Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
Which equation does not require the use of the multiplication property of equality to solve the
equation?
1)
A)
6x + 8 – (–5x – 5) = – 8
B)
–6x +5x = – 8
C)
–5
6x = – 8– 5
D)
–5x – (–6)x = – 8
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
2)
Which one of the following ratios is not the same as 1.3?
(a) 13 to 10 (b) 1 to 3
(c) 1.30 (d) 130 to 100
2)
3)
The solution set for the equation 3(7s – 2) =21s – 6 is given as 0. Is this correct? Explain.
3)
Answer the question.
4)
How would you express the product of two numbers, r and s?
4)
Provide an appropriate response.
5)
What is the Multiplication Property of Equality?
5)
Answer the question.
6)
If x represents a negative integer, how would you express its negative?
6)
7)
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) 42 (ii) 1 (iii) 1,000,010 (iv) 110
7)
8)
Express three consecutive integers, all in terms of x, if x is the largest integer.
8)
Provide an appropriate response.
9)
After working correctly through several steps of the solution of a linear equation, a student
obtains the equation 9x =8x. Then the student divides each side by x to get 9=8 and gives
as the answer. Is this correct? If not, explain why.
9)
Answer the question.
10)
Two angles are complimentary. One of the angles is r. How do you express the other
angle?
10)
Provide an appropriate response.
11)
If an equation has decimals as coefficients, what step will make work easier?
11)
12)
Write the steps you would use to solve this equation: 3(x – 1) + 5x = – 9x.
12)
13)
A student tried to solve the equation 9x =40 by dividing each side by 40. Why is this not
the correct procedure for solving this equation?
13)
14)
Which one of the following ratios is not the same as .75?
(a) 3 to 4 (b) 8 to 6
(c) .750 (d) 75 to 100
14)
15)
Explain why the equation x +9
6=x +7
6 has no solution.
15)
16)
State how you would find the solution of a linear equation if your next–to–last step reads
“–x =48.”
16)
17)
While solving an equation, why can’t you multiply both sides of the equation by zero?
17)
18)
Give three ratios that are equivalent to 19 to 41.
18)
Answer the question.
19)
If x represents a positive integer, how would you express its negative?
19)
20)
Two angles q and r are complimentary. The angle s is supplementary to q. Write an
equation showing the relationship between r and s.
20)
Provide an appropriate response.
21)
Which one of the following ratios is not the same as 4 to 6?
(a) 6 to 4 (b) 2 to 3
(c) 20 to 30 (d) 8 to 12
21)
22)
Which one of the following ratios is not the same as 5 to 2?
(a) 10 to 4 (b) 50 to 20
(c) 25 to 10 (d) 2 to 5
22)
23)
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.
23)
24)
Which one of the following ratios is not the same as 4 to 16?
(a) 40 to 160 (b) 0.25
(c) 2 to 8 (d) 4 to 1
24)
25)
If an equation has fractions as coefficients, what step will make work easier?
25)
Answer the question.
26)
One number is twice another. If the larger number is m, how do you express the other
number in terms of m?
26)
Provide an appropriate response.
27)
When does the solution of a linear equation not require the use of the Multiplication
Property of Equality?
27)
28)
Explain the distinction between ratio and proportion. Give examples.
28)
29)
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.
29)
30)
Which one of the following ratios is not the same as 5 to 6?
(a) 10 to 12 (b) 50 to 60
(c) 6 to 5 (d) 200 to 240
30)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation. First simplify the expression by combining like terms.
31)
–8(k – 6) – (–9k – 9) = – 4
31)
A)
{7}
B)
{– 61}
C)
{61}
D)
{53}
Solve the inequality and graph the solution set.
32)
–11x +5(x –8) 4x – (10 +5x) – 70
32)
A)
[8, )
B)
( , 8]
C)
( , 8)
D)
(8, )
Decide whether the proportion is true or false.
33)
12
44 = 60
220
33)
A)
True
B)
False
Solve the equation.
34)
–4
5x = – 20
34)
A)
16
B)
96
5
C)
104
5
D)
{25}
Solve the inequality and write the solution set in interval notation.
