Hsiang-Ping Huang math1010fall2008-4 WeBWorK assignment ...€¦ · Hsiang-Ping Huang...

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Hsiang-Ping Huang math1010fall2008-4 WeBWorK assignment number 2 is due : 10/21/2008 at 11:59pmMDT. 1. (1 pt) 1010Library/set2 Fundamentals of Algebra/e1.pg The purpose of this last and lengthy problem is to help you pre- pare for the first exam. There will be ten questions, all questions have equal weight, and you’ll be able to use only pen or pencil and the exam it- self, i.e., no notes, books, or calculators! To avoid distraction and disruption I will not be able to answer questions during the exam. Before the exam, read the guidelines for exams on your syl- labus. Work through the list below and make sure you understand the described items and can answer questions related to them. Fractions. You need to be able to add, multiply, subtract, and divide fractions. Moreover, you need to be able to recog- nize common factors in numerator and denominator, and cancel them. It does not hurt to practice, so here we go: 2 7 + 4 21 = / . 2 7 - 4 21 = / . 2 7 × 4 21 = / . 2 7 ÷ 4 21 = / . Here is a more complicated fraction problem: 4 3 - 1 2 2 5 + 1 3 = / . Language. Understand the language related to the four ba- sic arithmetic operations. Don’t use embarrassingly juvenile words like ”timesing” and ”minussing”. Use the proper terms ”multiplying” and ”subtracting”. Understand the words add, multiply, subtract, divide, sum, difference, product, quotient, factor, multiple, divisor, dividend. Also understand and know the names of the rules of arithmetic: the commutative and asso- ciative laws of addition and multiplication, and the distributive law. Use the Glossary and have someone quiz you if you are not sure. Know what kind of numbers (natural numbers, integers, rational numbers, real numbers) there are. The Distributive Law. Understand how to apply the Distribu- tive Law to simplify algebraic expressions. Precedence. Understand the conventions of arithmetic prece- dence. There are a large number of problems like this on set 1. Multiplication and division come before addition and sub- traction. If there are several operations of the same level of precedence we work from left to right. However, anything in parentheses is evaluated first. Addition and subtraction have the same level of precedence, and so do multiplication and division. You can also use superfluous parentheses to make your meaning clear if you are not sure. Know how to compute absolute values. of arithmetic expres- sions. There is a word problem on the set. It’s about buying a car, and I realize that you may never have bought a car. The problem also contains some words you may not have seen before, like ”in- voice price” (which is the dollar amount the dealer is charged by the manufacturer) and ”factory incentive” (which is a rebate given by the manufacturer to the dealer). However, the prob- lem can be solved just using common sense and understanding the language of percent. Here is another percent problem: You buy a used car listed as $ 10,000 at a discount of 10 percent. However, you also pay 10 percent sales tax. Thus you end up writing a check for $ . Correct Answers: 10 21 2 21 8 147 3 2 25 22 9900 2. (1 pt) 1010Library/set2 Fundamentals of Algebra/prob.pg The expression 4 9 - 9 12 8 11 + 4 11 can be written as a fraction a b where the integers a and b have no factor in common, and b is positive. Enter a= and b= Hint: Use what you have learned to compute the numerator and the denominator, and then divide the numerator by the denomi- nator. Correct Answers: -121 432 1

Transcript of Hsiang-Ping Huang math1010fall2008-4 WeBWorK assignment ...€¦ · Hsiang-Ping Huang...

Page 1: Hsiang-Ping Huang math1010fall2008-4 WeBWorK assignment ...€¦ · Hsiang-Ping Huang math1010fall2008-4 WeBWorK assignment number ... divide, sum, difference, product, quotient ...

Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 2 is due : 10/21/2008 at 11:59pm MDT.

1. (1 pt) 1010Library/set2 Fundamentals of Algebra/e1.pgThe purpose of this last and lengthy problem is to help you pre-pare for the first exam.

There will be ten questions, all questions have equal weight,and you’ll be able to use only pen or pencil and the exam it-self, i.e., no notes, books, or calculators! To avoid distractionand disruption I will not be able to answer questions during theexam.

Before the exam, read the guidelines for exams on your syl-labus.

Work through the list below and make sure you understandthe described items and can answer questions related to them.

Fractions. You need to be able to add, multiply, subtract,and divide fractions. Moreover, you need to be able to recog-nize common factors in numerator and denominator, and cancelthem. It does not hurt to practice, so here we go:27 + 4

21 = / .27 −

421 = / .

27 ×

421 = / .

27 ÷

421 = / .

Here is a more complicated fraction problem:43−

12

25 + 1

3= / .

Language. Understand the language related to the four ba-sic arithmetic operations. Don’t use embarrassingly juvenilewords like ”timesing” and ”minussing”. Use the proper terms”multiplying” and ”subtracting”. Understand the words add,multiply, subtract, divide, sum, difference, product, quotient,factor, multiple, divisor, dividend. Also understand and knowthe names of the rules of arithmetic: the commutative and asso-ciative laws of addition and multiplication, and the distributivelaw. Use the Glossary and have someone quiz you if you are notsure. Know what kind of numbers (natural numbers, integers,rational numbers, real numbers) there are.

The Distributive Law. Understand how to apply the Distribu-tive Law to simplify algebraic expressions.

Precedence. Understand the conventions of arithmetic prece-dence. There are a large number of problems like this on set1. Multiplication and division come before addition and sub-traction. If there are several operations of the same level ofprecedence we work from left to right. However, anything inparentheses is evaluated first. Addition and subtraction have thesame level of precedence, and so do multiplication and division.

You can also use superfluous parentheses to make your meaningclear if you are not sure.

Know how to compute absolute values. of arithmetic expres-sions.

There is a word problem on the set. It’s about buying a car, and Irealize that you may never have bought a car. The problem alsocontains some words you may not have seen before, like ”in-voice price” (which is the dollar amount the dealer is chargedby the manufacturer) and ”factory incentive” (which is a rebategiven by the manufacturer to the dealer). However, the prob-lem can be solved just using common sense and understandingthe language of percent.

Here is another percent problem: You buy a used car listed as $10,000 at a discount of 10 percent. However, you also pay 10percent sales tax. Thus you end up writing a check for $ .

Correct Answers:• 10• 21• 2• 21• 8• 147• 3• 2• 25• 22• 9900

2. (1 pt) 1010Library/set2 Fundamentals of Algebra/prob.pg

The expression

49 −

912

811 + 4

11

can be written as a fractionab

where the integers a and b have no factor in common, and b ispositive.

