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1 Table of Contents Chapter 1 Basic Concepts Pretests... 1 Mini-Lectures... Additional Exercises... 1 Chapter Tests Chapter Equations and Inequalities Pretests... 7 Mini-Lectures... 1 Additional Exercises... 7 Chapter Tests... Cumulative Tests (1 ) Chapter Graphs and Functions Pretests... 7 Mini-Lectures Additional Exercises Chapter Tests Chapter Systems of Equations and Inequalities Pretests... 1 Mini-Lectures Additional Exercises... 1 Chapter Tests Cumulative Tests (1 ) Chapter Polynomials and Polynomial Functions Pretests Mini-Lectures Additional Exercises Chapter Tests... 0 Chapter 6 Rational Expressions and Equations Pretests... Mini-Lectures... 7 Additional Exercises... Chapter Tests... Cumulative Tests (1 6)... 6 Chapter 7 Roots, Radicals, and Complex Numbers Pretests Mini-Lectures... 7 Additional Exercises Chapter Tests Chapter 8 Quadratic Functions Pretests Mini-Lectures Additional Exercises Chapter Tests... 8 Cumulative Tests (1 8)... 8

2 Chapter 9 Exponential and Logarithmic Functions Pretests... Mini-Lectures... 9 Additional Exercises Chapter Tests... 8 Chapter 10 Conic Sections Pretests... 0 Mini-Lectures Additional Exercises... 1 Chapter Tests... Cumulative Tests (1 10)... 0 Chapter 11 Sequences, Series, and the Binomial Theorem Pretests... Mini-Lectures... 7 Additional Exercises... 1 Chapter Tests... 7 Final Exams... 7 Answers... 01

3 Chapter 1 Pretest Form A Name the property illustrated. 1. ( ) x+ y + = x+ y ( 8) = 0. Date: Insert either < or > between the two numbers to make a true statement List each set in roster form.. A { x 1 x 1 and x I} = < <. 6. K = {x x is a whole number between and } For problems 7 8, consider the set of numbers,,,, 0,, 8, 1.,. List the elements of the set that are 7. whole numbers integers Let set A= {1,,}and B = {,,6}. Find A B and A B Evaluate: Simplify: Convert,000,000 to scientific notation Simplify and write the answer without exponents Illustrate the set x and < < on the number line Illustrate the set {x x } on the number line. 1. Evaluate the following expressions Copyright 01 by Pearson Education, Inc. 1

4 Chapter 1 Pretest Form A (cont.) 18. Simplify and write the answer without negative exponents: x y 19. Evaluate: ( ) ( ) Simplify and write the answer without negative exponents. 0. x y x y 1 Copyright 01 by Pearson Education, Inc.

5 Chapter 1 Pretest Form B 1. List A = {x x is a whole number less than 6} in roster form. 1. Indicate whether each statement is true or false.. Every integer is a whole number... The intersection of the set of rational numbers and the set of. irrational numbers is the empty set. Date: Consider the set of numbers, 8, 0,,, 1.6, 1. List the elements of the set that are 7. rational numbers.. whole numbers. For problems 6 7, let A = {1,,, 7, 9} and B = {,, 6, 7, 8}. 6. Find A B Find A B Indicate the set on the number line. 8. x < x 1 { } 9. List from smallest to largest:,, 7,,. 9. Name each property illustrated ( x + y) = 9( y+ x) ( xy) = (7 x) y 11. Evaluate each expression ( ) (10 ) Evaluate 7xy y when x = 1 and y =. 1. Simplify each expression and write the answer without negative exponents y x y 1x y Copyright 01 by Pearson Education, Inc.

6 Chapter 1 Pretest Form B (cont.) 19. Convert 78,000,000 to scientific notation Simplify (.1 10 )( ) and write the number without 0. exponents. Copyright 01 by Pearson Education, Inc.

