Cap01

Name:

Chapter 1 Pretest Form A

Date:

Name the property illustrated in problems 1 and 2. 1. 4 ( x + y + 2 ) = 4 x + 4 y + 8

1. ____________________________

2. 8 + (−8) = 0

2. ____________________________

Insert either < or > between the two numbers to make a true statement. 3. 0

−8

4. −6

3. ____________________________

−2

4. ____________________________

List each set in roster form. 5. A = { x | − 1 < x < 1 and x ∈ I }

5. ____________________________

6. K = {x|x is a whole number between 3 and 4}

6. ____________________________

⎧ ⎩

1 5 2 9

Consider the set of numbers ⎨−3, 4, , , 0, 2, 8, −1.23,

99 ⎫ ⎬ . List the 100 ⎭

elements of the set that are: 7. whole numbers

7. ____________________________

8. integers

8. ____________________________

9. Let set A = {1, 2,3} and B = {4,5, 6} . Find A ∪ B and A ∩ B .

9. ____________________________

3 5

10. Evaluate: − −

5 9

10. ____________________________

⎛ 3⎞

11. Simplify: ⎜ − ⎟ ÷ − 8 ⎝ 4⎠

11. ____________________________

12. Convert 242,000,000 to scientific notation.

12. ____________________________

13. Simplify

3.12 × 106 and write the answer without exponents. 1.2 × 10− 2 ⎧

5 2

6 5

⎫

13. ____________________________

14. Illustrate the set x ⎨ x − < x < and x ∈ I ⎬ on the number line.

14.

15. Illustrate the set {x|x ≥ 5} on the number line.

15.

⎩

⎭

Evaluate the following expressions. 16. 32 − 6 ⋅ 9 + 4 ÷ 22 − 3 17.

16. ____________________________

8+ 4 ÷ 2⋅3+ 4 52 − 32 ⋅ 2 − 7

17. ____________________________

1

Chapter 1 Pretest Form A (cont.) 18. Simplify and write the answer without negative exponents: −1

6 x y

Name:

18. ____________________________

−1

19. Evaluate: (2 ⋅ 5) −1 + (3 ⋅ 4) −1

19. ____________________________

20. Simplify and write the answer without negative exponents.

20. ____________________________

⎛ − 3x y ⎞ ⎜ −1 5 ⎟ ⎝ x y ⎠ 3

−2

−3

2

Name:

Chapter 1 Pretest Form B 1. List A = {x | x is a whole number less than 6} in roster form.

Date:

1. ____________________________

Indicate whether each statement is true or false. 2. Every integer is a whole number.

2. ____________________________

3. The intersection of the set of rational numbers and the set of irrational numbers is the empty set.

3. ____________________________

4 ⎧ ⎫ Consider the set of numbers ⎨3, − 8, 0, 5, , − 1.6, 12 ⎬ . List the elements 7 ⎩ ⎭ of the set that are

4. rational numbers

4. ____________________________

5. whole numbers

5. ____________________________

Let A = {1, 3, 5, 7, 9} and B = {4, 5, 6, 7, 8} 6. Find A ∪ B .

6. ____________________________

7. Find A ∩ B .

7. ____________________________

8. Indicate the set on the number line. { x −3 < x ≤ 1}

8.

9. List from smallest to largest: 2, −4 , − 7 , −5, −5.4

9. ____________________________

Name each property illustrated. 10. 9( x + y ) = 9( y + x)

10. ____________________________

11. 7( xy ) = (7 x) y

11. ____________________________

Evaluate each expression. 12. 15 – (5 – 2)

12. ____________________________

13. 8 + 20 ÷ 4

13. ____________________________

14. 7 2 − 5(10 − 2)

14. ____________________________

15. Evaluate 7 xy − y 2 when x = –1 and y = –4.

15. ____________________________

3

Chapter 1 Pretest Form B (cont.)

Name:

Simplify each expression and write the answer without negative exponents. 16. 9−2 ⎛ 6 ⎞ 17. ⎜ −3 ⎟ ⎝y ⎠

18.

16. ____________________________ 2

17. ____________________________

3x4 y 2 21x −1 y 5

18. ____________________________

19. Convert 78,000,000 to scientific notation.

19. ____________________________

20. Simplify (5.1× 105 )(1.7 × 102 ) and write the number without exponents.

20. ____________________________

4

Mini-Lecture 1.1 Study Skills for Success in Mathematics, and Using a Calculator Learning Objectives: 1. 2. 3. 4. 5.

Have a positive attitude. Prepare for and attend class. Prepare for and take examinations. Find help. Learn to use a calculator.

Examples: 1. Maintain a Positive Attitude a) To succeed in this course, students must give it a fair chance. b) Mathematics must be worked at. c) Maturity and desire to learn have an effect on one’s ability to succeed in mathematics. d) In order to succeed, students must believe they can succeed. 2. Prepare for and Attend Class a) Preview the material b) Read the textbook c) Complete homework assignments d) Attend and participate in class e) Find a proper place to study f) Be organized to avoid wasting time 3. Prepare for and Take Exams a) Review previous homework, class notes, quizzes, etc. b) Study relevant formulas, definitions, and procedures. c) Read the Avoiding Common Errors boxes and Helpful Hint boxes. d) Complete the Chapter Review, Mid-Chapter Test and Chapter Practice Test. f) When taking the exam, read the directions and problems carefully. g) Pace yourself and use all available time. Attempt every problem. 4. Find Help a) Seek help right away when needed. Do not wait! b) Utilize the supplements that come with this textbook 5. Learn to Use a Calculator Teaching Notes: • Many developmental students have math anxiety and hesitate to ask questions. • Discuss any resources that are available on your campus where students can get help with mathematics (such as a math lab or a tutoring center). • Point out the student supplements that are available for this textbook. • Recommending a specific model of calculator to the students will help to insure that students have one that is appropriate.

5

Mini-Lecture 1.2 Sets and Other Basic Concepts Learning Objectives: 1. 2. 3. 4. 5. 6.

Identify sets Identify and use inequalities. Use set builder notation. Find the union and intersection of sets. Identify important sets of numbers Key vocabulary: variable, constant, algebraic expression, set, elements, roster form, empty set (or null set), set builder notation, union, intersection, real numbers, natural numbers (or counting numbers), whole numbers, integers, rational numbers, irrational numbers, subset

Examples: 1. Using roster form, write the set of numbers consisting of the natural numbers that are less than or equal to 6. 2. Insert either < or > between the two numbers to make a true statement. a) 2 5 b) 3 −7 c) −8

−3

3. a) List A = {x | x is a natural number greater than 4} in roster form. b) Write B = {1, 2, 3, 4, 5} using set builder notation. 4. For A = {0, 4, 8, 12} and B = {0, 2, 4, 6}, find each of the following: b) A ∩ B a) A ∪ B 5. Consider the set of numbers ⎧⎨−34, 7, − 9 , −8.5, −6, 4 5 , 0, 6, π , 25,127 ⎫⎬ . List the elements of 16

⎩

the set that are: a) natural numbers d) rational numbers

8

b) whole numbers e) irrational numbers

⎭

c) integers f) real numbers

Teaching Notes:

