Deck : Fundamental Concepts of Algebra

Question 1

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. 2, -3

A) 2 < -3
B) 2 > -3

Answer 1

B

Question 2

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them.

A)
B)

Answer 2

A

Question 3

The lowest recorded January temperature for a city is and the highest recorded temperature is Find the distance between the numbers to determine the range of temperatures for January.

A)
B)
C)
D)
E)

Answer 3

E

Question 4

Determine which numbers in the set are irrational numbers.

A)
B)
C)
D)
E)

Question 5

Approximate the numbers and place the correct symbol (< or >) between them.

A) -3 < 3.75
B) -3 < -3.25
C) -3 < 3.25
D) -3 > 3.25
E) -3 > 3.75

Question 6

Determine which numbers in the set are natural numbers.

A)
B)
C)
D)
E)

Question 7

Use absolute value notation to describe the situation. The distance between z and 4 is no less than 2.

A) $\ge$ 2
B) $\le$ 2
C) <2
D) >2
E) $\ge$ 2

Question 8

Which graph represents the inequality? -2< x $\le$ 8

A) -2 8
B) -2 8
C) -2 8
D) -2 8
E) -2 8

Question 9

Determine which numbers in the set are integers.

A)
B)
C)
D)
E)

Question 10

The quality control inspector for a tire factory is testing the rim diameter of various tires.A tire is rejected if its rim diameter varies too much from its expected measure.The diameter should not differ by more than 0.11 inch or by more than of the expected diameter measure.Find the widest range of allowable values for the actual diameter if the expected diameter is 16.000 inches.Round to the nearest thousandth.

A) between 15.890 inches and 16.024 inches
B) between 15.976 inches and 16.110 inches
C) between 15.976 inches and 16.024 inches
D) between 15.890 inches and 16.000 inches
E) between 15.890 inches and 16.110 inches

Question 11

Give a verbal description of the subset of real numbers represented by the inequality. 6 < x $\le$ 9

A) all real numbers less than 6 and greater than 9
B) all real numbers between 6 and 9 not including 6 or 9
C) all real numbers between 6 and 9, including 6 but not including 9
D) all real numbers between 6 and 9, including 9 but not including 6
E) all real numbers between 6 and 9, including 6 and 9

Question 12

Place the correct symbol (<, >, or =) between the pair of real numbers.

A)
B)
C)

Question 13

Write the following expression without absolute value symbols.

A) 15
B) -15
C) -5
D) 0
E) 5

Question 14

Approximate the numbers and place the correct symbol (< or >) between them.

A)
B)
C)
D)
E)

Question 15

Use absolute value notation to describe the situation. w is more than nine units from -2.

A) > 9
B) $\le$ 9
C) < 9
D) > 9
E) $\ge$ 9

Question 16

Use inequality notation to describe the set. u is positive

A) u $\le$ $\infty$
B) u < $\infty$
C) u $\le$ 0
D) u $\ge$ 0
E) u > 0

Question 17

Use inequality notation to describe the set. p is at least -12 but less than -9

A) -9 $\le$ p < -12
B) -9 < p $\le$ -12
C) -12 $\le$ p < -9
D) -12 $\le$ p $\le$ -9
E) -12 < p < -9

Question 18

Determine which numbers in the set are rational numbers.

A)
B)
C)
D)
E)

Question 19

Evaluate the expression.

A) 3
B) -3
C) 15
D) -15
E) 54

Question 20

Place the correct symbol (<, >, or =) between the pair of real numbers.

A)
B)
C)

Question 21

Evaluate the expression for the given value of x. x = 6

A) 0
B) -9
C) 9
D) 54
E) -54

Question 22

Evaluate the expression.

A) 3
B) -18
C) -729
D)
E)

Question 23

Evaluate the expression.

A)
B)
C)
D)
E) -13

Question 24

Evaluate the expression for the given value of x. x = -5

A)
B)
C)
D) -35
E) 35

Question 25

Evaluate the expression for the given value of x. x = 3

A) 12
B)
C)
D) 81
E) -81

Question 26

Identify the terms of the algebraic expression below.

A) and
B) and
C) and
D) and
E) and

Question 27

Evaluate the expression.

A)
B)
C)
D) 5
E) -5

Question 28

Evaluate when and

A) -800
B) 40
C) 2000
D) 1600
E) -200

Question 29

Evaluate when and

A) 2
B) 4
C) 784
D) 197
E) 392

Question 30

Simplify the expression.

