Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
The three–part inequality a < x
b means “a is less than x and x is less than or equal to b”. Which of
these inequalities is not satisfied by any real number x?
1)
A)
–8 < x –7
B)
–2 < x 6
C)
–5 < x –11
D)
0 < x 4
2)
Which one of these is not a linear equation?
2)
A)
0.07x – 0.09x = 0.57
B)
5t – 11t = – 6t
C)
7x + 9(x – 2) = – 5x
D)
6y2– 3y + 1 = 0
3)
Which one of the following equations in x doesn’t require the use of the multiplication property of
equality (a, b, c, and d are real numbers, and x is the unknown)?
3)
A)
a
bx = d – c
B)
x =c – d
a – b
C)
ax = (b – c)x – d
D)
a – b + (c – d)x = 0
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Answer the question.
4)
How would you express the product of two numbers, r and s?
4)
5)
Which of the following would not be a reasonable answer in an applied problem that
requires finding the number of cars parked in a parking lot?
(i) 100 (ii) 19.125 (iii) 29 (iv) 4
5)
Provide an appropriate response.
6)
What is the difference between an expression and an equation?
6)
7)
When does the solution of a linear equation not require the use of the Multiplication
Property of Equality?
7)
Explanation:
Answer the question.
8)
If x represents a negative integer, how would you express its negative?
8)
Explanation:
Provide an appropriate response.
9)
Write an equation that requires the use of the multiplication property of equality, where
both sides must be multiplied by 100 and where the solution isn’t an integer.
9)
Explanation:
10)
This pair of equations is equivalent.
3x – 3 =12 and 3x + 6 =21
10)
Explanation:
11)
What value of K makes this equation equivalent to x =5? 4x + 18x – 6 = K + 7
11)
Explanation:
12)
Write an equation that requires the use of the multiplication property of equality, where
both sides must be multiplied by 13
5 and where the solution is a negative number.
12)
Explanation:
Answer the question.
13)
One number is twice another. If the larger number is m, how do you express the other
number in terms of m?
13)
Explanation:
14)
Two angles are complimentary. One of the angles is r. How do you express the other
angle?
14)
Explanation:
Explanation:
15)
If x represents a positive integer, how would you express its negative?
15)
Provide an appropriate response.
16)
If you graphed x 5, would you use a parenthesis or a square bracket? Explain why.
16)
17)
If you graphed x <1, would you use a parenthesis or a square bracket? Explain why.
17)
18)
If b < 0, is it true that b2> b? Explain.
18)
19)
What is the Multiplication Property of Equality?
19)
20)
The solution set for the equation 2(8s – 3) =16s – 6 is given as 0. Is this correct? Explain.
20)
Answer the question.
21)
Two angles q and r are complimentary. The angle s is supplementary to q. Write an
equation showing the relationship between r and s.
21)
22)
Express three consecutive integers, all in terms of x, if x is the largest integer.
22)
Provide an appropriate response.
23)
What value of K makes this equation equivalent to x = 3? 4x – 6 = K
23)
24)
Under what conditions must the inequality symbol be reversed when solving an
inequality?
24)
25)
While solving an equation, why can’t you multiply both sides of the equation by zero?
25)
26)
Write the steps you would use to solve this equation: 9(x – 1) + 9x = – 3x.
26)
27)
In solving the inequality 3x –12, would you have to reverse the inequality symbol?
Explain why.
27)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
28)
Elaine had 46 buttons. Her grandmother donated 6 cards of buttons to the collection. Elaine sorted
the buttons into 10 piles, putting 10 buttons in each pile. How many buttons were on each card
from Elaine’s grandmother?
28)
A)
91 buttons
B)
94 buttons
C)
9 buttons
D)
44 buttons
Solve the formula for the specified variable.
29)
V =1
3Bh for h
29)
A)
h=V
3B
B)
h=3V
B
C)
h=3B
V
D)
h=B
3V
A formula is given along with the values of all but one of the variables in the formula. Find the value of the variable not
given. Round to the nearest hundredth where necessary.
30)
I = prt; I =18, p =300, r =0.06
30)
A)
1
B)
324
C)
3.24
D)
0.1
Solve the equation.
31)
12(x – 1) =2(6x + 2) – 16
31)
A)
B)
{–12}
C)
{0}
D)
{all real numbers}
A formula is given along with the values of all but one of the variables in the formula. Find the value of the variable not
given. Round to the nearest hundredth where necessary.
32)
A =1
2bh; b =10, h =8
32)
A)
80
B)
18.5
C)
40
D)
18
C
Graph the inequality.