35)
4x > 0
35)
A)
(–, 0)
B)
(–, )
C)
(0, )
D)
Decide whether the proportion is true or false.
36)
3
7=21
49
36)
A)
True
B)
False
Solve the problem.
37)
Best Office Machines spent $46,130 this year on health insurance alone. If total sales were $467,900,
what percent of total sales was spent on health insurance? Round to the nearest tenth of a percent,
if necessary.
37)
A)
1%
B)
101%
C)
9.9%
D)
10.1%
Decide whether the perimeter or area would be used to solve a problem concerning the measure of the quantity.
38)
Measuring a garden for tilling
38)
A)
Area
B)
Perimeter
Solve the problem.
39)
The appliance store where the Jordans shop offers a 8% discount for paying cash. The Jordans
received a discount of $25. What was their total bill before the discount? Round to the nearest
dollar.
39)
A)
$200
B)
$313
C)
$2
D)
$3
40)
Find the measure of an angle whose supplement is 6 times the measure of its complement.
40)
A)
15°
B)
72°
C)
30°
D)
36°
Solve the equation.
41)
x + 6
3=x + 8
6
41)
A)
{–12}
B)
{–4}
C)
{4}
D)
{3}
Provide an appropriate response.
42)
Tell whether you would use the addition or multiplication property of equality to solve the
equation: 7a = – 21.
42)
A)
Addition property
B)
Multiplication property
Solve the problem.
43)
A convention manager finds that she has $1440 made up of twenties and fifties. She has a total of 45
bills. How many fifty–dollar bills does the manager have?
43)
A)
45 fifty–dollar bills
B)
27 fifty–dollar bills
C)
18 fifty–dollar bills
D)
12 fifty–dollar bills
Use a formula to solve the problem.
44)
A square plywood platform has a perimeter which is 8 times the length of a side, decreased by 24.
Find the length of a side.
44)
A)
6
B)
1
C)
10
D)
4
Write an inequality involving the variable x that describes the set of numbers graphed.
45)
45)
A)
x < – 2
B)
x –2
C)
x > – 2
D)
x –2
Solve the problem.
46)
Sue drove her car 391 miles in January, 414 miles in February, and 266 miles in March. If her
average mileage for the four months from January to April is to be at least 384 miles, how many
miles must she drive in April?
46)
A)
at least 465 miles
B)
at most 384 miles
C)
at most 465 miles
D)
at least 364 miles
Solve the equation.
47)
–2.5c = – 15.0
47)
A)
{2.0}
B)
{6.0}
C)
{–12.5}
D)
{12.5}
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.
48)
A =r2; r =2, = 3.14
48)
A)
19.72
B)
6.28
C)
5.14
D)
12.56
49)
V =1
3Bh; V =18, h =6
49)
A)
108
B)
24
C)
9
D)
3
Solve the equation.
50)
–x =1
3
50)
A)
{–2}
B)
1
3
C)
–1
3
D)
{1}
51)
n
5=3
51)
A)
{8}
B)
{0}
C)
{7}
D)
{15}
Solve the problem.
52)
Paul Nagel invested some money at 3.5% simple interest and $7000 more than that amount at 4.5%
simple interest. After 1 year, his total interest from the two accounts was $1275. How much did he
invest at each rate?
52)
A)
$13,000 at 3.5%; $19,000 at 4.5%
B)
$13,000 at 3.5%; $18,000 at 4.5%
C)
$12,000 at 3.5%; $20,000 at 4.5%
D)
$12,000 at 3.5%; $19,000 at 4.5%
Write the answer to the problem as an algebraic expression.
53)
A theater ticket for adults is A dollars and the price of a child’s ticket is c dollars. If 21 adults and 43
children attend the theater one night, how much money did the theater make?
53)
A)
903Ac dollars
B)
43A+ 21c dollars
C)
21c+ cA dollars
D)
21A+ 43c dollars
Solve the equation.
54)
0.32(50) + 0.5x =0.4(50 + x)
54)
A)
{50}
B)
{40}
C)
{30}
D)
{20}
Solve the problem.