• Contrast the difference between expressions and equations. • Point out that {∅} is not the empty set. • Students often confuse the inequality symbols. Point out that the inequality symbol should always point towards the smaller number. • Emphasize to students that for a number to be classified as a counting number, whole number, integer, etc., it only needs to be able to be written in the proper form, but it does not have to be in that form. For example,

10 is a whole number because it can be written as 5. 2

• Point out to students that if a rational number is written in decimal form, it will either terminate or repeat. If an irrational number is written in decimal form, it will neither terminate nor repeat. Answers: 1) {1,2,3,4,5,6}; 2a) <; 2b) >; 2c) <; 3a) {5,6,7,…}; 3b) {x | x < 6 and x ∈ N} ;

{

} { } { 9 5 25,127 ⎫⎬ ; 5e) { 7 , π } ; 5f) ⎧⎨−34, 7 ,− ,−8.5,−6,4 ,0,6, π , 16 8 ⎭ ⎩

}

4a) {0,2,4,6,8,12}; 4b) {0,4}; 5a) 6, 25 ,127 ; 5b) 0,6, 25 ,127 ; 5c) −34, −6,0,6, 25 ,127 ; 5d) ⎧⎨−34,− ⎩

9 5 , − 8.5,−6,4 ,0,6, 16 8

6

25 ,127 ⎫⎬ ⎭

Mini-Lecture 1.3 Properties of and Operations with Real Numbers Learning Objectives: 1. 2. 3. 4. 5. 6. 7.

Evaluate absolute values. Add real numbers. Subtract real numbers. Multiply real numbers. Divide real numbers. Use the properties of real numbers. Key vocabulary: additive inverse (or opposites), double negative property, absolute value, like signs, unlike signs, multiplicative property of zero, commutative properties, associative properties, identity properties, additive identity element, multiplicative identity element, inverse properties, multiplicative inverse (or reciprocal), distributive property.

Examples: 1. Evaluate each absolute value expression. b) − −24 c) a) −12

d)

0

0.64

Insert <, >, or = between the pair of numbers to make a true statement. e)

−5

5

f) − −7

−3 g) −

1 4

h) −(−6)

0

− −6

For Examples 2 – 5, evaluate. 5 6

2. a) −4 + (−7)

b) 5 + (−8)

c) − +

3. a) 8 − 15

b) −10 − (−2)

c)

4. a) (−9)(−6)

b) −0.8 ( 0.9 )

c)

5. a)

−48 4

b)

−35 −7

⎛ 7⎞ ⎛ 9⎞ ⎜ − ⎟ ⋅⎜ − ⎟ = 1 ⎝ 9⎠ ⎝ 7⎠

d) −3.15 + (−6.34)

7 ⎛ 2⎞ −⎜− ⎟ 10 ⎝ 15 ⎠ ⎛ 5 ⎞⎛ 4 ⎞ ⎜− ⎟⎜ − ⎟ ⎝ 8 ⎠ ⎝ 15 ⎠ ⎛ 5 ⎞ ⎛ −10 ⎞ ⎜ ⎟ ÷⎜ ⎟ ⎝6⎠ ⎝ 9 ⎠

c)

6. Name the property illustrated. b) 6 ⋅ 7 = 7 ⋅ 6 a) ( x + 8) + 5 = x + (8 + 5) d) 3( x + 8) = 3x + 3 ⋅ 8 e) −4m + 4m = 0 g) 6 + 10 = 10 + 6 h) (−10) ⋅1 = −10 j)

8 15

k) −(−6) = 6

d) −3.7 − 8.6 d) (−3)(−5)(−6) d) 22.96 ÷ ( −2.8 ) c) 3 ⋅ (10 ⋅ 5) = (3 ⋅10) ⋅ 5 f) −9 + 0 = −9 i) 0 ⋅ (−9) = 0 l)

2 ⎛1 1 2 1 2 1 ⋅ ⎜ x − ⎞⎟ = ⋅ ⎛⎜ x ⎞⎟ − ⋅ ⎛⎜ ⎞⎟ 3 ⎝2 4⎠ 3 ⎝2 ⎠ 3 ⎝4⎠

Teaching Notes:

• Remind students that absolute value can be thought of as the number of units the number is from 0 on the number line. The absolute value cannot be negative because it is a distance. • Remind students to always change subtraction to addition by “adding the opposite.”

Answers: 1a) 12; 1b) −24; 1c) 0; 1d) 0.64; 1e) =; 1f) <; 1g) >; 1h) >; 2a) −11 ; 2b) −3 ; 2c) − 2d) −9.49; 3a) −7; 3b) −8; 3c)

5 6

; 3d) −12.3; 4a) 54; 4b) −0.72; 4c)

1 6

3 ; 10

; 4d) −90; 5a) −12 ;

5b) −5 ; 5c) −8.2 ; 6a) assoc. prop. of add.; 6b) comm. prop. of mult.; 6c) assoc. prop. of mult.; 6d) dist. prop.; 6e) inv. prop. of add.; 6f) id. prop. of add.; 6g) comm. prop. of add.; 6h) id. prop. of mult.; 6i) mult. prop. of zero; 6j) inv. prop. of mult.; 6k) dbl. neg. prop.; 6l) dist. prop. 7

Mini-Lecture 1.4 The Order of Operations Learning Objectives: 1. Evaluate exponential expressions. 2. Evaluate square and higher roots. 3. Evaluate expressions using the order of operations. 4. Evaluate expressions containing variables. 5. Evaluate expressions on a graphing calculator. 6. Key vocabulary: factors, exponential expression, base, exponent, radical sign, radicand, principle square root, index, order of operations, grouping symbols Examples: 1. Evaluate. a) (−8) 2

e) (−10)3

b) −82

c) (−5) 4

f) −103

1 g) ⎛⎜ − ⎞⎟ 2

d) −54

3

⎝

h) −32 + (−3) 2 − 23 + (−2)3

⎠

Evaluate i) x 2 , j) − x 2 , and k) (− x) 2 for x = −6 . 2. Evaluate. a)

100

b)

9 64

c)

16

g) k)

e)

3

64

f)

4

i)

3

1 1000

j)

− 3 0.027

0.25

d) − 81

5

243

h)

3

4

16 81

l)

5−

3. Evaluate.

(

1 32

)

b) −9 + 3 ⎡ −5 + 36 ÷ 22 ⎤ ⎣ ⎦

a) 9 + 3 ⋅ 23 − 15 c)

−8

4 + 5(5 − 2) 2 −12 + 54 ÷ 2 − 8

1 4

8÷ +6 4−7

d)

5 + (2 − 17) ÷ 3

4. Evaluate each expression for the given value of the variable or variables. a) 3 x 2 − 4 x + 8 when x =

1 3

b) x 2 − 5 xy + 6 y 2 when x = −2 and y = −3

5. Use a graphing calculator to evaluate each expression for the given value of the variable(s). b) 0.23x 2 − 5.4 xy + 6.1y 2 when x = 4 and y = 5 a) 0.35 x 2 − 2.6 x + 12 when x = 10 Teaching Notes:

• The acronym PEMDAS may mislead some students to believe that multiplication must always be completed before division and that addition must always completed before subtraction. Emphasize that this is incorrect. 1 8

Answers: 1a) 64; 1b) −64 ; 1c) 625; 1d) −625 ; 1e) −1000 ; 1f) −1000 ; 1g) − ;1h) −16 ; 1i) 36; 1i) −36 ; 1k) 36; 2a) 10; 2b) 2k)

2 3

3 8

; 2c) 0.5; 2d) −9 ; 2e) 4; 2f) 2; 2g) 3; 2h) −2 ; 2i)

1 2

1 ; 2j) 0.3; 10

; 2l) − ; 3a) 18; 3b) 3; 3c) 7; 3d) undefined; 4a) 7; 4b) 28; 5a) 21; 5b) 48.18

8

Mini-Lecture 1.5 Exponents Learning Objectives:

1. 2. 3. 4. 5. 6. 7.

