Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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To which sets of numbers does the number belong?
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1.
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a. | irrational numbers, real numbers | b. | integers, rational numbers, real
numbers | c. | rational numbers, irrational numbers | d. | whole numbers, integers, rational numbers, real
numbers |
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2.
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–17
a. | integers, rational numbers, real numbers | b. | whole numbers,
integers, rational numbers, real numbers | c. | whole numbers, integers, real
numbers | d. | rational numbers, real numbers |
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3.
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a. | integers, rational numbers, real numbers | b. | rational numbers,
real numbers | c. | irrational numbers, real numbers | d. | rational numbers, irrational numbers, real
numbers |
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4.
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The formula  relates the speed S in miles per hour a car was
traveling to the length d in feet that the car skidded when brakes were applied. The variable
f is the coefficient of friction, which varies depending on the road surface and the condition
of the tires. Which sets of numbers contain the value of S for f = 0.8 and d =
51? a. | integers, rational numbers, real numbers | b. | irrational numbers,
real numbers | c. | whole numbers, integers, rational numbers, real numbers | d. | natural numbers,
whole numbers, integers, rational numbers, real numbers |
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5.
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An irrational number can ________ be expressed as a quotient of integers.
a. | always | b. | sometimes | c. | never |
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Graph the number on a number line.
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6.
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7.
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Insert <, >, or = to make the sentence true.
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8.
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9.
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10.
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20.28  
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11.
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12.
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Find the opposite and the reciprocal of the number.
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13.
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500
a. | –500,  | c. | 500,  | b. | –500,  | d. | 500,  |
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14.
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15.
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–1.74
a. |  ,  | c. |  ,
–1.74 | b. | 1.74,  | d. | 1.74,  |
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16.
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Name the property of real numbers illustrated by the equation.
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17.
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a. | Associative Property of Multiplication | b. | Distributive Property | c. | Commutative Property
of Addition | d. | Associative Property of Addition |
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18.
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a. | Distributive Property | b. | Associative Property of
Multiplication | c. | Commutative Property of Multiplication | d. | Associative Property of
Addition |
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19.
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a. | Associative Property of Multiplication | b. | Commutative Property of
Addition | c. | Commutative Property of Multiplication | d. | Closure
Property |
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20.
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–6 + 6 = 0
a. | Identity Property of Multiplication | b. | Inverse Property of
Multiplication | c. | Associative Property of Addition | d. | Inverse Property of
Addition |
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21.
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–2.5 + 0 = –2.5
a. | Inverse Property of Multiplication | b. | Identity Property of
Addition | c. | Inverse Property of Addition | d. | Identity Property of
Multiplication |
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22.
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Simplify  .
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Evaluate the expression for the given value of the variable(s).
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23.
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24.
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25.
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 ; b = 2
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26.
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 ; x = –3
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27.
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 ; x = –3
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28.
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The expression  models the height of an object t seconds after it has
been dropped from a height of 1800 feet. Find the height of an object after falling for 4.8
seconds. a. | 2168.64 ft | b. | 1431.36 ft | c. | 1723.2 ft | d. | 7698.24
ft |
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Simplify by combining like terms.
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29.
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30.
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31.
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32.
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Find the perimeter of the figure. Simplify the answer.  a. | 9x + 2y | b. | 10x + y | c. | 10x +
2y | d. | 9x + 3y |
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33.
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If a = b, then a – c ____ equals b –
c.
a. | always | b. | sometimes | c. | never |
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Solve the equation.
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34.
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35.
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36.
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37.
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38.
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39.
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Solve the equation or formula for the indicated variable.
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40.
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 , for t
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41.
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 , for U
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42.
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The formula for the time a traffic light remains yellow is  , where t
is the time in seconds and s is the speed limit in miles per hour. | a. | Solve the equation for
s. | | b. | What is the speed limit at a traffic light that remains yellow for 4.5 seconds? | | |
a. |  ; s = 28 mi/h | c. |  ; s =
35 | b. |  ; s = 36 mi/h | d. |  ; s = 28
mi/h |
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Solve for x. State any restrictions on the variables.
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43.
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44.
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45.
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A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the
dimensions of the rectangle. Round to the nearest tenth if necessary.
a. | 7.5 cm by 22.5 cm | c. | 20 cm by 60 cm | b. | 7.5 cm by 52.5 cm | d. | 15 cm by 22.5
cm |
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46.