Enter a= and b=Hint: Use what you have learned to compute the numerator andthe denominator, and then divide the numerator by the denomi-nator.

Correct Answers:• -121• 432

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3. (1 pt) 1010Library/set2 Fundamentals of Algebra/s2p11.pg

The expression 12 ×

23 ×

34 ×

45 ×

56 ×

67 is a fraction a

b where b ispositive, and a and b have no common factors.

Enter a= and b=

Hint: Cancel common factors before multiplying numeratorsand denominators.

Correct Answers:

• 1• 7

4. (1 pt) 1010Library/set2 Fundamentals of Algebra/s2p12.pgIf you are unfamiliar with the terminology in this and the nextproblem learn about it here.

The greatest common factor (GCF) of 14 and 21 is and theirleast common multiple (LCM) is The GCF of 12 and 42 is

and their least common multiple (LCM) is The GCF of3 and 5 is and their least common multiple (LCM) is

Correct Answers:

• 7• 42• 6• 84• 1• 15

5. (1 pt) 1010Library/set2 Fundamentals of Algebra/s2p13.pg

The least common multiple of 1,2,3,4 is .The least common multiple of 1,2,3,4,5 is .The least common multiple of 1,2,3,4,5,6 is .The least common multiple of 1,2,3,4,5,6,7 is .

Correct Answers:

• 12• 60• 60• 420

6. (1 pt) 1010Library/set2 Fundamentals of Algebra/s2p16.pg

The expression 12 ÷

23 ÷

34 ÷

45 ÷

56 ÷

67 is a fraction a

b where b ispositive, and a and b have no common factors.

Enter a= and b=Hint: Operations of the same precedence proceed from left toright. Cancel common factors before multiplying numeratorsand denominators.

Correct Answers:

• 7• 4

7. (1 pt) 1010Library/set2 Fundamentals of Algebra/s2p20.pgThe last few problems on this set deal with simple percentageproblems.You make $ 95000 a year, and you get a 10salary is $

. (Salaries in these problems are randomly chosenand range from $ 20,000 to $ 100,000.)The next year you get a 10$ . That is

Correct Answers:

• 104500• 94050• 1

8. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/prob10.pgIndicate whether the following statements are True (T) or False(F). You must get all answers correct in order to receive credit.

1. The difference of two integers is always a natural num-ber.

2. The quotient of two integers is always a rational num-ber (provided the denominator is non-zero).

3. The quotient of two integers is always an integer (pro-vided the denominator is non-zero).

4. The sum of two integers is always an integer.5. The ratio of two integers is always positive6. The product of two integers is always an integer.7. The difference of two integers is always an integer.

Correct Answers:

• F• T• F• T• F• T• T

9. (1 pt) 1010Library/set3 Linear Equations and Inequalities/s3p1.pgAs a warm up exercise evaluate 3(−4)(1−5−2(6))=Remember that a missing operator means multiplication, andmultiplication and division come before addition and subtrac-tion unless otherwise indicated by parentheses. Parentheses canalways be included even if they are not needed.

Correct Answers:

• 192

10. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p5.pgEvaluate the expression | |192−274|− |185−325| | =

Correct Answers:

• 58

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11. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p16.pgThe next three questions reinforce the vocabulary for the fourbasic arithmetic operations. Don’t use words like ”minussing”or ”timesing”, they are juvenile. Use the proper terminologyemployed in this class.

Match the verbs below with the letters labeling particularnouns.

1. multiply2. subtract3. add4. divideA. productB. sumC. differenceD. quotient

Correct Answers:

• A• C• B• D

12. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p20.pgMatch the phrases given below with the letters labeling the al-gebraic expression. You may have to simplify your expressionto recognize it as the correct one.You must get all of the answers correct to receive credit.

1. The square of x+92. The quotient of x and x+93. The sum of x and x+94. The product of x and x+95. The difference of x and x+9A. 2x+9B. x

x+9C. x2 +9xD. x2 +18x+81E. −9

Hint: To recognize the correspondence between the phrases andthe algebraic expressions write down the expression defined bythe phrase and manipulate it to get it in the form of the givenexpressions. You may want to do problems 22 through 36 be-fore doing this one. They deal with algebraic expressions moredirectly.

Correct Answers:

• D• B• A

• C• E

13. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p21.pgIndicate whether the following statements are True (T) or False(F).

1.√

49 is a rational number2. 2 is a real number3. 3

2 is an integer4.√

3 is a rational number5. -17 is an integer6. 0 is a natural number7. π is a real number

Correct Answers:• T• T• F• F• T• F• T

14. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p26.pgThe essence of Algebra is the manipulation of algebraic expres-sions. One application of algebraic expressions is the statementof formulas that describe general facts. In the next few ques-tions you are asked to enter some formulas which should be orbecome a permanent part of your Math background.

Enter here an algebraic expression that gives thearea of a rectangle with a length of a and a width of b. (Use anasterisk to denote multiplication.)

Correct Answers:• a*b

15. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p27.pgEnter here an algebraic expression that gives thearea of a triangle with a base of length of b and a height h.

Correct Answers:• b*h/2

16. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p28.pgEnter here an algebraic expression that gives thearea of a circle with a radius r. You may write ”pi” to denote thesymbol π, and you can use the symbol ˆor a double asterisk **to denote exponentiation. (Or you can express r2 as r*r.)

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Enter here an algebraic expression that gives thearea of a circle with a diameter d.

Correct Answers:

• pi*rˆ2• pi*dˆ2/4

17. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p30.pgThe basic idea of manipulating algebraic expressions is that theyobey the same laws as arithmetic expressions. The following aresome simple exercises along those lines. They ask you to enternumerical values for the variables A, B, C ...

The expression 7(7−4x) equals Ax+Bwhere A equals:and B equals:[NOTE: Your answers cannot be algebraic expressions.]

Correct Answers:

• -28• 49

18. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p31.pgThe expression (6x+4)(3x−5) equals Ax2 +Bx+Cwhere A equals:and B equals:and C equals:

Correct Answers:

• 18• -18• -20

19. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p32.pgThe expression (6t−6)(4t +3)+5t−7 equals At2 +Bt +Cwhere A equals:

and B equals:and C equals:

Correct Answers:• 24• -1• -25

20. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p33.pgThe expression (5x+2)2equals Ax2 +Bx+Cwhere A equals:and B equals:and C equals:

Correct Answers:• 25• 20• 4

21. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p34.pgThe expression (x−4)(x2 +4x+6)equals Ax3 +Bx2 +Cx+Dwhere A equals:and B equals:and C equals:and D equals:

Correct Answers:• 1• 0• -10• -24

22. (1 pt) 1010Library/set3 Linear Equations and Inequalities-/s3p35.pgThe expression 6(2x2 +4x+3)−3(5x2 +6x+5) equals

x2+ x+

Correct Answers:• -3• 6• 3

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 3 is due : 10/21/2008 at 11:59pm MDT.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set4 Linear Equations and Inequalities/s4p1.pg

The solution of the equation 9x = 10is x = .You may enter your answer as a decimal number or as a frac-tion. I recommend that in problems like this you use fractionsrather than decimal approximations. You don’t have to figureout your approximation, and you don’t have to worry about justhow accurately you should approximate the answer.