7 Mini-Lecture 1.1 Study Skills for Success in Mathematics, and Using a Calculator Learning Objectives: 1. Have a positive attitude.. Prepare for and attend class.. Prepare for and take examinations.. Find help.. Learn to use a calculator. Examples: 1. Have 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.. 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.. 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. e) When taking the exam, read the directions and problems carefully. f) Pace yourself and use all available time. Attempt every problem.. Find Help a) Seek help right away when needed. Do not wait! b) Utilize the supplements that come with this textbook.. 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. Copyright 01 by Pearson Education, Inc.

8 Mini-Lecture 1. Sets and Other Basic Concepts Learning Objectives: 1. Identify sets.. Identify and use inequalities.. Use set builder notation.. Find the union and intersection of sets.. Identify important sets of numbers. 6. Key vocabulary: variable, constant, algebraic expression, set, elements, roster form, natural/counting numbers, integers, empty/null set, endpoints, set builder notation, union, intersection, whole numbers, rational numbers, irrational numbers, real 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.. Insert either < or > between the two numbers to make a true statement. a) b) 7 c) 8. a) List A = {x x is a natural number greater than } in roster form. b) Write B = {1,,,, } using set builder notation.. For A = {0,, 8, 1} and B = {0,,, 6}, find each of the following: a) A B b) A B. Consider the set of numbers 9, 7,, 8., 6,, 0, 6, π,, List the elements of the set that are: a) natural numbers b) whole numbers c) integers d) rational numbers e) irrational numbers 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. Point out 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,,,,,6}; a) <; b) >; c) <; a) {,6,7, }; b) {x x < 6 and x N} ;, 6,0,6,,17 ; a) {0,,,6,8,1}; b) {0,}; a) { 6,,17 }; b) { 0,6,,17 }; c) { } 9 9 d),, 8., 6,,0,6,,17; e) { 7,π }; f) π 16 8, 7,, 8., 6,,0,6,,, Copyright 01 by Pearson Education, Inc.

9 Mini-Lecture 1. Properties of and Operations with Real Numbers Learning Objectives: 1. Evaluate absolute values.. Add real numbers.. Subtract real numbers.. Multiply real numbers.. Divide real numbers. 6. Use the properties of real numbers. 7. 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. a) 1 b) c) 0 d) 0.6. Insert <, >, or = between each pair of numbers to make a true statement. a) b) 7 c) For Examples 6, evaluate.. a) + ( 7) b) + ( 8) c). a) 8 1 b) 10 ( ) c). a) ( 9)( 6) 6. a) b) 0.8( 0.9) 8 b) c) 7 c) 1 0 d) ( 6) d).1 + ( 6.) d) d) ( )( )( 6) d).96 (.8) 7. Name each property illustrated. a) ( x+ 8) + = x+ (8+ ) b) 67 = 76 c) (10) = (10) d) ( x+ 8) = x+ 8 e) m+ m= 0 f) 9+ 0= 9 g) 6+ 10= h) ( 10) 1 = 10 i) 0 ( 9) = j) = 1 k) ( 6) = 6 l) x = x 9 7 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. Copyright 01 by Pearson Education, Inc. 7

10 Mini-Lecture 1. (cont.) Properties of and Operations with Real Numbers Answers: 1a) 1; 1b) ; 1c) 0; 1d) 0.6; a) =; b) <; c) >; d) >; a) 11 ; b) ; 10 c) ; d) 9.9; a) 7; b) 8; c) ; d) 1.; a) ; b) 0.7; 6 c) 1 ; d) 90; 6 6a) 1 ; 6b) ; 6c) 8. ; 6d) 8.; 7a) assoc. prop. of add.; 7b) comm. prop. of mult.; 7c) assoc. prop. of mult.; 7d) dist. prop.; 7e) inv. prop. of add.; 7f) id. prop. of add.; 7g) comm. prop. of add.; 7h) id. prop. of mult.; 7i) mult. prop. of zero; 7j) inv. prop. of mult.; 7k) dbl. neg. prop.; 7l) dist. prop. 8 Copyright 01 by Pearson Education, Inc.

