To Which Sets of Numbers Does the Number Belong?

REVIEW FOR MIDTERM #1

Multiple Choice

Identify the choice that best completes the statement or answers the question.

To which sets of numbers does the number belong?

____ 1.

a. / irrational numbers, real numbers
b. / integers, rational numbers, real numbers
c. / rational numbers, irrational numbers
d. / whole numbers, integers, rational numbers, real numbers

____ 2. –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

____ 3.

a. / integers, rational numbers, real numbers
b. / rational numbers, real numbers
c. / irrational numbers, real numbers
d. / rational numbers, irrational numbers, real numbers

____ 4. 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

____ 5. An irrational number can ______be expressed as a quotient of integers.

a. / always / b. / sometimes / c. / never

Graph the number on a number line.

____ 6.

a. / / c. /
b. / / d. /

____ 7.

a. / / c. /
b. / / d. /

Insert <, >, or = to make the sentence true.

____ 8.

a. / = / b. / c.

____ 9.

a. / b. / c. / =

____ 10. 20.28

a. / b. / = / c.

____ 11.

a. / b. / = / c.

____ 12.

a. / b. / c. / =

Find the opposite and the reciprocal of the number.

____ 13. 500

a. / –500, / c. / 500,
b. / –500, / d. / 500,

____ 14.

a. / , / c. / ,
b. / , / d. / ,

____ 15. –1.74

a. / , / c. / , –1.74
b. / 1.74, / d. / 1.74,

____ 16.

a. / , / b. / , / c. / , / d. / ,

Name the property of real numbers illustrated by the equation.

____ 17.

a. / Associative Property of Multiplication
b. / Distributive Property
c. / Commutative Property of Addition
d. / Associative Property of Addition

____ 18.

a. / Distributive Property
b. / Associative Property of Multiplication
c. / Commutative Property of Multiplication
d. / Associative Property of Addition

____ 19.

a. / Associative Property of Multiplication
b. / Commutative Property of Addition
c. / Commutative Property of Multiplication
d. / Closure Property

____ 20. –6 + 6 = 0

a. / Identity Property of Multiplication
b. / Inverse Property of Multiplication
c. / Associative Property of Addition
d. / Inverse Property of Addition

____ 21. –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

____ 22. Simplify .

a. / 14 / b. / 8 / c. / –8 / d. / –14

Evaluate the expression for the given value of the variable(s).

____ 23. ; ,

a. / –55 / b. / 55 / c. / 5 / d. / –5

____ 24.

a. / / b. / / c. / / d. /

____ 25. ; b = 2

a. / 19 / b. / 17 / c. / –11 / d. / 21

____ 26. ; x = –3

a. / 3 / b. / –1 / c. / 11 / d. / –17

____ 27. 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

Simplify by combining like terms.

____ 28.

a. / / b. / / c. / / d. /

____ 29.

a. / / b. / / c. / / d. /

____ 30.

a. / / b. / / c. / / d. /

____ 31. Find the perimeter of the figure. Simplify the answer.

a. / 9x + 2y / b. / 10x + y / c. / 10x + 2y / d. / 9x + 3y

____ 32. If a = b, then a – c ____ equals b – c.

a. / always / b. / sometimes / c. / never

Solve the equation.

____ 33.

a. / / b. / / c. / / d. /

____ 34.

a. / / b. / / c. / / d. /

____ 35.

a. / / b. / / c. / / d. /

____ 36.

a. / –0.5 / b. / –2 / c. / 0.5 / d. / 2

____ 37.

a. / x = or x = / c. / x = or x =
b. / x = or x = / d. / x = or x =

____ 38.

a. / x = or x = / c. / x = or x =
b. / x = or x = / d. / x = or x =

Solve the equation or formula for the indicated variable.

____ 39. , for t

a. / / b. / / c. / / d. /

____ 40. , for U

a. / / b. / / c. / / d. /

____ 41. 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

Solve for x. State any restrictions on the variables.

____ 42.

a. / ; / c. / ;
b. / ; / d. / ;

____ 43.

a. / ; / c. /
b. / ; / d. / ;

____ 44. 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

____ 45. 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

____ 46. 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

____ 47. 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%

____ 48. An inequality ____ has a real number solution.

a. / always / b. / sometimes / c. / never

Solve the inequality. Graph the solution set.

____ 49. 2 + 2k £ 8

a. / k ³ 3
/ c. / k £ 3

b. / k £
/ d. / k ³

____ 50. 2r – 9 ³ –6

a. / r £
/ c. / r ³

b. / r ³
/ d. / r £

____ 51. –4k + 5 £ 21

a. / k ³ –4
/ c. / k £ –4

b. / k ³
/ d. / k £

____ 52.

2(4y – 5) –10

a. / y 0
/ c. / y 0

b. / y
/ d. / y

____ 53. 2(2m – 5) – 6 –36

a. / m
/ c. / m –5

b. / m –5
/ d. / m

____ 54. 4(3b – 5) < –31 + 12b

a. / no solutions
/ c. / b >

b. / b <
/ d. / all real numbers

____ 55. 26 + 6b ³ 2(3b + 4)

a. / all real numbers
/ c. / b ³

b. / b £
/ d. / no solutions

Solve the problem by writing an inequality.

____ 56. 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.

a. / / c. /
b. / / d. /

____ 57. If the perimeter of a rectangular picture frame must be less than 200 in., and the width is 36in., 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.

Solve the compound inequality. Graph the solution set.

____ 58. 5x + 10 ³ 10 and 7x – 7 £ 14

a. / x ³ or x £
/ c. / x ³ or x £ 3

b. / x ³ 0 and x £
/ d. / x ³ 0 and x £ 3

____ 59. 4x – 5 < –17 or 5x + 6 > 31

a. / x < –3 or x > 5
/ c. / x < –3 or x >

b. / x < or x >
/ d. / x < or x > 5

____ 60.

a. / / c. /

b. /
/ d. /

____ 61. 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.

a. / / c. /
b. / / d. /

____ 62. 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

____ 63. An absolute value equation ____ has an extraneous solution.

a. / always / b. / sometimes / c. / never

Solve the equation. Check for extraneous solutions.

____ 64.

a. / / c. /
b. / / d. /

Solve the inequality. Graph the solution.

____ 65.

a. /
/ c. /

b. /
/ d. /

____ 66.

a. / –18 > x > 8
/ c. / –36 < x < 16

b. / –18 < x < 8
/ d. /

____ 67.

a. / < x <
/ c. / x < or x >

b. / < x <
/ d. / x < or x >

____ 68. A furniture maker uses the specification for the width w in inches of a desk drawer. Write the specification as an inequality.

a. / / c. /
b. / / d. /

____ 69. 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.

a. / ; / c. / ;
b. / ; / d. / ;

____ 70. Write the ordered pairs for the relation. Find the domain and range.

a. / {(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}
b. / {(5, –2), (2, –1), (1, 0), (2, 1), (5, 2)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}
c. / {(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {1, 2, 5}; range: {–2, –1, 0, 1, 2}
d. / {(5, –2), (2, –1), (1, 0), (2, 1), (5, 2)}; domain: {1, 2, 5}; range: {–2, –1, 0, 1, 2}

____ 71. Graph the relation. Find the domain and range.