55)
A reservation clerk worked 15.3 hours one day. She spent twice as much time entering new
reservations as she did verifying old ones and one and a half as much time calling to confirm
reservations as verifying old ones. How much time did she spend entering new reservations?
55)
A)
6.8 hours
B)
5.1 hours
C)
3.4 hours
D)
13.6 hours
56)
The formula for the perimeter of a rectangle is P = 2L + 2W. If P =56 and W =6, find the value of L.
56)
A)
20
B)
22
C)
21
D)
19
57)
In the previous baseball season, team A won the most games of any major league team. Team A
won 36 less than twice as many games as they lost. They played 162 regular–season games. How
many wins and losses did team A have?
57)
A)
Wins: 94; losses: 68
B)
Wins: 97; losses: 65
C)
Wins: 96; losses: 67
D)
Wins: 96; losses: 66
Solve the equation.
58)
–2x = – 12
58)
A)
{6}
B)
{2}
C)
{–10}
D)
{10}
Solve the problem.
59)
Find the measure of an angle such that the difference between its supplement and 3 times its
complement is 46°.
59)
A)
82.5°
B)
34°
C)
165°
D)
68°
Translate the statement into an inequality. Use x as the variable.
60)
The jet’s speed exceeded 530 mph.
60)
A)
x >530
B)
x 530
C)
x 530
D)
x <530
Solve the problem.
61)
A church steeple casts a shadow 109 ft long, and at the same time a 9.0–ft post cast a shadow 7.0 ft
long. How high is the steeple? Round to the nearest unit.
61)
A)
140 ft
B)
112 ft
C)
8 ft
D)
85 ft
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.
62)
0.2x =3; multiplied
62)
A)
3
B)
–2
3
C)
5
D)
0.2
A survey showed that students had these preferences for instructional materials. Use the graph to answer the question.
63)
About how many students would you expect to prefer computers in a school of 950 students?
63)
A)
About 190 students
B)
About 342 students
C)
About 171 students
D)
About 36 students
64)
About how many students would you expect to prefer lectures in a school of 900 students?
64)
A)
About 18 students
B)
About 162 students
C)
About 324 students
D)
About 180 students
Solve the inequality. Write the solution set in interval notation and graph it.
65)
12 + 6t – 6 5t + 10
65)
A)
( , 6)
B)
(6, )
C)
[4, )
D)
( , 4]
Solve the problem.
66)
Elaine had 38 buttons. Her grandmother donated 5 cards of buttons to the collection. Elaine sorted
the buttons into 7 piles, putting 9 buttons in each pile. How many buttons were on each card from
Elaine’s grandmother?
66)
A)
61 buttons
B)
58 buttons
C)
36 buttons
D)
5 buttons
A survey showed that students had these preferences for instructional materials. Use the graph to answer the question.
67)
About how many students would you expect to prefer radio in a school of 650 students?
67)
A)
About 117 students
B)
About 5 students
C)
About 234 students
D)
About 33 students
Solve the equation.
68)
0.7(x +60) +0.5(x –90) =81
68)
A)
{140}
B)
{80}
C)
{70}
D)
{60}
Write the answer to the problem as an algebraic expression.
69)
Elizabeth earned 10 dollars a day at her job. Assuming a 5–day work week, how much did she earn
in x weeks?
69)
A)
10 + x dollars
B)
10x dollars
C)
50x dollars
D)
50 + x
Use a formula to solve the problem.
70)
What is the area of a square with side 3.6 cm?
70)
A)
12.96 cm2
B)
46 cm2
C)
7.2 cm2
D)
51.84 cm2
Write each inequality in interval notation and graph the interval on a number line.
71)
x >5
71)
A)
(–, 5]
B)
(5, )
C)
(–, 5)
D)
[5, )
Solve the formula for the specified variable.
72)
A =1
2h(b1+ b2) for b1
72)
A)
b1=
A – h(b2)
2h
B)
b1=
2A – (h)(b2)
h
C)
b1=
(b2)2A – h
h
D)
b1=
h(b2) – 2A
h
Express the phrase as a ratio in lowest terms.