11 Mini-Lecture 1. Order of Operations Learning Objectives: 1. Evaluate exponential expressions.. Evaluate square and higher roots.. Evaluate expressions using the order of operations.. Evaluate expressions containing variables.. Key vocabulary: factors, exponential expression, base, exponent, radical sign, radicand, principle (or positive) square root, index, cube root, nth root, order of operations, grouping symbols, undefined Examples: Evaluate. 1. a) e) i) ( 8) b) ( 10) f) x for x = 6 j) 8 c) 10 g) x for x = 6 k) ( ) d) 1 h) ( x) for x = 6 + ( ) + ( ). a) 100 b). a) 9 6 c) 0. d) 81 e) 6 f) 16 g) h) 8 i) c) j) 0.07 k) l) + b) 9+ + ( 6 ) + ( ) d) ( 17). Evaluate each expression for the given value of the variable(s). 1 a) x x + 8 when x = b) x xy + 6y when x = and y = 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 Answers: 1a) 6; 1b) 6 ; 1c) 6; 1d) 6 ; 1e) 1000 ; 1f) 1000 ; 1g) 6; 1j) 6 ; 1k) 6; a) 10; b) ; c) 0.; d) 9 8 k) ; l) 1 ; a) 18; b) ; c) 7; d) undefined; a) 7; b) 8 ; e) ; f) ; g) ; h) 1 ; 1h) 16 ; 1i) 8 ; i) 1 10 ; j) 0.; Copyright 01 by Pearson Education, Inc. 9

12 Mini-Lecture 1. Exponents Learning Objectives: 1. Use the product rule for exponents.. Use the quotient rule for exponents.. Use the zero exponent rule.. Use the negative exponent rule.. Use the rule for raising a power to a power. 6. Use the rule for raising a product to a power. 7. Use the rule for raising a quotient to a power. 8. Key vocabulary: product rule for exponents, quotient rule for exponents, negative exponent rule, zero exponent rule, raising a power to a power (or power rule), raising a product to a power, raising a quotient to a power Examples: Simplify each expression. 1. a) 7 b) x x c) a a. a) 8 b) n n 9 c) y y 9. a) 0 0 b) 0 1x c) 0 8 d) (x ). Simplify and write each answer without negative exponents. a) b) x c) d) 7 8a c 6 y b e) x y f) mn g) h) +. Simplify. Assume that bases represented by variables are nonzero. a) ( ) b) ( x ) c) ( ) x 6. a) ( 6 x ) 7. a) b) ( ) 6 7 x Teaching Notes: b) a 6 b 7 c) d) ( ) x y 8mn 1 1m n d) 6 ( x y ) 7 ( x y ) 0 Students often have difficulty mastering the rules for exponents. Stress to them the importance of neatly working one step at a time. Answers: 1a) 11 ; 1b) 7 x ; 1c) a) 1 ; b) ; c) 6 y ; d) x 1 b) 1 x ; c) 1 6 ; d) 0 x ; 6a) a ; a) 7 8a b c ; e) 81x ; 6b) = 6; b) 6 n ; c) x ; f) m 8 81y 16n 6 x 16y 10 6 ; 7a) 1 x ; g) 1 6 ; 7b) y ; a) 1; b) 1; c) 1 ; d) 1 ; 8 a b ; h) ; a) 79; 7 ; 7c) m 1 n 0 ; 7d) 0 y x 10 Copyright 01 by Pearson Education, Inc.