Use the product rule for exponents. Use the quotient rule for exponents. Use the negative exponent rule. Use the zero exponent rule. Use the rule for raising a power to a power. Use the rule for raising a product to a power. Use the rule for raising a quotient to a power.

Examples:

1. Simplify. a) 34 ⋅ 37

b) x5 ⋅ x 2

c) a ⋅ a 3

2. Simplify. a)

48

n9

b)

45

c)

n3

y5 y9

3. Simplify. (Write each answer without negative exponents.) 5

8a 4 c 7

a) 5−2

b) 4 x −3

c)

e) 3−4 x 2 y −5

f) −2−4 m3n −8

g) 2−1 − 3−1

h) 3 ⋅ 2−3 + 5 ⋅ 3−2

b) 12 x 0

c) −80

d) −(2 x − 5)0

4. Simplify. a) 500

d)

y −6

b −2

5. Simplify (assume that the base is not 0). a)

( 32 )3

b)

( x3 )−5

c)

( 2−4 )2

b)

( 4x −3 y5 )

c)

⎛ 28m3 n −2 ⎞ ⎜ ⎟ ⎝ 14m −1n ⎠

d)

( x −5 )−4

6. Simplify. a)

( −3x6 )4

−2

7. Simplify. a)

⎛ 6 ⎞ ⎜ 7⎟ ⎝x ⎠

2

b)

⎛ −3a −7 ⎞ ⎜ 6 ⎟ ⎝ b ⎠

−4

5

−3

( 4 x −6 y5 ) d) −5 ( 2 x −4 y 7 )

Teaching Notes:

• Students often have difficulty mastering the rules for exponents. Stress to them the importance of neatly working one step at a time. Answers: 1a) 311 ; 1b) x7 ; 1c) a 4 ; 2a) 4 3 = 64 ; 2b) n6 ; 2c) y −4 ; 3a) 3d) 8a 4 b 2 c7 ; 3e) 5b)

1 x15

; 5c)

x2 81y 5

; 3f) −

m3 16n8

; 3g)

1 6

; 3h)

67 72

1 25

; 3b)

4 x

3

; 3c) 5y6 ;

; 4a) 1; 4b) 12; 4c) −1 ; 4d) −1 ; 5a) 729;

y 20 1 x6 36 a 28 b 24 32m 20 ; 5d) x 20 ; 6a) 81x 24 ; 6b) ; 7a) ; 7b) ; 7c) ; 7d) 256 81 16y10 x14 2 x2 n15

9

Mini-Lecture 1.6 Scientific Notation Learning Objectives:

1. 2. 3. 4.

Write numbers in scientific notation. Change numbers in scientific notation to decimal form. Use scientific notation in problem solving. Key vocabulary: scientific notation

Examples:

1. Express each number in scientific notation. a) 834,000 b) 0.000000923 c) 7,208,000,000 d) 0.000009804 2. Express each number without exponents. a) 5.6 ×108 b) 7.39 ×10−4 c) 2.07 × 104

d) 3.24 ×10−7

3. Perform the indicated operation. Express each result both in scientific notation and without exponents. b) (1.2 × 10−3 )( 9 × 10−1 ) a) (1.5 × 104 )( 3.4 × 102 ) c)

9.0 × 108 3.6 × 103

d)

5 × 10−9 8 ×10−3

Use scientific notation to solve each problem. e) A group of 50 coworkers pool their money to buy lottery tickets. The jackpot is $215,000,000. If they win, what will be each worker’s share of the jackpot? f) Light travels at a rate of 186,000 miles per second. How far does light travel in one hour (3600 seconds)? g) The diameter of a circular virus is 1×10−7 meters. Find the radius of the virus. h) The diameter of a circular virus is 1×10−7 meters. Find the circumference of the virus.

Teaching Notes:

• Be sure to point out to students that the results of computations involving scientific notation may not initially be in scientific notation.

Answers: 1a) 8.34 × 10 5 ; 1b) 9.23 × 10 −7 ; 1c) 7.208 × 10 9 ; 1d) 9.804 × 10 −6 ; 2a) 560,000,000; 2b) 0.000739; 2c) 20,700; 2d) 0.000000324; 3a) 5.1 × 106 or 5,100,000; 3b) 1.08 × 10 −3 or 0.00108; 3c) 2.5 × 10 5 or 25,000; 3d) 6.25 × 10 −7 or 0.000000625; 3e) $4,300,000 or $4.3 × 106 ; 3f) 669,600,000 miles or 6.696 × 10 8 miles; 3g) 5 × 10 −8 meters or 0.00000005 meters; 3h) 3.14 × 10 −7 meters or 0.000000314 meters

10

Name:

Additional Exercises 1.1

Date:

Instructor Information:

Name: ________________________________________________________________________________________ Office location: ________________________________________________________________________________ Office hours: __________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ Phone number: _________________________________________________________________________________ Email: _______________________________________________________________________________________

Classmate Information:

Obtain the names of at least two classmates whom you can contact for information or study questions. 1.

Name: ____________________________________________________________________________________ Phone number: _____________________________________________________________________________ Email address: _____________________________________________________________________________

2.

Name: ____________________________________________________________________________________ Phone number: _____________________________________________________________________________ Email address: _____________________________________________________________________________

Math Lab:

Location: _____________________________________________________________________________________ Hours: _______________________________________________________________________________________ Phone number: _________________________________________________________________________________

Tutoring Services:

Location: _____________________________________________________________________________________ Hours: _______________________________________________________________________________________ Phone number: _________________________________________________________________________________

Recommended Supplements:

_______________________________________________________________________________________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________

11

Name:

Additional Exercises 1.2

Date:

1. Describe {integers greater than 13} using the roster method.

1. ____________________________

2. Use braces to list the elements of the set of even natural numbers less than 8.

2. ____________________________

3. Use braces to list the elements of the set of even natural numbers less than 12.

3. ____________________________

4. Use set-builder notation to name the following set: the set of all real numbers less than or equal to 65

4. ____________________________

For Exercises 5 – 10, insert either < or > to make a true statement. 5. −10 6. 12

−7

5. ____________________________

−15

6. ____________________________

7. −2.5

3.6

7. ____________________________

8. −23

19

8. ____________________________

9. −

1 2

−

5 19

9. ____________________________

10. −

5 7

−

10 13

10. ____________________________

For Exercises 11 – 12, list each set in roster form. 11. {x | x is a counting number between 1 and 9}

11. ____________________________

12. {x | x is a natural number greater than 5}

12. ____________________________

For Exercises 13 – 14, write each set using set-builder notation. 13. {0, 1, 2, 3, …}