33)
–6
x –2
33)
A)
B)
C)
D)
B
D
Solve the problem.
34)
Pennies are packaged 50 in a roll. A mother gave her son 156 pennies for his bank and had 44
pennies left over. How many rolls of pennies did she use?
34)
A)
4 rolls
B)
7 rolls
C)
6 rolls
D)
5 rolls
Solve the equation.
35)
157 =13x + 14
35)
A)
{11}
B)
{134}
C)
{1}
D)
{130}
Solve the equation by first clearing the fractions.
36)
1
4p –3
8p =5
36)
A)
{–200}
B)
{–40}
C)
{200}
D)
{40}
Solve the inequality, then graph the solution.
37)
12 < – 3y + 3 24
37)
A)
[–7, –3)
B)
[3, 7)
C)
(3, 7]
D)
(–7, –3]
Determine the number by which both sides of the equation must be multiplied or divided, as specified, to obtain just x
on the left side.
38)
–x = – 0.33; multiply by
38)
A)
–100
33
B)
0.33
C)
–0.33
D)
–1
Provide an appropriate response.
39)
True or false: The solution set of the equation 7y – 6 = 7y + 3 is zero.
39)
A)
True
B)
False
7
Solve the problem.
40)
During the first four months of the year, Jack earned $1070, $1110, $1110 and $1020. If Jack must
have an average salary of at least $1090 in order to earn retirement benefits, what must Jack earn in
the fifth month in order to qualify for benefits?
40)
A)
at most $1090
B)
at most $1078
C)
at least $1140
D)
at least $1080
Use a formula to solve the problem.
41)
A water reservoir is shaped like a rectangular solid with a base that is 3 meters by 6 meters, and a
vertical height of 8 meters. How much water is in the reservoir if it is completely full?
41)
A)
144 m3
B)
384 m3
C)
108 m3
D)
72 m3
Solve the problem.
42)
For what values of x would the rectangle have a perimeter of at least 242?
2x +1
7x +12
42)
A)
25 or greater
B)
12 or less
C)
12 or greater
D)
25 or less
Solve the inequality, then graph the solution.
43)
–5c – 6 –6c – 16
43)
A)
( , –5)
B)
(–5, )
C)
[–10, )
D)
( , –10]
Solve the equation by first clearing the decimals.
44)
0.12(50) + 0.6x =0.3(50 + x)
44)
A)
{30}
B)
{40}
C)
{15}
D)
{20}
Solve the problem.
45)
Two pages that face each other in a book have 405 as the sum of their page numbers. What is the
number of the page that comes first?
45)
A)
203
B)
200
C)
201
D)
202
Write an inequality using the variable x that corresponds to the set graphed on the number line.
46)
46)
A)
x –4
B)
x < – 4
C)
x > – 4
D)
x –4
Solve the equation.
47)
3(x + 6) = (3x + 18)
47)
A)
B)
{0}
C)
{36}
D)
{all real numbers}
D
Use a formula to solve the problem.
48)
What is the perimeter of a rectangle of length 50 ft and width 14 ft?
48)
A)
114 ft
B)
128 ft
C)
256 ft
D)
64 ft
B
Solve the equation.
49)
–6a + 4 + 7a =13 – 26
49)
A)
{43}
B)
{–43}
C)
{17}
D)
{–17}
D
10
A
Solve the inequality, then graph the solution.
50)
–0.3z > – 0.48
50)
A)
(1.6, )
B)
(–1.6, )
C)
( , 1.6)
D)
( , –1.6)
A formula is given along with the values of all but one of the variables in the formula. Find the value of the variable not
given. Round to the nearest hundredth where necessary.
51)
P = 2L + 2W; L =8, W =7
51)
A)
112
B)
15
C)
23
D)
30
Solve the equation.
52)
x–4= – 3
52)
A)
{–1}
B)
{–7}
C)
{1}
D)
{7}
Write the answer to the problem as an algebraic expression.
53)
Today the Center City baseball team scored 9 runs. The day before yesterday they scored w. How
many runs did they score in these two days?
53)
A)
9w runs
B)
9+ w runs
C)
9+ 2w runs
D)
9– w runs
Solve the problem.
54)
Sue drove her car 297 miles in January, 376 miles in February, and 254 miles in March. If her
average mileage for the four months from January to April is to be at least 343 miles, how many
miles must she drive in April?
54)
A)
at least 318 miles
B)
at most 445 miles
C)
at most 343 miles
D)
at least 445 miles
Determine the number by which both sides of the equation must be multiplied or divided, as specified, to obtain just x
on the left side.