13 Mini-Lecture 1.6 Scientific Notation Learning Objectives: 1. 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) 8,000 b) c) 7,08,000,000 d) Express each number without exponents. a) b) c) d) Perform the indicated operation. Express each result both in scientific notation and without exponents. a) ( )( ) b) ( )( ) c) Use scientific notation to solve each problem. d) e) A group of 0 co-workers pool their money to buy lottery tickets. The jackpot is $1,000,000. 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 (600 seconds)? g) The diameter of a circular virus is meters. Find the radius of the virus. h) The diameter of a circular virus is 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) ; 1b) ; 1c) ; 1d) 6 b) ; c) 0,700; d) ; a) or,100,000; b) ; c). 10 or,000; d) or ; e) $,00,000 or 8 f) 669,600,000 miles or miles; g) 10 8 meters or meters; h) meters or meters ; a) 60,000,000; or 6 $. 10 ; Copyright 01 by Pearson Education, Inc. 11

14 Additional Exercises 1.1 Instructor Information: Office location: Office hours: Phone number: Date: Classmate Information: Obtain the names of at least two classmates whom you can contact for information or study questions. 1. Phone number: address:. Phone number: address: Math Lab: Location: Hours: Phone number: Tutoring Services: Location: Hours: Phone number: Recommended Supplements: 1 Copyright 01 by Pearson Education, Inc.

15 Additional Exercises Describe {integers greater than 1} using the roster method. 1.. List the elements of the set of even natural numbers less than 8,. in roster form.. List the elements of the set of even natural numbers less than 1,. in roster form.. Use set builder notation to name the following set:. the set of all real numbers less than or equal to 6 Insert either < or > to make a true statement. Date: List each set in roster form. 11. {x x is a counting number between 1 and 9} {x x is a natural number greater than } 1. Write each set using set builder notation. 1. {0, 1,,, } {,, 6, 8, } 1. Find both A B and A B. Be sure to identify which is which. 1. A = {7, 8, 9, 10, 17} and B = {, 7, 10, 1} A = {7, 9, 11, 1, } and B = {9, 11, 1, 1} A = {, e h,, i k, m} and B = {, e i, m, o} A = {6, 8, 9, 10, 17} and B = {, 6, 10, 1} 18. Consider the set of numbers 1 0,, 0.1, 0,1.7, π,, List the elements that are whole numbers List the elements that are rational numbers. 0. Copyright 01 by Pearson Education, Inc. 1

16 Additional Exercises Evaluate: 1.. Insert <, >, or = between the numbers to make a true statement.. ( ). List from smallest to largest:, 16,1,10.. List from largest to smallest: 6, 7,,7. Date: Evaluate.. + ( 10) ( 9) Subtract: 8 ( ) Find the difference: 10 ( 1) ( 8) ( 1)( ) Find the product: ( )( )( 7) Find the product: Multiply: Find the quotient: Find the quotient: Divide: Divide: Name the property illustrated. 19. ( x+ ) = x (+ ) = (8+ ) Copyright 01 by Pearson Education, Inc.

17 Additional Exercises 1. Evaluate each expression. Date: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Evaluate x when x = Evaluate ( c d) + when c = 1 and d = Evaluate x + xy + y when x = and y = Evaluate y ( x y) + when x = 6 and y = Evaluate ( ) x xy + 7 when x = and y =. 0. Copyright 01 by Pearson Education, Inc. 1

18 Additional Exercises 1. Simplify each expression. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 1. ( 9x )( 8x ) ( 6 )( 6 ) x y x y. Date: x y 7 x y 6 6x x a a 10 pqr pqr 7 10x x x y x y z f g h u y x abc 6 8 abc 0 abc 8 abc ( ) ( ) cd cd x y 0xy Copyright 01 by Pearson Education, Inc.

19 Additional Exercises 1. (cont.) 18. ( u p t ) ( x y ) ( x y ) x y x 0. Copyright 01 by Pearson Education, Inc. 17

20 Additional Exercises 1.6 Express each number in scientific notation. 1. 8,00, ,000,000, ,00, Express each number without exponents. Date: For Exercises 1 18, perform the indicated operation. Express the result both in scientific notation and without exponents. 1. (. 10 )( ) (.9 10 )(. 10 ) Divide by first converting each number to scientific notation. 19. Write the answer in scientific notation Subtract: Copyright 01 by Pearson Education, Inc.