Correct Answers:

• 1.11111111111111

2. (1 pt) 1010Library/set4 Linear Equations and Inequalities/s4p2.pg

The solution of the equation 9x+2 = 3is x = .

Correct Answers:

• 0.111111111111111

3. (1 pt) 1010Library/set4 Linear Equations and Inequalities/s4p3.pg

The solution of the equation 3x+9 = 4x+1is x = .(You may enter your answer as a decimal number or as a frac-tion.)

Correct Answers:

• 8

4. (1 pt) 1010Library/set4 Linear Equations and Inequalities/s4p4.pg

The solution of the equation 10y+11 = 3y+16is y = .(You may enter your answer as a decimal number or as a frac-tion.)

Correct Answers:

• 0.714285714285714

5. (1 pt) 1010Library/set4 Linear Equations and Inequalities/s4p5.pg

You are probably used to solving problems where the coeffi-cients are specific numbers. However, in many problems thecoefficients are variables themselves, and the answer dependson those variables. As you go on in mathematics, the role ofspecific numbers will keep decreasing, and the role of generalcoefficients (or parameters) will increase. The next couple ofproblems are our first foray into this new area.

The solution of the equation ax+b = cis x = .(Your answer will of course be in terms of a, b, and c. You mayassume that a is non-zero.)

Correct Answers:

• (c-b)/a

6. (1 pt) 1010Library/set4 Linear Equations and Inequalities-/s4p17.pgIndicate with T (true) if the equations below are linear, and F(false) if they are not.

1. 3x+4 = 172. x2 = 13. 3x+4 = 5x−44. x2 + x = 4

Hint: Study the definition and discussion of ’linear equation’.Correct Answers:

• T• F• T• F

7. (1 pt) 1010Library/set4 Linear Equations and Inequalities-/s4p21.pgThe remaining problems in this set are word problems. Youmay want to look for similar problems in the textbook for this

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class, if you have it, or any other textbook on Intermediate Al-gebra.

You are hiking along the California coast and wonder about theheight of a particular Giant Redwood tree. You are 5 feet andnine inches tall and your shadow is 3 feet long. The shadow ofthe tree is 96 feet long. How tall is the tree? Enter its heighthere: feet.Hint: Draw a picture. Think about similar triangles.

Correct Answers:

• 184

8. (1 pt) 1010Library/set4 Linear Equations and Inequalities-/s4p23.pgHow much 90 percent vinegar do you have to add to a gallon of5 percent vinegar to get 20 percent vinegar?

gallons.Hint: You want the final percentage of pure vinegar to be 201+xgallons of fluid where x is the number of gallons you add. Thinkabout how much pure vinegar is in those 1+ x gallons.

Correct Answers:

• 0.214285714285714

9. (1 pt) 1010Library/set4 Linear Equations and Inequalities-/s4p24.pgEnter here an algebraic expression that gives thearea of a circle with a circumference c.

Hint: The circumference of a circle with radius r is 2πr, and itsarea is πr2.

Correct Answers:

• cˆ2/4/pi

10. (1 pt) 1010Library/set4 Linear Equations and Inequalities-/s4p26.pg

This problem is just like the pot and lid problem on homework1.

You buy a house including the land it sits on for $ 169000. Thereal estate agent tells you that the land costs $ 11000 more thanthe house.

The price of the house is $ and the price of theland is $ .

Correct Answers:

• 79000• 90000

11. (1 pt) 1010Library/set4 Linear Equations and Inequalities-/s4p30.pg

The last two problems are examples of ”simple Hindu Alge-bra”, quoted on page 528 of ”The Story of Civilization”, v.1., by

Will Durant, Simon and Schuster, 1935. The problems are ap-proximately 1,800 years old. (Mental pursuits by women werediscouraged at that time. You ponder the significance of ficti-tiously directing the questions at women. Durant does not com-ment on this issue.)

Out of a swarm of bees one fifth part settled on a Kadamba blos-som; one third on a Silihindra flower; three times the differenceof those numbers flew to the bloom of a Kutaja. One bee, whichremained, hovered about in the air. Tell me, charming woman,the number of bees .Hint: Call the number of bees x and convert the story into anequation.

Correct Answers:• 15

12. (1 pt) 1010Library/set4 Linear Equations and Inequalities-/s4p31.pgHere is the other problem from ”The Story of Civilization”:

Eight rubies, ten emeralds, and a hundred pearls, which are inthy ear-ring, my beloved, were purchased by me for thee at anequal amount; and the sum of the prices of the three sort of gemswas three less than half a hundred; tell me the price of each, aus-picious woman.Enter the price of one pearl , the price of one emerald

, and the the price of one ruby .Hint: I had to ponder this a bit. The word ”equal” means thateight rubies cost as much as ten emeralds or a hundred pearls.The prices that add to ”three less than half a hundred” are theprices for one pearl, or one emerald, or one ruby. If you knewthe price of a pearl you could easily figure out the price of a rubyor an emerald, just try some suitable numbers for the price of apearl.

Correct Answers:• 2• 20• 25

13. (1 pt) 1010Library/set math1010fall2002-3/set3/s5p1.pg

Consider the inequality

8x+5 < 1

Below insert the appropriate symbol < or > and the appropriatenumber such that the two inequalities are equivalent.x (insert symbol) (insert number)

Hint: Figure out what bothers you and get rid of it by doing thesame thing on both sides of the inequality. Check this page!

(Show hint after 1 attempts. )

Correct Answers:• <

2

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• -0.5

14. (1 pt) 1010Library/set math1010fall2002-3/set3/s5p3.pg

Consider the inequality

8x+7 > 15x+4

Below insert the appropriate symbol < or > and the appropriatenumber such that the two inequalities are equivalent.x (insert symbol) (insert number)

Hint: Move the x’s all to one side.

(Show hint after 1 attempts. )

Correct Answers:• <• 0.428571428571429

15. (1 pt) 1010Library/set math1010fall2002-3/set3/s5p5.pg

The equation|8x−13|= 7

has two solutions. Enter the smaller here and thelarger here

Hint: Remember that there are two possibilities for the ab-solute value and check this page.

