Mth 075: Sample Test 1 (Unit I)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation.
1) 7p - 4 = 8p - 12
1)
2)
-3a + 3 + 4a = 5 - 23
2)
3)
5(2z - 5) = 9(z + 2)
3)
4)
4(6x - 4) = 8(3x + 6)
4)
1
a
4
5)
6)
5
1
d=
8
3
6)
7)
-5x - 8x + 8 = -2x
7)
8)
-5y - 10 = 2 - 2y
8)
9)
4(x + 6) - (4x + 24) = 0
9)
(y - 5) - (y + 5) = 4y
10)
5) -7 =
10)
Solve the problem.
11) The sum of twice a number and 9 less than the number is the same as the
difference between -41 and the number. What is the number?
11)
12)
The difference between two positive integers is 58. One integer is three times as
great as the other. Find the integers.
12)
13)
The sum of two consecutive integers is -389. Find the larger integer.
13)
14)
If three times the smaller of two consecutive integers is added to four times the
larger, the result is 95. Find the smaller integer.
14)
15)
If the first and third of three consecutive odd integers are added, the result is 81
less than five times the second integer. Find the third integer.
15)
1
Solve the formula for the specified variable.
16) a + b = s + r for s
17) V =
16)
1
Bh for h
3
17)
Solve the equation.
3x - 5 7x + 5
=
18)
3
5
18)
Solve the inequality, then graph the solution.
19) 12t + 3 10t + 1
19)
20) -4(x - 7) + 50x < -8(-6x + 5) - 3x
20)
2
Mth 075: Sample Test 2 (Unit II)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Decide whether or not the ordered pair is a solution to the equation.
1) 4x + y = 19; (4, 3)
1)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Complete the ordered pair for the equation.
2) y = -4x - 18 (-6, )
A) (-6, 6)
B) (-6, -6)
C) (-6, -18)
2)
D) (-6, 8)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Complete the table of values, and then plot the ordered pairs.
3) 2x - y = 4
3)
x y
0
0
1
-6
Complete the ordered pairs. Then graph the equation.
3
4) y = - x + 2
4
(0,
), (4,
), (-4,
4)
)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the intercepts for the graph of the equation.
5) -4x + 4y = 8
A) (0, -1); (0, 4)
B) (-2, 4); (-1, 8)
5)
C)
1
(-1, 0); (4, 0)
D)
(-2, 0); (0, 2)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Graph the linear equation.
6) x - y = 1
6)
7) x = -4
7)
Decide whether the slope is positive, negative, zero, or undefined.
8)
8)
2
9)
9)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the slope of the line through the pair of points.
10) (7, -7) and (-2, -8)
3
7
A)
B)
7
3
Find the slope of the line.
11) 4x - 5y = 27
5
A) 4
10)
C)
1
9
D)
9
11)
B) -
4
5
C)
5
4
D)
4
5
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular.
12) 3x - 4y = -14
12)
8x + 6y = -14
13)
13)
6x + 2y = 8
21x + 7y = 30
Write the equation of the line with the given slope and y-intercept.
14) slope -5;
y-intercept (0, 4)
14)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write an equation of the line through the given point with the given slope. Write the equation in
slope-intercept form.
15) (5, 4); m = - 8
15)
1
1
A) y = -8x + 44
B) y = -8x - 44
C) y = - x + 44
D) y = -8x +
8
44
3
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Graph the linear inequality.
16) x - y > -5
16)
17) y > 5
17)
18) y
18)
-5x + 4
4
Mth 075: Sample Test 3 (Unit III)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Combine like terms. Write the result with descending powers.
1) 7x7 + 7x2 + 6x7
1)
Identify the polynomial as a monomial, binomial, or trinomial. Give its degree.
8y3 - 8y2 + 1
2)
2)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the indicated operation.
(5n7 + 8n - 6n5) + (-7n5 + 3n7 + 3n)
3)
A)
C)
4)
3)
11n7 - 2n5 - 3n
8n7 - 13n5 + 11n
(-6x5 + 8x7 + 6 - 9x6) - (-3 - 4x6 + 6x7 - 9x5)
2x7 - 13x6 - 15x5+ 3
6n13
D)
8n - 13n7 + 11n5
4)
A)
C)
B)
B)
14x7 - 13x6 - 15x5 + 3
D)
14x7 - 13x6 - 15x5 + 9
2x7 - 5x6 + 3x5+ 9
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.
4
(2p4s2) (s3)
5)
5)
A)
16p16s11
B)
16p8s24
C)
16p8s9
D)
2p16s11
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Add or subtract as indicated.
6) (5a + 2b - c) - (7b - 3c - 5d)
6)
Use the product rule for exponents to simplify the expression. Write the answer in exponential form.
(-7p6)(-6p4)
7)
7)
Use the power rules for exponents to simplify. Write the answer in exponential form.
3
8) 52
8)
Write the number in scientific notation.
9) 3,750,800
9)
1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
10)
( 6 a - 1 )2
A) 36 a2 + 1
C) 6 a2 - 12 a + 1
10)
6 a2 + 1
D) 36 a2 - 12 a + 1
B)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the product.