21 Chapter 1 Test Form A Date: Answer true or false. 1. Every natural number is a whole number. 1.. The set of natural numbers is a finite set.. Insert <, >, or = to make a true statement ( ). List each set in roster form.. A = {x x is a whole number less than }. 6. B = {x x is an integer greater than or equal to } 6. Consider the set 1.,, 0,,, π, 6, List the elements of the set that are irrational numbers List the elements of the set that are integers. 8. Find A B and A B. 9. A {,, 6 }, B {,, 6, 8, 11} = = A { 0,,, 6, 8 }, B { 0,, 6, 9} = = 10. Evaluate Copyright 01 by Pearson Education, Inc. 19

22 Chapter 1 Test Form A (cont.) 1. (.1)( 7.8)( 9.1) ( ) ( ) Evaluate b b ac + a when a = 6, b = 11, and c =. 17. For problems 18 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 18. ( x y )( 6x y 7 ) b x y xz 1.. Express 0.01 in scientific notation... Express without using exponents.. Simplify and express each answer in scientific notation.. (0.0)(0.000).. 60, Copyright 01 by Pearson Education, Inc.

23 Chapter 1 Test Form B Date: Answer true or false. 1. Every whole number is a natural number. 1.. The set of integers between π and is the null set.. Insert <, >, or = to make a true statement ( ). List each set in roster form.. H = { l l is a whole number multiple of 7}. 6. B = {x x is a natural number less than 8} 6. Consider the set 1.,, 0,,, π, 6, List the elements of the set that are rational numbers List the elements of the set that are whole numbers. 8. Find A B and A B. 9. A { 1, 0, 1, e, i, π}, B { 1, 0, 1} = = A { 1,,, 8, 16 }, B {,, 6, 8, 10} = = 10. Evaluate Copyright 01 by Pearson Education, Inc. 1

24 Chapter 1 Test Form B (cont.) (0.) ( 1) + ( ) Evaluate b b ac a when a =, b= 1, and c= For problems 18 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 18. ( p )( p ) ( x y ) ( x y ) ( xy) 1.. Express in scientific notation... Express ( )(.1 10 ) without using exponents.. Simplify and express each answer in scientific notation.. (00)(7000) ,000. Copyright 01 by Pearson Education, Inc.

25 Chapter 1 Test Form C Date: Answer true or false. 1. Every real number is a rational number. 1.. Every integer is a rational number.. Insert <, >, or = to make a true statement ( 6). List each set in roster form. =.. A { x x is an odd integer between and } 6. B { x x 7 and x W} = < < 6. Consider the set 1.76,, 0,, 71, 8,. 7. List the elements of the set that are real numbers List the elements of the set that are natural numbers. 8. For problems 9 10, find A B and A B. 9. A {, 1, 1,, }, B { 1,,, 7, 9} = = A= {,, 6, 8, }, B = {,,, 1, 0, 1,,, } Indicate on the number line: { x.1 x } < List from smallest to largest: 0.9, 0.7, Copyright 01 by Pearson Education, Inc.

26 Chapter 1 Test Form C (cont.) Name the property illustrated. 1. a+ b= b+ a a ( b c) = ( a b) c 1. Evaluate ( 7) + ( 8) ( 1) ( ) ( ) ( ) ( 8) For problems 0 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 0. ( x ) ( x ) xy x y 1.. Convert 61,000 to scientific notation.. 7. Simplify ( )( 10 ) using exponents. and express the answer without.. Evaluate 7 x + when x = 6... Evaluate x xy y when x = and y =.. Copyright 01 by Pearson Education, Inc.