(Show hint after 1 attempts. )

Correct Answers:• 0.75• 2.5

16. (1 pt) 1090Library/set2 Linear Equations and Functions/p02.pgSolve for x: 2

5 x+ 37 =− 3

7 x+ 15

Answer: x =Correct Answers:

• -0.275862068965517

17. (1 pt) 1090Library/set2 Linear Equations and Functions/p15.pgYou wish to invest $600 over one year in two accounts paying5% and 6% annually. How much should you invest in each toearn $33?

Answer: in the 5% account and in the6% account.

Correct Answers:

• 300• 300

18. (1 pt) 1090Library/set2 Linear Equations and Functions/p17.pg62% or 558 employees in a company are female. How many aremale?

Answer:Correct Answers:

• 342

19. (1 pt) 1090Library/set2 Linear Equations and Functions/p22.pgA car dealer purchase 20 new automobiles for $ 8000 each. Ifhe sells 16 of them at a profit of 20%, for how much must hesell the remaining 4 to obtain an average profit of 18% ?Answer= $

Correct Answers:

• 8800

20. (1 pt) 1090Library/set2 Linear Equations and Functions/p23.pgThe length of a rectangular garden is 9 feet longer than its width.If the garden’s perimeter is 198 feet, what is the area of the gar-den in square feet?

Correct Answers:

• 2430

21. (1 pt) 1090Library/set2 Linear Equations and Functions/p24.pgA cash register contains only five dollar and ten dollar bills. Itcontains twice as many fives as tens and the total amount ofmoney in the cash register is 560 dollars. How many tens are inthe cash register?

Correct Answers:

• 28

22. (1 pt) 1090Library/set2 Linear Equations and Functions/p25.pg

What quantity of 60 percent acid solution must be mixed witha 30 percent solution to produce 90 mL of a 50 percent solution?

Correct Answers:

• 60

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 4 is due : 10/21/2008 at 11:59pm MDT.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set5 Graphs and Functions/s5p11.pgI recommend that instead of decimal numbers you enter an ex-pression using sqrt() to indicate a square root. For exampleinstead of 1.4142 you would enter sqrt(2) .

The distance between the points (8,9) and (7,6) is.

The distance between the points (2,8) and (7,6) is.

The distance between the points (−4,2) and (5,1) is.

The distance between the points (−3,−2) and (−8,−8) is.

Hint: Don’t try to memorize a formula. Draw a picture showingthe two points in a rectangular coordinate system and apply thePythagorean Theorem.

Correct Answers:

• 3.16227766016838• 5.3851648071345• 9.05538513813742• 7.81024967590665

2. (1 pt) 1010Library/set5 Graphs and Functions/s5p12.pgEach of the following phrases describes a point in the Cartesian(rectangular) coordinate system. Enter the coordinates x and yof the point.

The point is located 5 units to the left of the y axis and 2 unitsabove the x axis.x= and y=The point is located 10 units to the right of the y axis and 4 unitsbelow the x axis.x= and y=The coordinates of the point have equal absolute value, the pointis in the second quadrant, and the distance of the point from theorigin is 2.x= and y=

Hint: use ”sqrt(z)” to denote the square root of a number z.The point is the origin.x= and y=The point is on the positive x axis 10 units from the origin.x= and y=Hint: If you get stuck draw a picture.

Correct Answers:

• -5• 2• 10• -4• -1.4142135623731• 1.4142135623731• 0• 0• 10• 0

3. (1 pt) 1010Library/set5 Graphs and Functions/s5p13.pgThe slope of the line through the points (3,2) and (9,1) is

.The slope of the line through the points (8,9) and (9,6) is

.The slope of the line through the points (−6,8) and (7,5) is

.The slope of the line through the points (−2,−8) and

(−6,−2) is .

Hint: The slope of a line is the ratio of rise and run. Draw apicture if necessary.

Correct Answers:

• -0.166666666666667• -3• -0.230769230769231• -1.5

4. (1 pt) 1010Library/set5 Graphs and Functions/s5p14.pg

The line defined by the equation y = 5x + 4 has the x-intercept1

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and the y-intercept .The line defined by the equation y = 6.5x− 8.5 has the x-interceptand the y-intercept .Hint: The x intercept is the x coordinate of the point where theline intersects the x axis. Similarly, the y intercept is the y coor-dinate of the point where the line intersects the y axis. Draw thegraph of the line if necessary.

Correct Answers:• -0.8• 4• 1.30769230769231• -8.5

5. (1 pt) 1010Library/set5 Graphs and Functions/s5p15.pg

The equation6x+8y+8 = 0

has the x-intercept and the y-intercept .It defines a straight line of slopeThe line defined by the equation

8.5x+5.3y+2.1 = 0

has the x-intercept and the y-intercept .Its slope isThe line defined by the equation

−5.2x+4.4y−3.6 = 0

has the x-intercept and the y-intercept .Its slope isHint: See the hints for the preceding problems on graphs ofstraight lines for a definition of the terms involved.

Correct Answers:• -1.33333333333333• -1• -0.75• -0.247058823529412• -0.39622641509434• -1.60377358490566• -0.692307692307692• 0.818181818181818• 1.18181818181818

6. (1 pt) 1010Library/set5 Graphs and Functions/s5p16.pgFor the lines defined by the following equations indicate with a”V” if they are vertical, an ”H” if they are horizontal, and an ”S”(for slanted) if they are neither vertical nor horizontal.

3x+4y+5 = 04y+5 = 03x+5 = 0x = 1y = 1y = x

Hint: Draw the graphs of these lines.Correct Answers:

• S• H• V• V• H• S

7. (1 pt) 1010Library/set5 Graphs and Functions/s5p17.pgFor the pairs of lines defined by the following equations indicatewith an ”I” if they are identical, a ”P” if they are distinct but par-allel, an ”N” (for ”normal”) if they are perpendicular, and a ”G”(for ”general”) if they are neither parallel nor perpendicular.

3x+4y+5 = 0 and 6x+8y+10 = 0.3x+4y+5 = 0 and 3x+4y+7 = 0.3x+4y+5 = 0 and 3x+5y+7 = 0.−4x+3y+5 = 0 and 3x+4y+7 = 0.

Correct Answers:

• I• P• G• N

8. (1 pt) 1010Library/set5 Graphs and Functions/s5p18.pgFor the pairs of lines defined by the following equations indicatewith an ”I” if they are identical, a ”P” if they are distinct but par-allel, an ”N” (for ”normal”) if they are perpendicular, and a ”G”(for ”general”) if they are neither parallel nor perpendicular.