13. ____________________________

14. {2, 4, 6, 8, …}

14. ____________________________

For Exercises 15 – 18, find both A ∪ B and A ∩ B . Be sure to identify which is which. 15. A = {7, 8, 9, 10, 17} and B = {3, 7, 10, 12}

15. ____________________________

16. A = {7, 9, 11, 13, …} and B = {9, 11, 13, 15}

16. ____________________________

17. A = {e, h, i, k , m} and B = {e, i, m, o}

17. ____________________________

18. A = {6, 8, 9, 10, 17} and B = {4, 6, 10, 14}

18. ____________________________ ⎧ ⎩

For exercises 19 – 20, consider the set of numbers ⎨−20, −

12 ⎫ , −0.51, 0,1.75, π , 23,10⎬ . 7 ⎭

19. List the elements that are whole numbers.

19. ____________________________

20. List the elements that are rational numbers.

20. ____________________________

12

Name:

Additional Exercises 1.3

Date:

1. Evaluate: − −24 .

1. ____________________________

2. Insert <, >, or = between the pair of number to make a true statement. −(−32) −32

2. ____________________________

3. List from smallest to largest: −5 , −16 , 1, 10 .

3. ____________________________

4. List from largest to smallest: 6 , − 7 , − 5, 7 .

4. ____________________________

For Exercises 5 – 18, evaluate. 5. 5 + ( −10 )

5. ____________________________

6. 90 + ( −49 )

6. ____________________________

7. Subtract: −8 − ( −5 )

7. ____________________________

8. Evaluate the expression: 14 − 17 − 3

8. ____________________________

9. Find the difference: 10 − ( −1)

9. ____________________________

10. Simplify: −31 − ( −8 )

10. ____________________________

11. (−12)(−5)

11. ____________________________

12. Find the product: ( −5 )( 2 )( 7 )

12. ____________________________

⎛ −2 ⎞⎛ −3 ⎞ 13. Find the product: ⎜ ⎟⎜ ⎟ ⎝ 5 ⎠⎝ 5 ⎠

13. ____________________________

14. Multiply: 5.99 × 1.2

14. ____________________________

15. Find the quotient:

−152 −2

15. ____________________________

16. Find the quotient:

216 −6

16. ____________________________

17. Divide:

9 4 ÷ 4 5

17. ____________________________

⎛ 5 ⎞ ⎛ −10 ⎞ 18. Divide: ⎜ ⎟ ÷ ⎜ ⎟ ⎝8⎠ ⎝ 7 ⎠

18. ____________________________

For Exercises 19 – 20, name the property illustrated. 19. 3( x + 5) = 3 ⋅ x + 3 ⋅ 5

19. ____________________________

20. 8 + (2 + 4) = (8 + 2) + 4

20. ____________________________

13

Name:

Additional Exercises 1.4

Date:

For Exercises 1 – 15, evaluate each expression. 1. −32

1. ____________________________

( −5 )3

2. ____________________________

3. −5 + 9 ⋅ 42

3. ____________________________

4. −2 + 3 ⋅ 22

4. ____________________________

5.

169

5. ____________________________

6.

16 121

6. ____________________________

2.

7.

3

−27

7. ____________________________

8.

5

−243

8. ____________________________

⎡ 5 + ( −7 ) ⎤ ⎡12 + ( −4 ) ⎤ 9. ⎢ ⎥⎢ ⎥ ⎣ −6 − 2 ⎦ ⎣ 5 − 3 ⎦

9. ____________________________

10. 42 + 28 ÷ 7 − 2 ⋅ 3 11. − ⎡⎣9 − ( −3 − 2 ) ⎤⎦ 12.

10. ____________________________

2

11. ____________________________

−2 6 − 27 ÷ 3 + 3

12. ____________________________

4 + 64 ÷ 42 2 3

8 ÷ + 4 8 − 10

13.

13. ____________________________

5 + 3( 7 − 4)

14. −7 ⎡⎣ 2 + ( 3 − 45 ÷ 5 ) ⎤⎦

2

14. ____________________________

15. Evaluate: (−4) 2 − 32 + 36 + (−4)3

15. ____________________________

16. Evaluate: − x 2 when x = −12 .

16. ____________________________

17. Evaluate ( 4c + 3d ) when c = −1 and d = 4 .

17. ____________________________

18. Evaluate − x 2 + 5 xy + y 2 when x = 2 and y = 3.

18. ____________________________

19. Evaluate 2 y 2 ( x + y ) when x = 6 and y = 5.

19. ____________________________

20. Evaluate ( x − 5 ) + 7 xy 2 − 5 when x = 4 and y = −4 .

20. ____________________________

2

2

14

Name:

Additional Exercises 1.5

Date:

For Exercises 1 – 20, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 1.

( 9 x4 ) (8x )

1. ____________________________

2. 77 ⋅ 75 3.

4.

5.

6.

7.

8.

9.

10.

11.

2. ____________________________

( 6 x3 y3 )( 6 x 2 y 4 )

3. ____________________________

6 x6 y3

4. ____________________________

−2 x 2 y 7

6 x6

5. ____________________________

2 x3 a10

6. ____________________________

a4 p 2 q5 r 4 − pqr

7. ____________________________

10 x3

8. ____________________________

5 x7 3 x 2 y −2

9. ____________________________

z2 f −2 g −6

10. ____________________________

h −1 u −2 x − 5

11. ____________________________

y −4

12. 8 x 0 − 3 y 0

12. ____________________________

13. 4−1 + 6−1

13. ____________________________

⎛ −7 a 2 b 2 c 0 14. ⎜⎜ 4 6 8 ⎝ 3a b c

⎞ ⎟⎟ ⎠

⎛ −3a 2 b 2 c 0 15. ⎜⎜ 4 5 8 ⎝ 5a b c

⎞ ⎟⎟ ⎠

16.

( 2cd )

2 3

−5

14. ____________________________

−5

15. ____________________________

( cd )3

16. ____________________________

15

Additional Exercises 1.5 (cont.) ⎛ 5x4 y 17. ⎜⎜ 4 ⎝ 20 xy

⎞ ⎟⎟ ⎠

3

17. ____________________________

18.

( −3u

19.

(4 x y ) (4 x y )

2

Name:

p 4t 3

)

3

18. ____________________________

3 −3 2 −3

19. ____________________________

4 3 5 −4

⎛ 3x 2 y 4 20. ⎜⎜ 4 ⎝ −2 x

⎞ ⎟⎟ ⎠

2

20. ____________________________

16

Name:

Additional Exercises 1.6

Date:

For Exercises 1 – 7, express each number in scientific notation. 1. 8,400,000

1. ____________________________

2. 0.00048

2. ____________________________

3. 7900

3. ____________________________

4. 0.000051

4. ____________________________

5. 204,000,000,000

5. ____________________________

6. 17,200,000

6. ____________________________

7. 0.00921

7. ____________________________

For Exercises 8 – 14, express each number without exponents. 8. 7.94 × 108

8. ____________________________

9. 6.2 × 10−4

9. ____________________________

10. 3.14 × 10−2

10. ____________________________

11. 2.60 × 109

11. ____________________________

12. 8.54 × 108

12. ____________________________

13. 1.07 × 101

13. ____________________________

14. 8.09 × 10−5

14. ____________________________

For Exercises 15 – 18, perform the indicated operation. Express result both in scientific notation and without exponent. 15.