27 Chapter 1 Test Form D Date: Answer true or false. 1. The union of the set of whole numbers and {0} is the set 1. of natural numbers.. Every integer is a whole number.. Insert <, >, or = to make a true statement List each set in roster form.. C { x x is an integer between. and.1} =. 6. D { x x is a natural number between 1 and } = 6. Consider the set {.,8.7,7,,0, 6, 1}. 7. List the elements of the set that are integers List the elements of the set that are irrational numbers. 8. For problems 9 10, find A B and A B. 9. A {,, 6, 9 }, B { 1,,, 8} = = A { 0, 1,,, }, B {,,, 6, 7} = = Indicate on the number line: 6 x x< and x W List from smallest to largest:.,.7,.1 1. Copyright 01 by Pearson Education, Inc.

28 Chapter 1 Test Form D (cont.) Name the property illustrated. 1. ab = ba a+ ( b+ c) = ( a+ b) + c 1. Evaluate. 1. ( 7)( )( )( 1) ( 11+ ) ( 7 8 ) ( ) ( ) ( ) ( ) ( ) 19. For problems 0 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 0. ( xx x ) x y xy 1.. Convert to scientific notation... Simplify and express the answer without using exponents... Evaluate x 10 when x = 8... Evaluate x + 7xy + y when x = and y =.. 6 Copyright 01 by Pearson Education, Inc.

29 Chapter 1 Test Form E Date: Answer true or false. 1. Every irrational number is a real number. 1.. The intersection of the set of integers and the set of irrational numbers. is the set of rational numbers. Insert <, >, or = to make a true statement ( 1). List each set in roster form.. E = { x xis an odd integer greater than 7 and less than or equal to 0}. 6. F { x. x. and x W} = < < 6. Consider the set 1,,0, 8, 1,,, List the elements of the set that are rational numbers List the elements of the set that are whole numbers. 8. For problems 9 10, find A B and A B. 9. A { 0,,, 6,... }, B { 1,,, 7,... } = = A { 7,, 1,, }, B { 7,,, 1, 1,,, 7} = = Indicate on the number line: 16 x x and x N List from smallest to largest:.6,.,.7 1. Copyright 01 by Pearson Education, Inc. 7

30 Chapter 1 Test Form E (cont.) Name the property illustrated. 1. ( ab) c a ( bc) = a 1= 1 a = a 1. Evaluate ( 8 ) ( 6) ( ) ( ) ( ) ( ) ( ) () 7( ) 19. For problems 0 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 0. ( x ) ( x ) x x xx Convert 8,60,000 to scientific notation... Simplify ( )( 10 ). Write the answer without exponents.. An industrial laser printer is purchased in 007 for $70, and its value depreciates each year after its purchase. The value of the printer, in dollars, can be approximated by using the following formula: Value = 70 1x Substitute 1 for x to find the value of the printer in 008, substitute for x to find the value in 009, and so on.. Find the approximate value of the laser printer in Find the approximate value of the laser printer in Copyright 01 by Pearson Education, Inc.

31 Chapter 1 Test Form F Date: Answer true or false. 1. Every integer is a rational number. 1.. The intersection of the set of rational numbers and the set of. irrational numbers is the empty set. Insert <, >, or = to make a true statement ( 16). List each set in roster form.. A = {x x is an even integer between and 7}. 6. B { x x and x W} = < 6. Consider the set.17,,, 0,,,, List the elements of the set that are rational numbers List the elements of the set that are natural numbers. 8. For problems 9 10, find A B and A B. 9. A { 0,,, 6, 8 }, B { 1,,, 7, 9} = = A {,, 1, 0,1 }, B { 0,1,, } = = Indicate on the number line: 0 x x< and x N List from smallest to largest: 6.1, 6.08, Copyright 01 by Pearson Education, Inc. 9