3x+4y+5 = 0 and y =− 34 x− 5

4 .x =

√2 and y = π.

y = x+1 and 3x+5y+7 = 0.y =− 3

4 x and 3x+4y+7 = 0.Correct Answers:

• I• N• G• P

9. (1 pt) 1010Library/set5 Graphs and Functions/s5p19.pg

The slope-intercept equation of the line through the points (9,9)and (4,5) isy = mx+b

where m = and b = .Hint: Compute the slope first and then use one of the points tocompute the y-intercept.

Correct Answers:

• 0.8• 1.8

2

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10. (1 pt) 1010Library/set5 Graphs and Functions/s5p21.pgLet F denote a certain temperature in degrees Fahrenheit, and Cthe same temperature in degrees Celsius. Then you can convertbetween F and C by the formula

F = 32+95

C.

Suppose the temperature is 11 degrees Celsius.

Enter here the corresponding temperature in degreesFahrenheit.Hint: Substitute the value of C in the given formula.

Correct Answers:

• 51.8

11. (1 pt) 1010Library/set5 Graphs and Functions/s5p22.pg

Suppose the temperature is 52 degrees Fahrenheit.

Enter here the corresponding temperature in degreesCelsius.Hint: Substitute the value of F in the formula given in the pre-ceding problem and solve for C.

Correct Answers:

• 11.1111111111111

12. (1 pt) 1010Library/set5 Graphs and Functions/s5p30.pgFor the next few problems you need to understand what it meansto evaluate a function. You simply replace the value of the vari-able with the number at which you evaluate the function. Forexample, the answer to the first question below is 81 since

81 = 8∗9+9.

Let the function f be defined by

f (x) = 8x+9.

Then f (9) = and f (10) =Correct Answers:

• 81• 89

13. (1 pt) 1010Library/set5 Graphs and Functions/s5p31.pg

Let the function f be defined by

f (x) =−9x−5.

Then f (−2) = and f (−1) =Correct Answers:

• 13• 4

14. (1 pt) 1010Library/set5 Graphs and Functions/s5p32.pg

Let the function f be defined by

f (x) = 8x+8.

Then f (5)+ f (2) = and f (5)− f (2) =Correct Answers:

• 72• 24

15. (1 pt) 1010Library/set5 Graphs and Functions/s5p33.pg

Let the function f be defined by

f (x) = 8x+5.

Then f (3)× f (5) = and f (3)/ f (5) =Correct Answers:

• 1305• 0.644444444444444

16. (1 pt) 1010Library/set5 Graphs and Functions/s5p34.pg

Let the function f be defined by

f (x) = 9x+3.

Then f (2)+ f (7) = and f (2+7) =Correct Answers:

• 87• 84

17. (1 pt) 1010Library/set5 Graphs and Functions/s5p35.pg

Let the function f be defined by

f (x) = 7x+9.

Then f (5)× f (8) = and f (5×8) =Correct Answers:

• 2860• 289

18. (1 pt) 1010Library/set5 Graphs and Functions/s5p37.pg

Let the function f be defined by

f (x) = 5x+3.

Then f ( f (9)) = and f ( f (10)) =Hint: As always, first figure out what’s inside the parentheses.

Correct Answers:

• 243• 268

3

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19. (1 pt) 1010Library/set5 Graphs and Functions/s5p38.pgThe next few problems are exercises in identifying the (natural)domain of a function. The concept of a function is very generalbut for our purposes the inputs and outputs of a function are realnumbers. The domain is the set of real numbers at which thefunction can be evaluated, and the range is the set of all possibleoutputs. To determine the domain ask yourself at what pointsthe function can NOT be evaluated. Usually this is because of anundefined operation, which practically speaking means dividingby zero, or extracting the square root of a negative number.

Let the function f be defined by

f (x) =8x+89x+6

.

The domain of f contains all real numbers x except x =

Hint: Never divide by zero.Correct Answers:

• -0.666666666666667

20. (1 pt) 1010Library/set5 Graphs and Functions/s5p39.pg

Let the function f be defined by

f (x) =√

6x+3.

Then x is in the domain of f provided x≥

Hint: There is no real number that is the square root of a nega-tive real number.

Correct Answers:

• -0.5

21. (1 pt) 1010Library/set5 Graphs and Functions/s5p40.pg

Let the function f be defined by

f (x) =√−3x+3.

Then x is in the domain of f provided x≤

Hint: There is no real number that is the square root of a nega-tive real number.

Correct Answers:

• 1

22. (1 pt) 1010Library/set math1010fall2005-90/set5/s5p25/prob.pgMatch the functions with their graphs.

1. F(x) = x+12. F(x) = x−13. F(x) =−x+14. F(x) =−x−1

A B C D

(Click on image for a larger view )

Hint: Draw the graphs of the functions.

(Show hint after 1 attempts. )

Correct Answers:

• A• D• C• B

23. (1 pt) 1010Library/set math1010fall2005-90/set5/s5p26/prob.pgMatch the functions with their graphs.

1. F(x) = 2x+12. F(x) = x+23. F(x) = 2x−14. F(x) = x−2

A B C D

(Click on image for a larger view )

Hint: Draw the graphs of the functions.

(Show hint after 1 attempts. )

Correct Answers:

• B• A• D• C

24. (1 pt) 1010Library/set math1010fall2005-90/set5/s5p27/prob.pgMatch the equations with their graphs.

1. 2y−2x−2 = 02. 2y−2x−4 = 03. y+ x−1 = 04. y+ x+1 = 0

4

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A B C D

(Click on image for a larger view )

Hint: Draw the graphs of the equations.

(Show hint after 1 attempts. )

Correct Answers:

• D• C• B• A

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

5

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 5 is due : 10/21/2008 at 11:59pm MDT.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p1.pgThe first few problems are exercises in solving inequalities andusing interval notation, as described in sections A1 and A6 ofthe textbook. For example, the set of inequalities

−1 < x≤ 3

describes the interval (−1,3] Enter that interval by typing around opening parenthesis, the number -1, the number 3, anda square closing parenthesis in the following four answer fields:

, .In this problem, WeBWorK will tell for each answer individu-ally if it is correct, so you can check what you are doing. In thefollowing problems you will need to get all answers right beforegetting credit.

Correct Answers:• (• -1• 3• ]

2. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p2.pgThe inequalities

5≤ x < 12describe the interval:

, .Correct Answers:

• [• 5• 12• )

3. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p23.pgSuppose you have a circle with diameter d. Then its radius is

, its circumference is , and its area is . All youranswers should be in terms of d. Use pi to denote π.