A)
B)
C)
D)
E)

Question 31

Identify the rule of algebra illustrated by the statement. 7n + 2n = (7 + 2)n

A) associative property of addition
B) commutative property of addition
C) associative property of multiplication
D) commutative property of multiplication
E) distributive property

Question 32

Simplify the expression below.

A)
B)
C)
D)
E)

Question 33

Simplify the expression.

A)
B)
C)
D)
E)

Question 34

Evaluate the expression for the given value of x. expression: value: x = -6

A)
B)
C) 0
D) not possible since numerator is 0
E) not possible since denominator is 0

Question 35

Evaluate the expression for the given value of x. x = 4

A) 48
B)
C)
D) 768
E) -768

Question 36

Write the rational expression in simplest form.

A)
B)
C)
D)
E)

Question 37

Identify the rules of algebra illustrated from left to right by the following statement.

A) associative property of multiplication; multiplicative inverse property; multiplicative identity property
B) commutative property of multiplication; multiplicative inverse property; multiplicative identity property
C) associative property of multiplication; multiplicative identity property; multiplicative inverse property
D) commutative property of multiplication; multiplicative identity property; multiplicative inverse property
E) distributive property; multiplicative identity property; multiplicative inverse property

Question 38

The percent of people in a research study that have a particular health risk is 35.5%.The total number of people in the study is 12,392.How many people have the health risk?

A) 3594 people
B) 12,392 people
C) 16,791 people
D) 4399 people
E) 7993 people

Question 39

Evaluate the expression for the given value of x. expression: value: x = -4

A) 29
B) -115
C) 77
D) -94
E) 50

Question 40

Identify the rules of algebra illustrated from left to right by the following statement. (t - 9) + 9 = t + (-9 + 9) = t + 0 = t

A) commutative property of addition; additive inverse property; additive identity property
B) associative property of addition; additive inverse property; additive identity property
C) commutative property of addition; additive identity property; additive inverse property
D) associative property of addition; additive identity property; additive inverse property
E) distributive property; additive identity property; additive inverse property

Question 41

Write each number in the expression below in scientific notation.Perform the operation and write your answer in scientific notation.

A)
B)
C)
D)
E)

Question 42

In 1985, the movie The Satin Slipper was released and its running time was 410 minutes long. Assuming that this film's speed was 24 frames per second, approximate the total number of frames in the film. Express the answer in scientific notation rounding to two places after the decimal..

A) 9.84
B) 4.96
C) 5.90
D) 2.46
E) 1.64

Question 43

The average yearly cost of tuition, fees, and room and board at private four-year colleges in the United States was $21,294 for the academic year 1998/1999 and $27,461 for the academic year 2003/2004.Find the average yearly rate of inflation over this six-year period.Round to the nearest hundredth of a percent.

A) 4.15%
B) 4.50%
C) 4.33%
D) 4.99%
E) 5.16%

Question 44

The compound interest formula can be rewritten as Find the principal amount that could have been invested on the day you were born at 8.5% annual interest compounded monthly to make you a millionaire on your 21st birthday.

A) $211,070.25
B) $168,856.20
C) $242,730.79
D) $94,981.61
E) $126,642.15

Question 45

Perform the indicated operation below and write the answer in scientific notation.

A)
B)
C)
D)
E)

Question 46

Evaluate the expression without using a calculator.

A)
B)
C)
D) 16
E) -16

Question 47

Rationalize the denominator.Then simplify your answer.

A)
B)
C)
D)
E)

Question 48

Write the number in scientific notation. One milligram is about 0.015430 grain.

A) 0.1543 $\times$ 10^-1
B) 15.43 $\times$ 10^-3
C) 1.543 $\times$ 10^-2
D) 1.543 $\times$ 10^-3
E) 0.015430 $\times$ 10^-2

Question 49

Rewrite the expression below by rationalizing the denominator.Simplify your answer.

A)
B)
C)
D)
E)

Question 50

Evaluate the expression without using a calculator. 4 ^{-3 / 2}

A) -8
B) 4
C) -4
D)
E)

Question 51

Rewrite the expression with positive exponents and simplify.

A)
B)
C)
D)
E)

Question 52

Use a calculator to evaluate the expression.Write your answer in scientific notation. (Round values to three decimal places.)