32 Chapter 1 Test Form F (cont.) Name the property illustrated. 1. ab ( + c) = ab+ ac a+ 0= 0+ a = a 1. Evaluate. 1. ( )(7)( ) [ 7 + ( ) ] ( ) ( ) () + ( 9) () 7 ( 7) + 11 ( ) 8 + ( ) 9+ () For problems 0 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 0. ( ) ( ) x x ( x y ) ( xy ) 1.. Convert to scientific notation... Simplify and express the answer without using exponents.. An automobile purchased in 006 for $,000 depreciates in value every year. The approximate resale value of the vehicle, in dollars, can be found using the following formula: Resale value =, x Substitute 1 for x to find the vehicle s resale value in 007, substitute for x to find its resale value in 008, etc.. Find the approximate resale value of the vehicle in Find the approximate resale value of the vehicle in Copyright 01 by Pearson Education, Inc.

33 Chapter 1 Test Form G Indicate which answer makes a true statement. 1. The union of the set of natural numbers and {0} is Date: (a) the set of whole numbers (c) {0} (b) the set of natural numbers (d) the empty set. Every integer is a(n) (a) natural number (b) whole number (c) rational number (d) irrational number List each set in roster form.. C = { x x> 7 and x N} (a) C = {7, 8, 9, } (b) C = {8, 9, 10, } (c) C = {1,,,,, 6} (d) C = {1,,,,, 6, 7}. D = { x x is an odd integer} (a) D = {,,,, 1} (c) D = {,,, 1, 0, 1,,, } (b) D = {1,,,, } (d) D = {,,, 1, 1,,, } 1 6 Consider the set,.1, 0,, 6,.,, 7.. List the elements of the set that are rational numbers. (a) 1 6, (b) 7 (c) 6 (d) 6. List the elements of the set that are whole numbers ,,., 7 1 6,.1, 0,,.,, 7 (a) 0, (b), 0, (c),.1, 0,., (d) Consider the sets A {, 0, } and B { 0, 1,, } 7. Find A B. = =. 1 6,.1,0,, 6,.,, 7 (a) {0, } (b) {, 0, } (c) {0, 1,, } (d) {, 0, 1,, } 8. Find A B. (a) {0, } (b) {, 0, } (c) {0, 1,, } (d) {, 0, 1,, } For problems 9 10, identify which set is illustrated by the number line. 9. (a) { x < x and x I} (b) { x x< and x I} (c) { x < x and x R} (d) { x x< and x R} Copyright 01 by Pearson Education, Inc. 1

34 Chapter 1 Test Form G (cont.) 10. (a) { x < x< and x I} (b) { x < x< and x W} (c) { x 1< x< and x I} (d) { x 1< x< and x W} List from smallest to largest: 11.,, (a),, (b),, (c),, (d),, 1.,, (a),, (b),, (c),, (d),, Name the property illustrated a a 1 a = a = (a) commutative (b) associative (c) identity (d) inverse 1. ( ) = (a) commutative (b) associative (c) identity (d) double negative Evaluate (a) 8 (b) (c) (d) ( 7 ) (a) 9 (b) 7 (c) (d) (a) 6 7 (b) 7 (c) 9 (d) 6 7 Copyright 01 by Pearson Education, Inc.

35 Chapter 1 Test Form G (cont.) 18. ( ) ( ) ( ) (a) (b) 8 1 (c) 1 (d) 19. ( ) (a) (b) (c) (d) For problems 0 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. x y 0. ( ) (a) y x 6 (b) y x 6 9 (c) 6 y x (d) y 1. x x 1 1 (a) 7 x (b) 1 x (c) x (d) 7 x. Convert 7,000,000 to scientific notation. (a) (b) (c) (d) Simplify ( 10 )( ) and write the number as a decimal number. (a) (b) (c) (d) During the 000s, the value of the land surrounding a town was increasing at a phenomenal rate. One plot of land was purchased in 000 for $10,000, and its value could be approximated using the following formula: Value = 10, x Substitute 1 for x to find the value of the plot in 001, substitute for x to find the value in 00, and so on.. Find the approximate value of the plot of land in 006. (a) $1,00 (b) $16,000 (c) $11,00 (d) $17,000. Find the approximate value of the plot of land in 010. (a) $160,00 (b) $16,000 (c) $169,00 (d) $17,000 Copyright 01 by Pearson Education, Inc.