Correct Answers:

• d/2• pi*d• pi*d*d/4

4. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p24.pgConsider the line passing through the points (2,6) and (−2,5).It can be written in slope-intercept form as

y = x+ .Correct Answers:

• 0.25• 5.5

5. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p25.pgConsider the line of slope −2 passing through the point (1,1) Itcan be written in slope-intercept form as

y = x+ .Correct Answers:

• -2• 3

6. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p26.pgConsider the line with x intercept 2 and y-intercept −2. It canbe written in slope intercept form as

y = x+ .Correct Answers:

• 1• -2

7. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p27.pgConsider two lines. One has slope 2 and y intercept -3. Theother passes through the points (1,2) and (−2,3). The two linesintercept in the point ( , ).

Correct Answers:

• 2.28571428571429• 1.57142857142857

1

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8. (1 pt) 1050Library/set4 Functions and Their Graphs/1050s4p29.pgThe next three problems explore some techniques of data anal-ysis.

According to the US Bureau of the Census, the world pop-ulation in the year 1950 was A = 2555360972, and in 2000 itwas B = 6079006982. We’ll use A and B so we don’t have tokeep writing those large and idiosyncratic numbers. We usuallyuse y and x in the equation of a line, but in this and the followingproblem let’s use N and t instead. t stands for time and N for thesize of the population.

If

N(t) = mt +b

such that N(1950) = A and N(2000) = B, thenm = and and b = .

Suppose you want to estimate the population in 1975. To thatend you compute N(1975) = . (Round your answers to thenearest integer. The process illustrated in this problem is calledlinear interpolation .)

Correct Answers:

• 70472920• -134866833018• 4317183982

9. (1 pt) 1050Library/set5 Functions and Their Graphs/1050s5p1.pgThe first five problems in this set were motivated by the feed-back I received on problem 22 (that airplane problem...) of set2. I thought of it as a routine problem, but it seems to havebeen quite difficult for a good number of people. These first fiveproblems illustrate a major principle of problem solving:

If a problem is hard simplify it and first solve the simplerproblem.

Put a little more loosely: If at first you don’t succeed, dosomething easier.

To appreciate this lesson, before you start on this problem,try problem 5 on this set. You’ll see it’s tricky. But it will be apiece of cake after you solve the first four problems.

So if you find yourself again (in this class, or much beyond it)facing a hard problem, attack it by building a sequence of easierproblems, the easiest being very easy, that lead to the difficultproblem and, in the end, make it easy to solve the hard problem.

You and your friend part at an intersection. You drive offnorth at 50 mph, and your friend drives east at 50mph. Af-ter three hours the distance between you and your friend is

miles.Hint: Use the Pythagorean Theorem.

Correct Answers:

• 212.132034355964

10. (1 pt) 1050Library/set5 Functions and Their Graphs/1050s5p7.pgConsider the function f defined by

f (x) =x2 +3x−5

ThenA. f (1) =B. f (−3) =C. f

( 23

)=

Correct Answers:

• -1• -1.5• -0.794871794871795

11. (1 pt) 1050Library/set5 Functions and Their Graphs-/1050s5p23.pgThe next few problems deal with the question of whether anequation defines one of the variables as a function of the other.You can answer all of these questions by seeing if the equationcan be solved for one variable in terms of the other.

For example, the equation

y− x2 = 0

can be rewritten asy = x2

and so any choice of x uniquely determines y. We can think of yas being given by the function

y = f (x) = x2.

On the other hand, for a particular value of y, e.g., y = 1, thereare two values of x, i.e., x =±1, and so the equation y− x2 = 0does not define x as a function of y. Similarly, by switching theroles of x and y we see that the equation

y2− x = 0

defines x as a function of y, but not y as a function of x.

By contrast, the equation

3x+4y = 5

determines x as a function of y and also determines y as a func-tion of x, while the equation

x2 + y2 = 1

defines neither variable as a function of the other.

You can verify all of the above statements by applying the ver-tical and horizontal line tests.

For the following equations, enter

2

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y if the equation defines y as a function of x but not vice versa,

x if the equation defines x as a function of y but not vice versa,

b (for ”both”) if the equation defines x as a function of y andalso y as a function of x, and

n (for ”neither”) if the equation defines neither variable as afunction of the other.

These equations are the same as discussed above, so you cancheck that you understand how to answer this and the followingquestions:

y− x2 = 0 .

y2− x = 0 .

3x+4y+5 = 0 .

x2 + y2 = 1 .

Correct Answers:

• y• x• b• n

12. (1 pt) 1010Library/set13 Systems of Equations and Inequalities-/s13p3.pgA linear system may have a unique solution, no solution, or in-finitely many solutions. Indicate the type of the system for thfollowing examples by U , N , or I , respectively.

1.2x+3y = 52x+3y = 6

2.2x+3y = 54x+6y = 10

3.2x+3y = 52x+4y = 6

Hint: The issues are discussed here. If you can’t tell the na-ture system by inspection try to solve the system and see whathappens.

Correct Answers:

• N• I• U

13. (1 pt) 1010Library/set13 Systems of Equations and Inequalities-/s13p4.pgA linear system may have a unique solution, no solution, or in-finitely many solutions. Indicate the type of the system for thfollowing examples by U , N , or I , respectively.

1.2x+3y = 5

x+6y = 7

2.−2x+ y = 5

2x− y = −5

3.x− y = 15y− x = 15

4.2x+3y = 14x+6y = 1

5.x+ y = 5

x+2y = 10

Hint: This is like the preceding problem. If you are stuck, solvethe linear systems and see if you come up with a contradiction(i.e., no solution), a unique solution, or infinitely many solu-tions.

Correct Answers:

• U• I• N• N• U

14. (1 pt) 1050Library/set10 Systems of Equations and Inequalities-/1050s10p10.pg

The solution of the linear system

x +y = 73x −y = 1

isx = and y = .Correct Answers:

• 2• 5

15. (1 pt) 1050Library/set10 Systems of Equations and Inequalities-/1050s10p11.pg

The solution of the linear system

x +y = 13x −y = 2

isx = and y = .Correct Answers:

• 0.75• 0.25

3

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16. (1 pt) 1010Library/set13 Systems of Equations and Inequalities-/s13p1.pgAs a warm-up solve the following linear system:

2x +3y = 1x −y = 3

The solution of this system isx = and y = .Hint: Subtract twice the second equation from the first, or addthree times the second equation to the first.