73)
135 cm to 75 cm
73)
A)
9
5
B)
5
9
C)
34
19
D)
19
34
Use a formula to solve the problem.
74)
What is the perimeter of a rectangle of length 15 ft and width 13 ft?
74)
A)
56 ft
B)
43 ft
C)
112 ft
D)
28 ft
Solve the formula for the specified variable.
75)
I =nE
nr + R for n
75)
A)
n =
–IR
Ir – E
B)
n =
–R
Ir – E
C)
n =IR
Ir + E
D)
n = IR(Ir – E)
A
Find the measure of each marked angle.
76)
(x + 2)°(4x –122)°
76)
A)
60° and 120°
B)
62° and 28°
C)
62° and 118°
D)
64° and 116°
C
A
Write each inequality in interval notation and graph the interval on a number line.
77)
x0
77)
A)
[0, )
B)
(–, 0)
C)
(0, )
D)
(–, 0]
Solve the equation. First simplify the expression by combining like terms.
78)
–4(–8x – 8) + 7(7 – 2x) = (16 + 19x)
78)
A)
{65}
B)
{–33}
C)
{81}
D)
{97}
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.
79)
A =1
2bh; b =8, h =18
79)
A)
26.5
B)
144
C)
26
D)
72
Solve the equation.
80)
x
30 =7
15
80)
A)
{14}
B)
450
7
C)
7
2
D)
{28}
Write an inequality involving the variable x that describes the set of numbers graphed.
81)
81)
A)
2 x 6
B)
2< x 6
C)
2 x <6
D)
2< x <6
Solve the problem.
82)
If three times the smaller of two consecutive integers is added to four times the larger, the result is
137. Find the smaller integer.
82)
A)
19
B)
57
C)
18
D)
20
Solve the equation.
83)
7
3=x +2
10
83)
A)
68
3
B)
3
8
C)
64
3
D)
76
3
Write the answer to the problem as an algebraic expression.
84)
Today the Center City baseball team scored 11 runs. The day before yesterday they scored y. How
many runs did they score in these two days?
84)
A)
11 – y runs
B)
11y runs
C)
11 + y runs
D)
11 + 2y runs
Decide whether the perimeter or area would be used to solve a problem concerning the measure of the quantity.
85)
Measuring a garden for a border fence?
85)
A)
Perimeter
B)
Area
Solve the equation.
86)
–2b =30
86)
A)
{1}
B)
{–15}
C)
{–32}
D)
{32}
Write an inequality involving the variable x that describes the set of numbers graphed.
87)
87)
A)
x <1
B)
x >1
C)
x 1
D)
x 1
Solve the problem.
88)
A bank teller has some five–dollar bills and some twenty–dollar bills. The teller has 5 more of the
twenties. The total value of the money is $750. Find the number of five–dollar bills that the teller
has.
88)
A)
36 five–dollar bills
B)
31 five–dollar bills
C)
26 five–dollar bills
D)
21 five–dollar bills
89)
One side of a triangle is twice as long as a second side. The third side of the triangle is 16 feet long.
The perimeter of the triangle cannot be more than 61 feet. Find the longest possible values for the
other two sides of the triangle.
89)
A)
15 feet and 30 feet
B)
14 feet and 28 feet
C)
23 feet and 23 feet
D)
39 feet and 39 feet
Solve the equation. First simplify the expression by combining like terms.
90)
2
11 x +2
9=1
2–9
11 x +1
2
90)
A)
5
18
B)
11
9
C)
–11
9
D)
7
9
Solve the equation.
91)
(y – 8) – (y + 7) =4y
91)
A)
–5
2
B)
–15
4
C)
–15
8
D)
3
4
Solve the problem.
92)
The parking lot at a golf course has 90 cars in it. 40% of the cars are four–door. How many cars are
four–door?
92)
A)
360 cars
B)
225 cars
C)
23 cars
D)
36 cars
Translate the sentence into an equation using the variable x.
93)
A number minus 2 equals 4.
93)
A)
2– x =4
B)
x =2– 4
C)
x =4–2
D)
x – 2 =4