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The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each
side if the perimeter of the triangle is 90 cm?
a. | 10.5 cm, 11.5 cm, and 12.5 cm | c. | 7.5 cm, 11.5 cm, and 32.1
cm | b. | 22.5 cm, 30 cm, and 37.5 cm | d. | 19.3 cm, 25.7 cm, and 32.1 cm |
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47.
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Two cars leave Denver at the same time and travel in opposite directions. One
car travels 10 mi/h faster than the other car. The cars are 500 mi apart in 5 h. How fast is each car
traveling?
a. | 35 mi/h and 45 mi/h | c. | 45 mi/h and 55 mi/h | b. | 55 mi/h and 35 mi/h | d. | 55 mi/h and 65
mi/h |
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48.
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Michael has $12,500 to invest. He invests part in an account which earns 4.2%
annual interest and the rest in an account which earns 6.2% annual interest. He earns $669.50 in
interest at the end of the year. How much was invested at each rate?
a. | $5,000 at 4.2%, $7,500 at 6.2% | c. | $7,500 at 4.2%, $5,000 at
6.2% | b. | $7,225 at 4.2%, $5,275 at 6.2% | d. | $5,275 at 4.2%, $7,225 at
6.2% |
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49.
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An inequality ____ has a real number solution.
a. | always | b. | sometimes | c. | never |
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Solve the inequality. Graph the solution set.
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50.
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2 + 2k £ 8
a. | k ³ 3
 | c. | k £ 3
 | b. | k £ 
 | d. | k ³ 
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51.
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2r – 9 ³ –6
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52.
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–4k + 5 £ 21
a. | k ³ –4
 | c. | k £ –4
 | b. | k ³ 
 | d. | k £ 
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53.
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2(4y – 5) < –10
a. | y > 0
 | c. | y < 0
 | b. | y < 
 | d. | y > 
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54.
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2(2m – 5) – 6 >
–36
a. | m < 
 | c. | m < –5
 | b. | m >
–5
 | d. | m > 
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55.
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4(3b – 5) < –31 + 12b
a. | no solutions
 | c. | b > 
 | b. | b < 
 | d. | all real numbers
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56.
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26 + 6b ³ 2(3b + 4)
a. | all real numbers
 | c. | b ³ 
 | b. | b £ 
 | d. | no
solutions
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Solve the problem by writing an inequality.
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57.
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A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8
per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club
needs to make and sell in order to profit at least $100.
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58.
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If the perimeter of a rectangular picture frame must be less than 200 in., and
the width is 36 in., what must the height h of the frame be?
a. | h < 64 in. | b. | h > 128 in. | c. | h > 64 in. | d. | h < 128
in. |
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Solve the compound inequality. Graph the solution set.
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59.
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5x + 10 ³ 10 and 7x – 7
£ 14
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60.
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4x – 5 < –17 or 5x + 6 > 31
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61.
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62.
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The perimeter of a square garden is to be at least 22 feet but not more than 36
feet. Find all possible values for the length of its sides.
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63.
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Students tested the acidity of the campus pond over a three-day period. On
Monday and Tuesday, the pH values were 6.75 and 7.86. Find the range of pH values for
Wednesday’s reading that will result in a mean pH greater than 7.1 and less than 7.6.
a. | 7.01 < x < 7.5 | c. | 21.3 < x <
22.8 | b. | 16.69 < x < 8.19 | d. | 10.65 < x <
11.4 |
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64.
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An absolute value equation ____ has an extraneous solution.
a. | always | b. | sometimes | c. | never |
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Solve the equation. Check for extraneous solutions.
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65.
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Solve the inequality. Graph the solution.
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66.
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67.
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a. | –18 > x > 8
 | c. | –36 < x <
16
 | b. | –18 < x < 8
 | d. | 
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68.
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69.
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A furniture maker uses the specification  for the width w in
inches of a desk drawer. Write the specification as an inequality.
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70.
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When Spheres-R-Us ships bags of golf balls, the number of balls in each bag must
be within 6 balls of 300. Write an absolute value inequality and a compound inequality for an
acceptable number of golf balls b in each bag.
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71.