Correct Answers:

• 2• -1

17. (1 pt) 1010Library/set13 Systems of Equations and Inequalities-/s13p2.pgThe solution of the linear system

2x +3y = 3x −y = 1

x = and y = .Hint: Only the right hand side makes this system different fromthe preceding one. So proceed similarly. I would enter my an-swers as fractions.

Correct Answers:

• 6/5• 1/5

18. (1 pt) 1090Library/set2 Linear Equations and Functions/p15.pgYou wish to invest $900 over one year in two accounts paying5% and 6% annually. How much should you invest in each toearn $50?

Answer: in the 5% account and in the6% account.

Correct Answers:

• 400• 500

19. (1 pt) 1090Library/set2 Linear Equations and Functions/p23.pgThe length of a rectangular garden is 10 feet longer than itswidth. If the garden’s perimeter is 192 feet, what is the area ofthe garden in square feet?

Correct Answers:

• 2279

20. (1 pt) 1090Library/set2 Linear Equations and Functions/p24.pgA cash register contains only five dollar and ten dollar bills. Itcontains twice as many fives as tens and the total amount ofmoney in the cash register is 720 dollars. How many tens are inthe cash register?

Correct Answers:• 36

21. (1 pt) 1090Library/set2 Linear Equations and Functions/p25.pg

What quantity of 60 percent acid solution must be mixed with a25 percent solution to produce 336 mL of a 50 percent solution?

Correct Answers:• 240

22. (1 pt) 1090Library/set6 Linear Equations and Functions/p11.pgFind an equation of the horizontal line passing through the point(-4, -1).

y =Correct Answers:

• -1

23. (1 pt) 1090Library/set6 Linear Equations and Functions/p12.pgFind an equation of the vertical line passing through the point(-4, -2).

x =Correct Answers:

• -4

24. (1 pt) 1090Library/set6 Linear Equations and Functions/p15.pgFind an equation of a line parallel to y = 4x + 4 and passingthrough the point (4, 2).

y =Correct Answers:

• 4(x-4)+2

25. (1 pt) 1090Library/set6 Linear Equations and Functions/p21.pgThe consumers will demand 39 units when the price of a prod-uct is $52, and 52 units when the price is $37. Find the demandfunction (express thr price p in terms of the quantity q), assum-ing it is linear.

p =Correct Answers:

• -15/13(q-39)+37+15

26. (1 pt) 1090Library/set6 Linear Equations and Functions/p24.pgDetermine the linear function f knowing the slope is 3 andf (15) = 16.

f (x) =Correct Answers:

• 3(x-15)+16

4

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Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

5

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 6 is due : 10/21/2008 at 11:59pm MDT.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1050Library/set3 Polynomial and Rational Functions-/1050s3p6.pgThe next few problems reinforce your mastery of exponents.Remember that you multiply powers with the same base byadding the exponents, you divide them by subtracting the ex-ponents, and you take a power to a power by multiplying theexponents.

We begin by reviewing some basic identities.

aman = az

where z = .

(am)n = az

where z = .Correct Answers:

• m+n• m*n

3. (1 pt) 1050Library/set3 Polynomial and Rational Functions-/1050s3p8.pgIf

2x×23 = 27

then x = .Correct Answers:

• 4

5. (1 pt) 1050Library/set3 Polynomial and Rational Functions-/1050s3p10.pgIf

2x

23 = 27

then x = .Correct Answers:

• 10

6. (1 pt) 1050Library/set3 Polynomial and Rational Functions-/1050s3p11.pgIf

23

2x = 27

then x = .Correct Answers:

• -4

7. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p7.pgLet the polynomial p be defined by

p(x) = 2x3−3x2 +4x−5

Thenp(1) = ,p(2) = , andp(−1) = .

Correct Answers:

• -2• 7• -14

8. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p10.pgLet the polynomial p be defined by

p(x) =−6x3−2x2 +3x−9.

The degree of p is ,its leading coefficient is ,and its constant term is ,

Correct Answers:

• 3• -6• -9

1

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9. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p11.pgLet the polynomial p be defined by

p(x) =−6x3−2x2 +3x.

The degree of p is ,its leading coefficient is ,and its constant term is ,

Correct Answers:

• 3• -6• 0

10. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p13.pgLet the polynomial p be defined by

p(x) = (9x−8)(6x+9).

The degree of p is ,its leading coefficient is ,and its constant term is ,Hint: Apply the distributive law to convert the polynomial tostandard form.

Correct Answers:

• 2• 54• -72

11. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p15.pgLet the polynomial p be defined by

p(x) = (x−1)(x−2)(x−3)(x−4)

The degree of p is ,its leading coefficient is ,and its constant term is ,Hint: You can answer these questions without converting thepolynomial to standard form.

Correct Answers:

• 4• 1• 24

12. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p19.pgLet the polynomial p be defined by

p(x) = (x−1)(x2 + x+1).

Thenp(x) = x3 + x2 + x +Note: some of the coefficients may be negative.Hint: Once again, apply the Distributive Law.

Correct Answers:

• 1• 0• 0• -1

13. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p24.pgIndicate with true (T) or false (F) whether the following func-tions are polynomials.

f (x) = x+2.

f (x) =√

2.f (x) =

√x.

f (x) = |x|.f (x) = 1

x .

f (x) = (x+1)200000.

f (x) =√

1+ x2.Hint: You need to understand the definition of the wordpolynomial.

Correct Answers:

• T• T• F• F• F• T• F

14. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p25.pgMatch the verbal descriptions with the given polynomials. Youneed to use all polynomials and all descriptions. Recall thatpolynomials of degrees 0, 1, 2, 3, 4, 5, are called constant, lin-ear, quadratic, cubic, quartic, and quintic , respectively. Alsorecall the definitions of the terms monomial, binomial, trinomial, given here.

You must get all of the answers correct to receive credit.

1. The square of a cubic polynomial2. A quintic monomial.3. A trinomial4. A quartic binomial5. A cubic polynomial

A. x3 +3x2 +3x+1B. πx5

C. (x3 +1)2

D. x2 +2x+1E. x4−2x3

Hint: Check here for the relevant definitions.l.Correct Answers:

• C• B• D• E• A

2

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15. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p27.pgThink about the following statements and indicate whether theyare true (T) of false (F).

You need to get all answers correct before obtaining credit.

The product of 2 linear polynomials is quadratic.

The sum of two cubic polynomials cannot have a degreegreater than 3.

The sum of two cubic polynomials may have a degree lessthan 3.

The sum of a cubic and a quartic polynomial may have adegree different from 4.

The product of two monomials is a monomial.

The product of two binomials is a binomial.