(3.2 ×10 )( 9.0 ×10 )

15. ____________________________

16.

( 2.9 ×10 )( 4.5 ×10 )

16. ____________________________

17.

18.

3

19

−5

−4

8 × 10−5

17. ____________________________

4 × 10−9 1.44 × 106

18. ____________________________

3.2 × 108

19. Divide by first converting each number to scientific notation form. 4900 Write the answer in scientific notation form. 0.07

19. ____________________________

20. Subtract: 9.67 × 1015 − 2.25 × 1014

20. ____________________________

17

Name:

Chapter 1 Test Form A

Date:

For problems 1 – 2, answer true or false. 1. Every natural number is a whole number.

1. ____________________________

2. The set of natural numbers is a finite set.

2. ____________________________

For problems 3 – 4, insert <, >, or = to make a true statement. 3. −21 4. − −6

−25

3. ____________________________

−(−3)

4. ____________________________

For problems 5 – 6, list each set in roster form. 5. A = {x | x is a whole number less than 5}

5. ____________________________

6. B = {x | x is an integer greater than or equal to −2 }

6. ____________________________

⎧ ⎩

⎫ ⎭

1 4

For problems 7 – 8, consider the set ⎨−4.2, −3, 0, , 5, π , 6, 7.1⎬ .

7. List the elements of the set that are irrational numbers.

7. ____________________________

8. List the elements of the set that are integers.

8. ____________________________

For problems 9 – 10, find A ∪ B and A ∩ B . 9. A = {2, 4, 6} , B = {2, 4, 6,8,11}

9. ____________________________

10. A = {0, 2, 4, 6,8} , B = {0,3, 6,9}

10. ____________________________

For problems 11 – 16, evaluate.

11.

−5 −1 ÷ 6 2

11. ____________________________

1 ⎛ 1⎞ 12. − + ⎜ − ⎟ 8 ⎝ 16 ⎠

12. ____________________________

13. (–2.1)(–7.8)(–9.1)

13. ____________________________

18

Chapter 1 Test Form A (cont.) ⎛3⎞ 14. − ⎜ ⎟ ⎝5⎠

Name:

4

14. ____________________________

4 − ( 2 + 3) − 8 2

15.

15. ____________________________

4 ( 3 − 2 ) − 32

2 1 16. − ⎡⎣8 − − 6 ÷ 3 − 4 ⎤⎦ 4

17. Evaluate

16. ____________________________

− b + b 2 − 4ac when a = 6 , b = −11 , and c = 3 . 2a

17. ____________________________

For problems 18 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 18.

(2x

−3

)(

y− 4 6x− 4 y7

)

18. ____________________________

19. 5−1 + 2−1 ⎛ 4b ⎞ 20. ⎜ ⎟ ⎝ 3 ⎠

19. ____________________________

−2

⎛ 6 x2 y ⎞ 21. ⎜ ⎟ ⎝ 3 xz ⎠

20. ____________________________

−3

21. ____________________________

22. Express 0.031 in scientific notation.

23. Express

22. ____________________________

6.75 × 10− 3 without using exponents. 2.5 × 102

23. ____________________________

For problems 24 – 25, simplify and express each answer in scientific notation. 24. (0.03)(0.0005)

24. ____________________________

560, 000 0.0008

25. ____________________________

25.

19

Name:

Chapter 1 Test Form B

Date:

For problems 1 – 2, answer true or false. 1. Every whole number is a natural number.

1. ____________________________

2. The set of integers between π and 4 is the null set.

2. ____________________________

For problems 3 – 4, insert <, >, or = to make a true statement. 3. −19

4.

−22

−17

3. ____________________________

−(−25)

4. ____________________________

For problems 5 – 6, list each set in roster form. 5. H = { l | l is a whole number multiple of 7}

5. ____________________________

6. B = {x | x is a natural number less than 8}

6. ____________________________

⎧ ⎩

⎫ ⎭

1 4

For problems 7 – 8, consider the set ⎨−4.2, −3, 0, , 5, π , 6, 7.1⎬ .

7. List the elements of the set that are rational numbers.

7. ____________________________

8. List the elements of the set that are whole numbers.

8. ____________________________

For problems 9 – 10, find A ∪ B and A ∩ B . 9. A = {−1, 0,1, e, i, π } , B = {−1, 0,1}

9. ____________________________

10. Let A = {1, 2, 4,8,16} , B = {2, 4, 6,8,10}

10. ____________________________

For problems 11 – 16, evaluate.

11.

−

1 −3 ⋅ 2 4

11. ____________________________

⎛ 2 ⎞⎛ 5 ⎞ 12. 3 ⎜ − ⎟ ⎜ − ⎟ ⎝ 3 ⎠⎝ 2 ⎠

12. ____________________________

⎛ 1⎞ 13. − 4 ÷ ⎜ − ⎟ ⎝ 4⎠

13. ____________________________

20

Chapter 1 Test Form B (cont.) 14. (0.3) 2

15.

16.

Name: 14. ____________________________

8 − ⎡⎣ 4 − (3 − 1) 2 ⎤⎦

15. ____________________________

5 − (−3) 2 + 4 ÷ 2 2 2 ⎡3 27 − − 9 + 5 − 32 ⎤⎦ ⎣ 5

− b − b 2 − 4ac

17. Evaluate

2a

16. ____________________________

when a = 2, b = 1, and c = −10.

17. ____________________________

For problems 18 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 18.

( − 3 p )( − p ) −2

3

18. ____________________________

19. 4− 2 + 8−1

19. ____________________________

20.

( 4x 2 y 3 )

20. ____________________________

21.

( 3x− 4 y 2 ) 3 ( 2 x3 y 5 )

−3

3

21. ____________________________

22. Express 0.000000718 in scientific notation.

22. ____________________________

23. Express ( 6.7 × 10− 3 )( 4.1 × 105 ) without using exponents.

23. ____________________________

For problems 24 – 25, simplify and express each answer in scientific notation. 24. (2500)(7000)

24. ____________________________

0.00046 23, 000

25. ____________________________

25.

21

Name:

Chapter 1 Test Form C

Date:

For problems 1 – 2, answer true or false. 1. Every real number is a rational number.

1. ____________________________

2. Every integer is a rational number.

2. ____________________________

For problems 3 – 4, insert <, >, or = to make a true statement. 3. −

4.

5 8

−4

2 3

3. ____________________________

−(−6)

4. ____________________________

−

For problems 5 – 6, list each set in roster form. 5. A = { x x is an odd integer between –3 and 5}

5. ____________________________

6. B = { x −2 < x < 7 and x ∈ W }

6. ____________________________

1 4⎫ ⎧ For problems 7 – 8, consider the set ⎨−3.76, − 2, 0, , 71, − 8, − ⎬ . 2 5⎭ ⎩

7. List the elements of the set that are real numbers.

7. ____________________________

8. List the elements of the set that are natural numbers.

8. ____________________________

For questions 9 – 10, find A ∪ B and A ∩ B . 9. A = {−3, − 1, 1, 3, 5} , B = {1, 3, 5, 7, 9}

9. ____________________________

10. A = {2, 4, 6, 8, …} , B = {… , − 3, − 2, − 1, 0, 1, 2, 3, …}

10. ____________________________

11. Indicate on the number line: { x −2.14 ≤ x < 3}

11.