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Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the
experimental probability of tossing heads using Lynn and Dawn’s results?
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72.
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A biologist has determined that a particular osprey has a 70% chance of catching
a fish on any given day. Carry out a simulation of twenty trials using the random number table below
to find the probability that the osprey will actually catch a fish on all of the next three days.
Explain your method. 945 | 025 | 354 | 793 | 236 | 106 | 746 | 981 | 105 | 012 | 832 | 180 | 250 | 871 | 835 | 793 | 726 | 864 | 496 | 947 | | | | | |
a. | Using the digits 0–7 to represent a caught fish, the probability of catching a
fish on each of the next three days is 70%. | b. | Using the digits 0–7 to represent a
caught fish, the probability of catching a fish on each of the next three days is
65%. | c. | Using the digits 0–6 to represent a caught fish, the probability of catching a
fish on each of the next three days is 35%. | d. | Using the digits 0–7 to represent a
caught fish, the probability of catching a fish on each of the next three days is
7%. |
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73.
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This is a spinner used in a board game. What is the probability that the spinner
will land on a multiple of 3 and 4? 
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74.
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The theoretical probability of an event is ____ a negative number.
a. | always | b. | sometimes | c. | never |
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75.
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A spinner is numbered from 1 through 10 with each number equally likely to
occur. What is the probability of obtaining a number less than 2 or greater than 7 in a single
spin?
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76.
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A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find
P(red or blue).
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77.
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Assume a rabbit variety can be either long-haired (dominant) or short-haired
(recessive). If a parent has one of each type of gene, then the two genes are equally likely to be
passed to its offspring. If a rabbit has one or two dominant genes, it will be long-haired. What is
the probability that a rabbit will be short-haired? Gene from
Father | | | | G | g | Gene from | G | GG | Gg | Mother | g | Gg | gg | | | | |
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78.
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If a dart hits the target at random, what is the probability that it will land
in the shaded region? 
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79.
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On the following dartboard, the radius of the bulls-eye (area A) is 4
inches. The radius of each concentric circle is 4 inches more than the circle inside it. If a person
throws randomly onto the dartboard, what is the probability that the dart will hit in area B?
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Short Answer
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80.
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In the following expression: the number of people p required to paint
n square feet of wall in 24 hours, which set of numbers best describes the values for each
variable?
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81.
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Name the property used in each step of simplification. 
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Simplify the expression.
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82.
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Solve the equation. Check for extraneous solutions.
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83.
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84.
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An engineer predicts that a machine will manufacture good parts 80% of the time.
Use a simulation of twelve trials and the random number chart below to find the probability that the
machine will make good parts on all of the next four attempts. 9295 | 6742 | 7980 | 5522 | 3376 | 2187 | 6217 | 8811 | 1243 | 4500 | 4665 | 2860 | | | | |
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Essay
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85.
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Air temperature drops approximately 5.5ºF for each 1,000-foot rise in
altitude above Earth’s surface (up to 30,000 ft). | a. | Write a formula that relates temperature t in
degrees Fahrenheit at altitude h (in thousands of feet) and a ground temperature of 65ºF.
State any restrictions on h. | | b. | Find the temperature at 11,000 ft above Earth’s
surface. | | |
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86.
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The manufacturing specification for a bolt calls for a tolerance of 0.2 cm and a
length of 6 cm. | a. | Write the specification as an absolute value inequality. | | b. | Write the specification as a compound
inequality. | | c. | An engineer selects two bolts to check the machine’s accuracy. One is 5.92 cm long and
the other is 6.21 cm long. Do these bolts fall within the specification? | | |
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87.
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Suppose 10 out of 25 students in your class have dogs for pets. | a. | What is the theoretical
probability that a student selected at random from your class has a dog? | | b. | Using your result from
part (a), predict how many dog-owning students you can expect among the 200 students in your grade.
Show your work. | | |
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Other
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88.
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What is the maximum number of 3.5-to-5-min songs that can fill a 120-min CD?
What is the minimum number? Write your answer as a compound inequality. Explain your
reasoning.
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89.
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Describe the difference in the graphs of  , where a is a
positive real number.
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90.
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a. Make three graphs showing the solutions of each inequalities. b.Write a compound inequality that describes all of the numbers which
are solutions to both inequalities.
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