-4x4(10x6 + 3x3)
11)
11)
12)
(7y - 3)(49y2 + 21y + 9)
12)
13)
(5x + 3)(x - 10)
13)
14)
( 5 y2 - 4 )( 5 y2 + 4 )
14)
15)
(3k + 1)3
15)
Use rules for exponents to simplify. Write answers with only positive exponents. Assume that all
variables represent nonzero real numbers.
5
x4y-5
16)
16)
x-2y4
3x-7
17)
y-5z6
17)
Perform the division.
8x3y3 - 32xy - x2y2
18)
18)
8xy
5m2 + 38m - 63
19)
m+9
19)
x4 + 6x2 + 8
x2+ 1
20)
20)
2
Mth 075: Sample Test 4 (Unit IV)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor completely.
1) 24m9 - 60m6 + 12m4
1)
A) 12(2m9 - 5m6 + 1m4)
B)
no common factor (except 1)
D) m4(24m5 - 60m2 + 12)
C) 12m4 (2m5 - 5m2 + 1)
2)
3)
2)
7m(2 - m) + 3n(2 - m)
A) (7m + 3n)(2 - m)
C) no common factor (except 1)
B)
(7m - 3n)(2 - m)
D) m(7 + 3n)(2 - 1)
8x2y2 + 10xy2 - 3y2
A)
(2x - 1y)(4x + 3y)
C)
(4x - 1y)(2x + 3y)
3)
y2(x - 1)(8x + 3)
D) y2(4x - 1)(2x + 3)
B)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4)
-5x2 + 40x
4)
5)
12x2 - 9xy - 16xy + 12y2
5)
6)
x2 - 6x - 27
6)
7) 5x7 - 35x6 + 30x5
7)
8)
x2 + 5xy - 14y2
8)
9)
8x2 + 18x + 9
9)
10)
15z2 - 4z - 4
10)
11)
x2 - x - 35
11)
12)
49k2 - 121m2
12)
13)
6x2 - 17xt + 12t2
13)
1
Factor completely.
14) 4x2 + 81
15)
14)
4x2 - 28x + 49
15)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
16) 15b2 + 22b - 6 = -14
A)
-
5 2
,4 3
16)
B)
5 3
,
4 2
C)
4 2
,
5 3
D)
-
4 2
,5 3
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
17)
7k2 - 41k - 6 = 0
17)
18)
12n2 + 27n = 0
18)
19)
x(x - 7) = 44
19)
20)
16r2 = 4r
20)
2
Mth 075: Sample Test 5 (Unit V)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find all values that make the expression undefined.
x2 - 25
1)
1)
x2 - 13x + 40
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the rational expression in lowest terms.
16x + 28
2)
20x + 35
A)
B)
1
2)
5
4
C)
4
D)
4
5
Multiply. Write the answer in lowest terms.
3r - 9
8r + 16
·
3)
16r2 + 32r 18 - 6r
A) -
1
4r
B)
-
3)
3
43-r
C)
1
4
D)
r-3
4r 3 - r
Perform the indicated operation and write the answer in lowest terms.
2 - 8y 2 - 7y
4)
21
27
A)
-23y + 4
189
B)
-23y + 32
189
C)
-121y + 32
189
4)
D)
-121y + 4
189
Solve the equation.
y
y
y
+
=
5)
y2 + 13y + 36 y2 - 16 y2 + 5y - 36
A)
{ -1 , 0}
B)
5)
C)
{ 1 , 0}
{ 8 , 0}
D)
{ -8 , 0}
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write the rational expression in lowest terms.
3x - 3y - bx + by
6)
3x - 3y + bx - by
6)
1
Write the expression in lowest terms.
m2 - 9m
7)
8)
7)
9-m
y2 + 3y - 18
y2 + 5y - 24
8)
Perform the indicated operation and write the answer in lowest terms.
5m
-30
+
9)
m-6 m-6
9)
10)
4r2 -29r + 7
7-r
·
16r2 - 4r
r2 -14r + 49
10)
11)
-5k3 (4k)6
÷
4k6
20k8
11)
12)
m2 + 2mp - 3p2 m2 + 4mp + 3p2
÷
m2 - 5mp + 4p2 m2 + 2mp - 24p2
12)
13)
3a + 2b 3a - 2b
2
2
13)
14)
2k2 + 14k + 20 4k2 + 26k + 36
÷
2k - 10
k2 - 25
14)
15)
3
6
6 -y y- 6
15)
Find the least common denominator (LCD).
2
7
,
16)
9a + 45 a2 + 5a
16)
Perform the indicated operation and write the answer in lowest terms.
7x
3
+
17)
x+6 x-6
2
17)
18)
4
1
+
x+5 x
18)
19)
8
32
x
+
x - 4 x + 4 x2 - 16
19)
Solve the equation.
3
1
20) x - x = 10
5
3
20)
21)
1
1
5
+
=
x - 4 4 x - 16 4
21)
22)
6
1
= 1m+5
m-5
22)
3