A) 1.167 $\times$ 10¹²
B) 1.167 $\times$ 10¹³
C) 1.889 $\times$ 10¹¹
D) 1.889 $\times$ 10¹³
E) 1.889 $\times$ 10¹²

Question 53

Simplify the radical expression.

A)
B)
C)
D)
E)

Question 54

Rewrite the expression below with positive exponents and simplify.

A)
B)
C)
D)
E)

Question 55

Change the following number from scientific notation to decimal notation.

A) 0.195
B) 0.00195
C) 1.95
D) 19.5
E) 0.0195

Question 56

Write the number in decimal notation. One milligram equals approximately 3.5 $\times$ 10^-5 ounces.

A) 0.000035
B) 0.0035
C) 0.00035
D) -0.000035
E) 3.5

Question 57

Simplify the expression below.

A)
B)
C)
D)
E)

Question 58

Simplify the following radical expression.

A)
B)
C)
D)
E)

Question 59

Write the following number in scientific notation. 2,720,000

A)
B)
C)
D)
E)

Question 60

Rewrite the expression below by rationalizing the denominator.Simplify your answer.

A)
B)
C)
D)
E)

Question 61

The length L of the hypotenuse of a right triangle is where x and y are the lengths of the other two sides.Find the length of the hypotenuse when the other sides measure 1 unit and units.

A) 1 unit
B) units
C) units
D) units
E) units

Question 62

Identify the degree and leading coefficient of the polynomial. 5 - 6x² + 4x

A) degree: 3 leading coefficient: 4
B) degree: 2 leading coefficient: 6
C) degree: 3 leading coefficient: 6
D) degree: 2 leading coefficient: -6
E) degree: 2 leading coefficient: 5

Question 63

Perform the indicated operation below and simplify if possible by combining like terms.Write the result in standard form.

A)
B)
C)
D)
E)

Question 64

Perform the operation and write the result in standard form.

A)
B)
C)
D)
E)

Question 65

Use a calculator to approximate the number.(Round your answer to three decimal places.)

A) -0.178
B) 0.133
C) 0.015
D) 1.390
E) 2.435

Question 66

Simplify the expression below.

A)
B)
C)
D)
E)

Question 67

Find the special product. (-4x - 5)²

A) 16x² + 40x + 25
B) 16x² + 20x + 25
C) -8x² - 10
D) 16x² - 25
E) 16x² + 25

Question 68

Perform the operation and write the result in standard form.

A)
B)
C)
D)
E)

Question 69

Find the product below.

A)
B)
C)
D)
E)

Question 70

Write the polynomial in standard form.
9 + 7x² + 8x

Question 71

Simplify the expression below.

A)
B)
C)
D)
E)

Question 72

A stream of water moving at a rate of feet per second can carry particles of size inches.Find the size of the largest particle that can be carried by a stream flowing at the rate of feet per second.Round to the nearest thousandth of an inch.

A) 0.028 inch
B) 0.032 inch
C) 0.016 inch
D) 0.025 inch
E) 0.038 inch

Question 73

Find the special product. (3x - 9)(3x + 9)

A) 6x
B) 6x²
C) 9x² - 81
D) 9x² + 81
E) 9x² - 54x - 81

Question 74

Perform the operation and write the result in standard form.

A)
B)
C)
D)
E)

Question 75

Multiply. (-x - 6)(-2x - 8)

A) -3x - 14
B) -3x² - 14
C) 22x + 48
D) -3x² - 17x - 14
E) 2x² + 20x + 48

Question 76

Write the expression as a single radical.Then simplify your answer.

A)
B)
C)
D)
E)

Question 77

A wind chill temperature is a measure of how cold it feels outside.The wind chill temperature (in degrees Fahrenheit) is given by where is the actual temperature (in degrees Fahrenheit) and is the wind speed (in miles per hour).Find the wind chill temperature for the given conditions below. Actual temperature: wind speed: mph

A)
B)
C)
D)
E)

Question 78

Evaluate the following polynomial for the indicated value of the variable. , for

A) 9
B) 2
C) -3
D) -10
E) 14

Question 79

Use a calculator to approximate the number.(Round your answer to three decimal places.)

A) 2.924
B) 75.000
C) 5.000
D) 8.333
E) 28.000

Question 80

Reduce the index of the radical.

A)
B)
C)
D)
E)