12. List from smallest to largest: −0.9 , − 0.7 , − 0.6 .

12. ____________________________

For problems 13 – 14, name the property illustrated. 13. a + b = b + a

13. ____________________________

14. a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c

14. ____________________________

22

Chapter 1 Test Form C (cont.)

Name:

For problems 15 – 19, evaluate.

15.

8 2 ÷− 3 15

15. ____________________________

16. − ( 2 − −7 ) + ( −5 ⋅ −8 )

17.

18.

19.

( −1)

0

+ ( −2 ) − ( 3 ) 3

16. ____________________________

2

17. ____________________________

3 ( 42 ) + 2 16

18. ____________________________

− 81 + 10 ÷ 2 3 − 8 + 4(3 − 8) 4−6÷

19. ____________________________

2 3

For problems 20 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero.

20.

(−x ) ( x ) 2 3

−3 3

⎛ 2 xy 3 ⎞ 21. ⎜ −2 2 ⎟ ⎝ 3x y ⎠

20. ____________________________

2

21. ____________________________

22. Convert 613,000 to scientific notation.

(

)(

22. ____________________________

)

23. Simplify 1.2 × 10−3 2 × 10−7 and express the answer without

23. ____________________________

using exponents. 2 24. Evaluate − x 2 + 7 when x = 6. 3

24. ____________________________

25. Evaluate 2 x 2 − 3 xy − y 2 when x = −4 and y = 2.

25. ____________________________

23

Name:

Chapter 1 Test Form D

Date:

For problems 1 – 2, answer true or false. 1. The union of the set of whole numbers and {0} is the set of natural numbers.

1. ____________________________

2. Every integer is a whole number.

2. ____________________________

For problems 3 – 4, insert <, >, or = to make a true statement. 3. −258

−256

3. ____________________________

4. − −9

−9

4. ____________________________

For problems 5 – 6, list each set in roster form. 5. C = { x x is an integer between − 2.3 and 4.1}

5. ____________________________

6. D = { x x is a natural number between 1 and 2}

6. ____________________________

{

}

For problems 7 – 8, consider the set −4.24,8.37, 7, −4, 0, 6, − 13 . 7. List the elements of the set that are integers.

7. ____________________________

8. List the elements of the set that are irrational numbers.

8. ____________________________

For problems 9 – 10, find A ∪ B and A ∩ B . 9. A = {3, 4, 6, 9} , B = {1, 4, 5, 8}

9. ____________________________

10. A = {0, 1, 2, 3, 4} , B = {3, 4, 5, 6, 7}

10. ____________________________

⎧ 36 ⎫ 11. Indicate on the number line: ⎨ x x < and x ∈ W ⎬ 5 ⎩ ⎭

11.

12. List from smallest to largest: −5.24 , − 5.27, − −5.31 .

12. ____________________________

For problems 13 – 14, name the property illustrated. 13. ab = ba

13. ____________________________

14. a + (b + c) = (a + b) + c

14. ____________________________

24

Chapter 1 Test Form D (cont.)

Name:

For problems 15 – 19, evaluate. 15.

( −7 )( −4 )( 2 )( −1)

15. ____________________________

16.

( −11 + −5 ) − ( 7 ⋅ −8 )

16. ____________________________

3

⎛1⎞ ⎛ 1⎞ 17. ⎜ ⎟ − ⎜ − ⎟ ⎝ 2⎠ ⎝ 3⎠

18.

19.

0

17. ____________________________

−4 25 + 23 ( 5 )

18. ____________________________

−3 ( −5 ) ÷ 9

11 − 12 + 3 ( 4 − 7 )

19. ____________________________

2(−2) − (−4)

For problems 20 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero.

20.

( xx x ) 2 3

4

⎛ 2 x −2 y ⎞ 21. ⎜ −3 ⎟ ⎝ xy ⎠

20. ____________________________

3

21. ____________________________

22. Convert 0.0000053 to scientific notation.

22. ____________________________

23. Simplify

7.2 × 106 and express the answer without using exponents. 1.2 × 104

23. ____________________________

24. Evaluate

3 2 x − 10 when x = 8. 4

24. ____________________________

25. Evaluate 3x 2 + 7 xy + y 2 when x = 4 and y = −2.

25. ____________________________

25

Name:

Chapter 1 Test Form E

Date:

For problems 1 – 2, answer true or false. 1. Every irrational number is a real number.

1. ____________________________

2. The intersection of the set of integers and the set of irrational numbers 2. ____________________________ is the set of rational numbers.

For problems 3 – 4, insert <, >, or = to make a true statement. 3. −27

4.

−12

−25

3. ____________________________

−(−12)

4. ____________________________

For problems 5 – 6, list each set in roster form. 5. E = { x x is an odd integer greater than –7 and less than or equal to 0}

5. ____________________________

6. F = { x −2.3 < x < 5.2 and x ∈ W }

6. ____________________________

⎧2 1 ⎫ For problems 7 – 8, consider the set ⎨ , , 0, − 8, 12, − 5, 3, 2.15⎬ . ⎩7 5 ⎭

7. List the elements of the set that are rational numbers.

7. ____________________________

8. List the elements of the set that are whole numbers.

8. ____________________________

For problems 9 – 10, find A ∪ B and A ∩ B . 9. A = {0, 2, 4, 6,...} , B = {1, 3, 5, 7,...}

9. ____________________________

10. A = { –7, – 4, – 1, 2, 5} , B = { –7, − 5, − 3, − 1, 1, 3, 5, 7}

10. ____________________________

⎧ 16 ⎫ 11. Indicate on the number line: ⎨ x x ≤ and x ∈ N ⎬ 3 ⎩ ⎭

11.

12. List from smallest to largest: 4.6, − 4.2 , − −4.7 .

12. ____________________________

For problems 13 – 14, name the property illustrated. 13.

( ab ) c = a ( bc )

13. ____________________________

14. a ⋅1 = 1 ⋅ a = a

14. ____________________________

26

Chapter 1 Test Form E (cont.)

Name:

For problems 15 – 19, evaluate. 8 −4 15. − ÷ 3 15

15. ____________________________

16.

( −8 ⋅ 2 ) − ( 3 − 6 )

17.

( −2 ) + ( −3)

18.

19.

3

2

+ ( −4 )

16. ____________________________ 0

17. ____________________________

4 ( −3) + 5.2 − 32

18. ____________________________

−3 ⋅ ( −3) − 92 3

−2(3)2 + 7(−2) 5−6÷

19. ____________________________

2 3

For problems 20 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero.

20.

(−x ) ( x ) 2

3

⎛ x10 x −8 ⎞ 21. ⎜ 5 −2 ⎟ ⎝x x ⎠

−2

3

20. ____________________________

−1

21. ____________________________

22. Convert 8,630,000 to scientific notation.

(

)(

23. Simplify −1.5 × 10−3 2 × 10−5

)

22. ____________________________

and express the answer without

23. ____________________________

using exponents. A laser printer is purchased in 2007 for $750, and its value depreciates each year after its purchase. The value of the printer, in dollars, can be approximated by using Value = 750 − 125x . Substitute 1 for x to find the value of the printer in 2008, substitute 2 for x to find the value in 2009, and so on. 24. Find the approximate value of the laser printer in 2010.

