x
3
x4  0
x4
4
125x12
Remember that exponents
add when you multiply this.
14.
9 36 3 3 
(E) 15
(F)
(G)
2
2
3
1
1
3
2

3
1
1
3
Use the reverse FOIL method
(factoring):
=
(H)
14 3
15 3
15 6  3
15 3  3 =
14 3
Use the FOIL method:
(G)
x2  3 y 2
x2  9 y 2
x2  3xy  9 y 2
(H)
x2  6 xy  9 y 2
(E)
(F)
11. Which of the following is
a factor of
x  7 x  10 ?
2
(E)
(F)
(G)
(H)
x2
x2
x  10
x5
12. Arty downloaded 45 apps
per hour for t hours. In
terms of t, what number
of apps did he download?
(E)
(F)
45
t
t
45
(G) 45t
(H)
45+t
 x  3 y  x  3 y 
x  3xy  3xy  9 y
2
x  6 xy  9 y
2
1
1
𝑥
2
15. If + 3 =
2
2
Use the reverse FOIL
method (factoring):
 x  5 x  2 
x  2 x  5x  10 
x 2  7 x  10
2
(E)
5
3
(F)
−5
(G)
−
(H)
−2
, then x =
2
1
1
+3=
𝑥
2
-3
-3
2
3
1 1
= −3
𝑥 2
3
1 1 6
= −
𝑥 2 2
1
5
=−
𝑥
2
Cross multiply &solve for x:
5𝑥 = −2
Rate = 45 apps per hour
Rate =
45𝑎𝑝𝑝𝑠
ℎ𝑜𝑢𝑟
2
𝑥 = −5
# of hours = time (t hour)
Multiply by number of
hours to give number of
apps.
45𝑎𝑝𝑝𝑠
ℎ𝑜𝑢𝑟
(t hour) = 45t apps
GO ON TO THE NEXT PAGE
16.
x 3x
 =
8 7
x 3x
 =
8 7
(E) 56
10 x
(F)
23
31x
(G)
56
4x
(H)
15
Find the least common
denominator:
Try some “test” coordinates
20. Which of the following could
represent the graph
3x = y ?
(C)
7 x 24 x


56 56
(C)
y
y
x
x
31x
56
(D)
(D)
y
y
17. The length of a rectangle
x
is 7 inches greater than its
width. Which of the following
expressions represents its area
in terms of its width, w ?
Area = l x w
2w  w  7 
(E)
21.
(F)
2  2w  7 
(G)
2  w  7
(w)idth = w
(E)
(H)
w w  7
Area = w  w  7 
(F)
(G)
(H)
(E) 0
(F) 5
(G) 20
(H) 25
3 4b  =
2
(l)ength = w + 7
18. If x 2  9 x  25 is
divided by x  4 , the
remainder is
1st:
Multiply
6 4b
12 b
18b
36b
5
3
x6  x,
2
5
then x =
2
(E) 7
5
3
(F)
5
7
(G) 
5
60
(H)
19
Y
0
1
2
3
-1
-2
0
3
6
9
-3
-6
So the line must pass through the
(0,0) coordinate which eliminates
answers (C) & (B). Since the
values of X & Y are either both
positive or both negative (D)
cannot be the correct answer.
3 4b  =
2
3 4b  3 4b =
9 16b2 =
9  4b 
36b
x 5
x  3y  6
2 x  5 y  10
x  4 x 2  9 x  25
Use the FOIL method:
x  4 x  5x  20
2
x2  9 x  20
2nd: Compare
Remainder: 25 – 20 = 5
22. In the solution of the system
of equations above, what is the
value of y ?
(E)
19. If
x
X
5
3
x6  x
2
5
5
5
 x
 x
2
2
3
5
6  x  x
5
2
6
25
6  x  x
10
10
19
6   x
10
Cross multiply:
2
11
(F) -1
2
(G)
5
5
(H) 5
11
Solve for x:
𝑥 + 3𝑦 = 6
-3y
-3y
x  6  3y
Now substitute for x in:
2𝑥 − 5𝑦 = 10
2  6  3 y   5 y  10
Now solve for y:
12  6 y  5 y  10
12  11y  10
-12
-12
−11𝑦 = −2
y
2
11
GO ON TO THE NEXT PAGE
60  19x ; 𝑥 =
23.
If
𝑥+3
2
=
3𝑥−4
3
(F)
(G)
19
17
3
𝑥 + 3 3𝑥 − 4
=
2
3
Cross multiply & solve for x:
1
3(𝑥 + 3) = 2(3𝑥 − 4)
3𝑥 + 9 = 6𝑥 − 8
+8
+8
3𝑥 + 17 = 6𝑥
-3x
-3x
17 = 3𝑥
2
17
9
1
(H) 3
17
𝑥=
3
If 𝑎𝑥 − 𝑏 = 𝑐𝑥 − ⅇ,
𝑡ℎⅇ𝑛 𝑥 =
(F)
(G)
𝑏−ⅇ
𝑎𝑐
𝑎𝑥 − 𝑏 = 𝑐𝑥 − ⅇ
-cx -cx
25.
𝑏+ⅇ
𝑎+𝑐
𝑎𝑥 − 𝑐𝑥 = 𝑏 − ⅇ
𝑏−ⅇ
𝑥(𝑎 − 𝑐) = 𝑏 − ⅇ
𝑎−𝑐
(F) 5𝑏 3 + 5𝑏 2 + 4
5𝑏 3 + 3𝑏 2 − 2𝑏 2 + 4
(G) 5𝑏 3 − 𝑏 2 − 4
5𝑏 3 + 𝑏 2 + 4
(H) 5𝑏 3 + 𝑏 2 + 4
27.
1
𝑥
1
− =
𝑦
(E) 0
(F)
(H)
1
𝑥−𝑦
𝑦−x
𝑥𝑦
1 1
−
𝑥 𝑦
Find the least common
denominator:
𝑦
𝑥
−
=
𝑥𝑦 𝑥𝑦
𝑦−𝑥
𝑥𝑦
−𝑥𝑦
𝑥𝑦
𝑏−ⅇ
𝑎−𝑐
𝑎𝑐
=
𝑎−𝑎2
(E) −
(G)
5𝑏 3 + 3𝑏 2 − (2𝑏 2 − 4)
𝑏−ⅇ
𝑎
(F)
(E) 5𝑏 3 + 5𝑏 2 − 4
𝑎𝑥 − 𝑐𝑥 − 𝑏 = −ⅇ
+b
+b
𝑥=
(H)
5𝑏 3 + 3𝑏 2 − (2𝑏 2 − 4)
(G)
24.
(E)
26.
,
then x =
(E)
60
𝑎
=
𝑎 − 𝑎2
1
𝑎2
𝑎
=
𝑎(1 − 𝑎)
1
1
1−𝑎
1−𝑎
1
1−𝑎2
(H) 1 −
1
𝑎2
STOP!