55)
5
6x = – 1; multiply by
55)
A)
–1
B)
–5
6
C)
6
5
D)
6
Solve the equation.
56)
1
25 a = 0
56)
A)
{1}
B)
{–25}
C)
{0}
D)
{25}
Graph the inequality.
57)
x > – 7
57)
A)
B)
C)
D)
Solve the equation by first clearing the fractions.
58)
1
2a –1
2= – 2
58)
A)
{–5}
B)
{5}
C)
{–3}
D)
{3}
Find the measure of each marked angle.
59)
(x + 2)°(4x –147)°
59)
A)
65° and 115°
B)
67° and 23°
C)
67° and 113°
D)
69° and 111°
60)
x° 3x°
60)
A)
45° and 55°
B)
90° and 270°
C)
60° and 120°
D)
45° and 135°
Solve the equation.
61)
6x + 1x =42
61)
A)
{42
5}
B)
{–6}
C)
{–42
5}
D)
{6}
Solve the problem.
62)
The sum of the measures of the angles of any triangle is 180°. In triangle ABC, angles A and B have
the same measure, while the measure of angle C is 30° larger than each of A and B. What are the
measures of the three angles?
62)
A)
A and B: 60°; C: 60°
B)
A and B: 50°; C: 80°
C)
A and B: 80°; C: 50°
D)
A and C: 60°; B: 60°
14
Solve the inequality, then graph the solution.
63)
9x + 8 – 2x <4+ 5x + 8
63)
A)
( , 10)
B)
( , 2)
C)
(2, )
D)
(10, )
Write an inequality using the variable x that corresponds to the set graphed on the number line.
64)
64)
A)
x < – 4
B)
x > – 4
C)
x –4
D)
x –4
A
Solve the equation.
65)
4(3x – 1) =16
65)
A)
1
B)
5
3
C)
17
12
D)
5
4
B
B
A formula is given along with the values of all but one of the variables in the formula. Find the value of the variable not
given. Round to the nearest hundredth where necessary.
66)
A =r2; r =9, = 3.14
66)
A)
12.14
B)
88.74
C)
254.34
D)
28.26
Solve the equation.
67)
6x + 3x – 2 = – 8x
67)
A)
–2
17
B)
2
17
C)
–17
2
D)
– 2
68)
11 =6x – 7
68)
A)
{16}
B)
{12}
C)
{8}
D)
{3}
Solve the problem.
69)
A paint mixture contains 28 gallons of base for every gallon of color. In 290 gallons of paint, how
many gallons of color are there?
69)
A)
10 gallons
B)
96 gallons
C)
145 gallons
D)
280 gallons
Solve the equation.
70)
5.5p + 24 =6.5p + 12
70)
A)
{13}
B)
{5.5}
C)
{12}
D)
{11}
16
Provide an appropriate response.
71)
5x2– 7 = 3x. Is this a linear equation?
71)
A)
Yes
B)
No
Decide whether perimeter or area would be used to solve a problem concerning the measure of the quantity.
72)
Determining the cost for painting a wall
72)
A)
Area
B)
Perimeter
Provide an appropriate response.
73)
Is it true that the equation 411x + 615 =543 and the equation 411x + 615 – 543 = 0 are always
equivalent equations?
73)
A)
True
B)
False
Solve the equation.
74)
6(k + 4) – (5k – 1) = – 4
74)
A)
{21}
B)
{29}
C)
{– 29}
D)
{9}
Use a formula to solve the problem.
75)
A square plywood platform has a perimeter which is 10 times the length of a side, decreased by 18.
Find the length of a side.
75)
A)
1 unit
B)
6 units
C)
9 units
D)
3 units
Solve the equation by first clearing the fractions.
76)
–2
3r+ 2r=6
5r+8
5
76)
A)
–24
5
B)
{0}
C)
{12}
D)
8
15
Solve the equation.
77)
2
3x +1=1
2–1
3x +1
2
77)
A)
–2
B)
0
C)
–1
2
D)
2
B
78)
2
5x –1
3x =3
78)
A)
{–45}
B)
{90}
C)
{–90}
D)
{45}
D
79)
18(2x – 2) =12(3x +9)
79)
A)
{0}
B)
C)
{all real numbers}
D)
{144}
B
Decide whether perimeter or area would be used to solve a problem concerning the measure of the quantity.
80)
Tilling a garden
80)
A)
Area
B)
Perimeter
A
C