24. ____________________________

25. Find the approximate value of the laser printer in 2013.

25. ____________________________

27

Name:

Chapter 1 Test Form F

Date:

For problems 1 – 2, answer true or false. 1. Every integer is a rational number.

1. ____________________________

2. The intersection of the set of rational numbers and the set of irrational numbers is the empty set.

2. ____________________________

For problems 3 – 4, insert <, >, or = to make a true statement. 3. −127 4. − −16

−129

3. ____________________________

−(−16)

4. ____________________________

For problems 5 – 6, list each set in roster form. 5. A = {x | x is an even integer between –5 and 7}

5. ____________________________

6. B = { x x < 5 and x ∈ W }

6. ____________________________

−4 5 ⎧ ⎫ For problems 7 – 8, consider the set ⎨3.147, − 2, , 0, , 2, − 3, 8⎬ . 5 3 ⎩ ⎭

7. List the elements of the set that are rational numbers.

7. ____________________________

8. List the elements of the set that are natural numbers.

8. ____________________________

For problems 9 – 10, find A ∪ B and A ∩ B . 9. A = {0, 2, 4, 6, 8} , B = {1, 3, 5, 7, 9}

9. ____________________________

10. A = { –3, –2, –1, 0, 1} , B = {0, 1, 2, 3}

10. ____________________________

20 ⎧ ⎫ and x ∈ N ⎬ 11. Indicate on the number line: ⎨ x x < 3 ⎩ ⎭

11.

12. List from smallest to largest: −6.14, − 6.08 , − −6.37 .

12. ____________________________

For problems 13 – 14, name the property illustrated. 13. a(b + c) = ab + ac

13. ____________________________

14. a + 0 = 0 + a = a

14. ____________________________

28

Chapter 1 Test Form F (cont.)

Name:

For problems 15 – 19, evaluate. 15. (−4)(7)(−3)

15. ____________________________

[ −7 + (−5)] ÷ (2 − 4)

16. ____________________________

17. (−2)3 − (5) 2 + (−9) 2

17. ____________________________

16.

18.

19.

52 − 3(4) − 7 2

18. ____________________________

2(−7) + 121 8 + (−3) − 2 ( 9 + −3 ) 2(3) 2 + 1

19. ____________________________

For problems 20 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero.

20.

( x3 )2 ( x 4 )−2

20. ____________________________

21.

( 2 x −3 y −1 ) 2 ( 4 xy −2 )

21. ____________________________

5

22. Convert 0.0000074 to scientific notation.

23. Simplify

22. ____________________________

8.1× 109 and express the answer without using exponents. 3 × 105

23. ____________________________

An automobile purchased in 2006 for $25,000 depreciates in value every year. The approximate resale value of the vehicle, in dollars, can be found using Resale value = 25, 000 − 2100x . Substitute 1 for x to find the vehicle’s resale value in 2007, substitute 2 for x to find its resale value in 2008, and so on. 24. Find the approximate resale value of the vehicle in 2010.

24. ____________________________

25. Find the approximate resale value of the vehicle in 2013.

25. ____________________________

29

Name:

Chapter 1 Test Form G

Date:

For problems 1 – 2, indicate which answer makes a true statement. 1. The union of the set of natural numbers and {0} is (a) the set of whole numbers (c) {0}

(b) the set of natural numbers (d) the empty set

2. Every integer is a(n) (a) natural number

(c) rational number

(b) whole number

(d) irrational number

For problems 3 – 4, list each set in roster form. 3. C = { x x > 7 and x ∈ N } (a) C = {7, 8, 9, …}

(b)

C = {8, 9, 10, …}

(c) C = {1, 2, 3, 4, 5, 6}

(d) C = {1, 2, 3, 4, 5, 6, 7}

4. D = { x x is an odd integer} (a) D = {…,, –5, –3, –1} (c) D = {…, –5, –3, –1, 0, 1, 3, 5, …}

(b) D = {1, 2, 3, 5, …} (d) D = {…, –5, –3, –1, 1, 3, 5,…}

1 6⎫ ⎧ For problems 5 – 6, consider the set ⎨−4, −2.1, 0, − , 6, 3.2, 5, ⎬ . 2 7⎭ ⎩

5. List the elements of the set that are rational numbers 1 6 (a) − , 2 7 (c)

6

6. List the elements of the set that are whole numbers (a) 0, 5

1 6 (b) −2.1, − ,3.2, 2 7 1 6 (d) −4, −2.1, 0, − , 3.2, 5, 2 7

(b) −4, 0, 5 1 6 (d) −4, −2.1, 0, − , 6, 3.2, 5, 2 7

(c) −4, −2.1, 0, 3.2, 5

For problems 7 and 8, consider the sets A = {−3, 0, 2} and B = {0, 1, 2, 3} . 7. Find A ∪ B . (a) {0, 2}

(b) {–3, 0, 2}

(c) {0, 1, 2, 3}

(d) {–3, 0, 1, 2, 3}

8. Find A ∩ B . (a) {0, 2}

(b) {–3, 0, 2}

(c) {0, 1, 2, 3}

(d) {–3, 0, 1, 2, 3}

For problems 9 – 10, identify which set is illustrated by the number line: 9.

—2 —1

(a) (c) 10.

0

1

(c)

3

4

5

6

{ x −2 < x ≤ 5 and x ∈ I } { x −2 < x ≤ 5 and x ∈ R}

—4 —3 —2 —1

(a)

2

0

1

2

3

(b) (d)

{ x −2 ≤ x < 5 and x ∈ I } { x − 2 ≤ x < 5 and x ∈ R}

4

{ x −2 < x < 3 and x ∈ I } { x −1 < x < 2 and x ∈ I }

(b) (d)

30

{ x −2 < x < 3 and x ∈ W } { x −1 < x < 2 and x ∈ W }

Chapter 1 Test Form G (cont.)

Name:

For problems 11 – 12, list from smallest to largest: 11.

12.

−3 −3 −3 , ,− 4 5 2 −3 −3 −3 , ,− (a) 4 5 2 −4 −5 −2 , ,− 3 3 3 −2 −4 −5 , , (a) − 3 3 3

(b) −

−3 −3 −3 , , 2 4 5

(c)

−3 −3 −3 , ,− 5 4 2

(d)

−3 −3 −3 ,− , 4 2 5

(b) −

−2 −5 −4 , , 3 3 3

(c)

−4 −2 −5 ,− , 3 3 3

(d)

−5 −2 −4 ,− , 3 3 3

For problems 13 – 14, name the property illustrated. 1 1 = ⋅a =1 a a (a) commutative

13. a ⋅

(b) associative

(c) identity

(d) inverse

(b) associative

(c) identity

(d) double negative

14. − ( −3) = 3 (a) commutative

For problems 15 – 19, evaluate. 12 ÷ −4 5 −48 (a) 5

15. −

(b)

−3 5

(c)

3 5

(d)

48 5

16. 8 ⋅ −4 − 3 ( 7 − 2 ) (a) –59 3

(b) –47 2

⎛ −1 ⎞ ⎛ −2 ⎞ ⎛ 5 ⎞ 17. ⎜ ⎟ + ⎜ ⎟ − ⎜ ⎟ ⎝ 3 ⎠ ⎝ 3 ⎠ ⎝ 3⎠ −64 (a) 27

18.