36 Chapter 1 Test Form H 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. The union of the set of rational numbers and the set of irrational numbers is Date: (a) the set of whole numbers (c) {0} (b) the null set (d) the set of real numbers List each set in roster form.. H = { x x is an integer multiple of } (a) H = {, 9, 6,, 0,, 6, 9, } (c) H = {0,, 6, 9, } (b) H = {, 9, 6,,, 6, 9, } (d) H = {, 6, 9, }. J = { x x< 7 and x is an odd natural number} (a) J = {0, 1,, } (b) J = {0, 1,,, 7} (c) J = {1,, } (d) J = {1,,, 7} 6 Consider the set 9,.77,, 0,, 17, List the elements of the set that are irrational numbers. (a), 17 (b) 6 6 (c) 9,.77,, 0, (d) 9,.77,, 0,, 17, List the elements of the set that are integers. (a) 9, 0 (b),0 0 (c) 0 (d) none Consider the sets A { 1,, } and B { 0, 1,,, } 7. Find A B. = =. (a) {1,,,, } (b) {0, 1,,,, } (c) {1,, } (d) {1, } 8. Find A B. (a) {1,,,, } (b) {0, 1,,,, } (c) {1,, } (d) {1, } For problems 9 10, identify which set is illustrated by the number line. 9. (a) { x x< and x W} (b) { x x and x N} < (c) 17 x x< and x W (d) 17 x x< and x N Copyright 01 by Pearson Education, Inc.

37 Chapter 1 Test Form H (cont.) 10. (a) { x < x and x I} (b) { x x< and x I} (c) { x < x and x R} (d) { x x< and x R} List from smallest to largest. 11.,, (a),, (b),, (c),, (d),, 1. 1, 1, (a) 1, 1, (b) 1, 1, (c), 1, 1 (d), 1, 1 Name the property illustrated. 1. ( ) x + y = x+ y (a) associative (b) commutative (c) distributive (d) identity 1. ( ) 1= 1 ( ) = (a) associative (b) commutative (c) inverse (d) identity Evaluate (a) 18 (b) 6 7 (c) (d) 16. ( 7 + ) 8( 6) (a) 17 (b) 1 (c) 11 (d) ( 8) ( 7) ( ) (a) 10 (b) 86 (c) 1 (d) 18. ( ) 6 ( 6 ) (a) (b) 1 (c) 1 (d) Copyright 01 by Pearson Education, Inc.

38 Chapter 1 Test Form H (cont.) (a) (b) (c) (d) For problems 0 1, simplify. Leave no negative or zero exponents in the answer. Assume no variable base is zero. 0. ( x y ) (a) x 6 y (b) 6x 6 y (c) 9x 6 y (d) 9x y 1. x ( ) x y 0 (a) y x (b) xy (c) 1 (d) undefined. Convert to scientific notation. (a) (b) (c) (d) Simplify and write the number as a decimal number. (a) 8,000,000 (b) 80,000,000 (c) 800,000,000 (d) 8,000,000,000 The graduate student enrollment at a particular university has been decreasing since 00. We can find the approximate number of graduate students enrolled at this university by using the following formula: Enrollment = 800 0x Substitute 1 for x to find the enrollment in 006, substitute for x to find the enrollment in 007, and so on.. Find the approximate number of graduate students enrolled in 009. (a) 7680 (b) 70 (c) 700 (d) 960. Find the approximate number of graduate students enrolled in 01. (a) 680 (b) 10,080 (c) 670 (d) Copyright 01 by Pearson Education, Inc.