(d) 17

2

(b)

−22 27

(c)

−22 9

(d)

(b)

−38 31

(c)

−34 31

(d) 2

62 27

7 ( −2 ) − 64 ( 32 − 3) 1 − 5 ( −6 )

(a) –2

19.

(c) 5

5 − −9 + 8 ( −2 − 3) −11 − 8 (a) –4

(b) –2

(c) 2

31

(d) 4

Chapter 1 Test Form G (cont.)

Name:

For problems 20 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 20.

(x

−3

(a)

y2

)

3

y5 x6

(b)

y6 x9

(c) y 5 x 6

(d) y 5

(b)

1 x

(c) x

(d) x 7

(c) 3.74 × 108

(d) 3.74 × 10−8

−1

⎛ x −3 ⎞ 21. ⎜ −4 ⎟ ⎝x ⎠ 1 (a) 7 x

22. Convert 374,000,000 to scientific notation. (a) 37.4 × 107 (b) 37.4 × 10−7

(

)(

)

23. Simplify 4 × 10−4 1.2 × 10−3 and write the number as a decimal number. (a) 0.000048

(b) 0.0000048

(c) 0.00000048

(d) 0.000000048

During the 1990’s, the value of the homes in a particular neighborhood were increasing at a phenomenal rate. One such home was purchased in 1990 for $120,000, and its value could be approximated by using Value = 120, 000 + 4500x . Substitute 1 for x to find the value of the home in 1991, substitute 2 for x to find the value in 1992, and so on. 24. Find the approximate value of the home in 1996. (a) $142,500 (b) $156,000

(c) $151,500

(d) $147,000

25. Find the approximate value of the home in 2000. (a) $160,500 (b) $165,000

(c) $169,500

(d) $174,000

32

Name:

Chapter 1 Test Form H

Date:

For problems 1 – 2, indicate which answer makes a true statement. 1. The set of integers contains the set of (a) real numbers (b) whole numbers

(c) rational numbers

(d) irrational numbers

2. The union of the set of rational numbers and the set of irrational numbers is (a) the set of whole numbers (b) the null set (c) {0} (d) the set of real numbers

For problems 3 – 4, list each set in roster form. 3. H = { x x is an integer multiple of 3} (a) H = {…, –9, –6, –3, 0, 3, 6, 9, …} (c) H = {0, 3, 6, 9, …}

(b) H = {…, –9, –6, –3, 3, 6, 9, …} (d) H = {3, 6, 9, …}

4. J = { x x < 7 and x is an odd natural number} (a) J = {0, 1, 3, 5}

(b) J = {0, 1, 3, 5, 7}

(c) J = {1, 3, 5}

(d) J = {1, 3, 5, 7}

3 6⎫ ⎧ For problems 5 – 6, consider the set ⎨−92, −4.77, , 0, 5, − 17, − ⎬ . 20 7 ⎩ ⎭

5. List the elements of the set that are irrational numbers. (a) 5, − 17 3 −6 , 0, (c) −92, −4.77, 20 7 6. List the elements of the set that are integers. 3 ,0 (a) –92, 0 (b) 20

5

(b)

(d) −92, −4.77,

(c) 0

3 −6 , 0, 5, − 17, 20 7

(d) none

For problems 7 and 8, consider the sets A = {1, 3, 5} and B = {0, 1, 2, 3, 4} . 7. Find A ∪ B . (a) {1, 2, 3, 4, 5}

(b) {0, 1, 2, 3, 4, 5}

(c) {1, 3, 5}

(d) {1, 3}

8. Find A ∩ B . (a) {1, 2, 3, 4, 5}

(b) {0, 1, 2, 3, 4, 5}

(c) {1, 3, 5}

(d) {1, 3}

For problems 9 – 10, identify which set is illustrated by the number line: 9.

—4 —3 —2 —1

(a)

10.

(c)

1

2

3

{ x x < 4 and x ∈ W }

—4 —3 —2 —1

(a)

0

0

1

2

4

(b)

3

{ x x < 4 and x ∈ N }

⎧ 17 ⎫ ⎧ 17 ⎫ and x ∈ W ⎬ (d) ⎨ x x < and x ∈ N ⎬ (c) ⎨ x x < 4 4 ⎩ ⎭ ⎩ ⎭

4

{ x −2 < x ≤ 2 and x ∈ I } { x −2 < x ≤ 2 and x ∈ R}

(b) (d)

33

{ x −2 ≤ x < 2 and x ∈ I } { x −2 ≤ x < 2 and x ∈ R}

Chapter 1 Test Form H (cont.)

Name:

For problems 11 – 12, list from smallest to largest: 11. 2, −3 , − −2 (a) − −2 , 2, −3

(b) − −2 , −3 , 2

(c)

−3 , − −2 , 2

(d) −3 , 2, − −2

(b) −1 , − −1 , 2

(c) −2, −1 , − −1

(d) −2, − −1 , −1

(b) commutative

(c) distributive

(d) identity

(b) commutative

(c) inverse

(d) identity

12. − −1 , −1 , − 2 (a) − −1 , −1 , − 2

For problems 13 – 14, name the property illustrated. 13. 2 ( x + y ) = 2 x + 2 y (a) associative 14.

( −2 ) ⋅ 1 = 1 ⋅ ( − 2 ) = − 2 (a) associative

For problems 15 – 16, evaluate. 15.

16.

−6 ÷ −3 25 −18 (a) 25

(b)

(c)

−2 25

(d)

2 25

( −7 + 4 ) − 8 ( 3 ⋅ − 6 ) (a) –147

17.

−6 75

( −8)

2

− ( −7 ) − ( −3) 2

(a) –140

(b) –133

(c) 141

(d) 155

(b) –86

(c) –12

(d) 42

(b) –1

(c) 1

(d) 5

(b) –2

(c) 2

(d) 4

3

4 ( −3) − 36 2

18.

19.

64 − ( 52 − 23) (a) –5 −7 − −3 + 12 6 − 8 −13 + −6

(a) –4

For problems 20 – 21, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 20.

( −3x 2 y −3 ) (a)

21.

−3x 4 y6

2

(b)

−6x 4 y6

(c)

(b)

3xy 2 5

(c) 1

9x 4 y6

(d)

9x 4 y

−3 x −2 y 2

( −5 x −3 )0 (a)

−3 y 2 x2

34

(d) undefined

Name:

Chapter 1 Test Form H 22. Convert 0.000000091 to scientific notation. (a) 9.1× 10−7 (b) 9.1× 107

Date:

(c) 9.1× 10−8

2.4 × 106 and write the number as a decimal number. 3.0 × 10−2 (a) 8,000,000 (b) 80,000,000 (c) 800,000,000

(d) 9.1× 108

23. Simplify

(d) 8,000,000,000

The graduate student enrollment at a particular university has been decreasing since 2005. We can find the approximate number of graduate students enrolled at this university by using Enrollment = 8400 − 240 x . Substitute 1 for x to find the enrollment in 2006, substitute 2 for x to find the enrollment in 2007, and so on. 24. Find the approximate number of graduate students enrolled in 2009. (a) 7680

(b) 7440

(c) 7200

(d) 9360

25. Find the approximate number of graduate students enrolled in 2012. (a) 6480

(b) 10,080

(c) 6720

35

(d) 6960