Hint: Look at an example. Try to prove the statement wrong byfinding an example where it does not hold.

Correct Answers:• T• T• T• F• T• F

16. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p28.pgThink about the following statements and indicate whether theyare true (T) or false (F).

You need to get all answers correct before obtaining credit.

The graph of a linear polynomial is a straight line.

The degree of a trinomial is at least 2.

The product of two polynomials is always a polynomial.

The quotient of two polynomials is always a polynomial.

The sum of two polynomials is always a polynomial.

The difference of two polynomials is always a polynomial.

Hint: Look at an example. Try to prove the statement wrong byfinding an example where it does not hold.

Correct Answers:

• T• T• T• F• T• T

17. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p32.pgThe obelisk in the movie 2001 has the shape of a rectangularbox with lengths x, 4x, and 9x, where x is a parameter.The volume V of the obelisk is a polynomial expression in x ofdegree and leading coefficient .In fact, V = (enter an expression in x).Hint: The volume of a brick shaped object equals length timeswidth times height.

Correct Answers:

• 3• 36• 36*x*x*x

18. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p33.pgThe area A of that same obelisk is a polynomial expression in xof degree and leading coefficient .In fact, A = (enter an expression in x).Hint: Compute the area of each face and add those areas.

Correct Answers:

• 2• 98• 98*x*x

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

3

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 1 is due : 10/21/2008 at 11:59pm MDT.The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making

some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set1 WebWork Demo/m1p165.pgEnter here the expression 1

a + 1b .

Enter here the expression 1a+b .

Correct Answers:

• 1/a+1/b• 1/(a+b)

2. (1 pt) 1010Library/set1 WebWork Demo/s1.p29.pg

For each of the WeBWorK phrases below enter a T (true)if the two given phrases describe the same algebraic expressionand a F (false) otherwise. One way you can decide whether thephrases are equivalent is to substitute specific values for a, b,etc. If you get two different results the two phrases are certainlynot equivalent. If you get the same values there is small chancethis happened accidentally for just that choice of particular val-ues. In any case, pay close attention to when these phrases areequivalent and when they are not, it will help you tremendouslywith future WeBWorK assignments.

a+b2 (a+b)2

a2 +b2 (a+b)2

a∗b∗ c a∗ (b∗ c)

a/b/c a/(b/c)

Correct Answers:

• F• F• T• F

3. (1 pt) 1010Library/set1 WebWork Demo/s1p1.pgThis first question is just an exercise in entering answers intoWeBWorK. It also gives you an opportunity to experiment withentering different arithmetic and algebraic expressions intoWeBWorK and seeing what WeBWorK really thinks you are do-ing (as opposed to what you believe it should think).

Notice the buttons on this page and try them out before moving

to the next problem. Use the ”Back” Button on your browser toget back here when needed.

”Prob. List” gets you back to the list of all problems in this set.

”Next” gets you to the next question in this set.

”Submit Answer” submits your answer as you might expect, butthere may be other ways to do so. Specifically, in this problem,there is only one question. In that case you can submit youranswer by typing it into the answer window and then pressing”Return” (or ”Enter”) on your keyboard. But even in this case,you can also type the answer and click on the ”submit” button.There is no harm in submitting an answer even if you are notquite sure that it’s correct, since if it is not you have an unlim-ited number of additional tries. On the other hand, it is usuallymore efficient to print your own private problems set, work outthe answers in a quiet environment like your home, and then sitdown in front of a computer and enter your answers. If someare wrong you can try to fix them right at the computer, or youmay want to go back and work on them quietly elsewhere beforereturning to the computer.

Pressing on the ”Preview Answer” Button makes WeBWorKdisplay what it thinks you entered in the answer window. Afterusing ”Preview” you can modify your answer and use a ”Pre-view Again” button.

”images” denotes the ordinary display mode on your worksta-tion.

”Logout” terminates this WeBWorK session for you. You canof course log back in and continue.

”Feedback” enables you to send a message to your instructor,and the WeBWorK assistants. If you use this way of sendinge-mail the recipients receive information about your WeBWorKstate, in addition to your actual message.

The ”Help” Button transports you to an official WeBWorK helppage that has a more information than this first problem.

1

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”Problem Sets” transports you back to the page where you canselect a certain problem set. When you do this particular prob-lem in this first set, there is only one set, but eventually therewill be 13 of them.

For all problems in this course you will be able to see the An-swers to the problems after the due date . Go to a problem,click on ”show correct answers”, and then click on ”submit an-swer”. You can also download and print a hard copy with theanswers showing. These answers are the precise strings againstwhich WeBWorK compares your answer. If the answer is analgebraic expression your answer needs to be equivalent to theWeBWorK answer, but it may be in a different form. For ex-ample if WeBWorK thinks the answer is 2 ∗ a, it is OK for youto type a + a instead. If WeBWorK expects a numerical an-swer then you can usually enter it as an arithmetic expression(like 1/7 instead of .142857), and usually WeBWorK will ex-pect your answer to be within one tenth of one percent of whatit thinks the answer is.

Most of the problems (including this one) in this course willalso have solutions attached that you can see after the due dateby clicking on ”show solutions” followed by ”submit answers”.The solutions are text typed by your instructor that gives moreinformation than the ”answers”, and in particular often explainshow the answers can be obtained.

Now for the meat of this problem. Notice that the answer win-dow is extra large so you can try the things suggested above.

Type the number 3 here:.

Try entering other expressions and use the preview buttonto see what WeBWorK thinks you entered. Return to thisproblem to try out things when you get stuck somewhereelse.

Here are some good examples to try. Check them all out usingthe Preview button. (In later questions on this set you will getto use what you learn here.) Never mind that you may have al-ready answered the correct answer 3. Once you get credit for ananswer it won’t be taken away by trying other answers.

a/2b versus a/2/b versus a/(2b)

a/b+c versus a/(b+c)

a+b**2 versus (a+b)**2

sqrt a+b versus sqrt(a+b)

4/3 pi r**2 versus (4/3) pi r**2 (In other words, if you are notsure use parentheses freely.)

Note: WeBWorK will not usually let you enter algebraic ex-pressions when the answer is a number, and it will only let youuse certain variables when the answer is in fact an algebraic ex-pression. So the above window, and the opportunity for exper-imentation that it offers is unique. Make good use of it!

Presumably this has been your first encounter with WeBWorK.Come back here to try things out and to refresh your memory ifyou get stuck somewhere down the line.

Correct Answers:

• 3

4. (1 pt) 1010Library/set1 WebWork Demo/s1p2.pgThe purpose of this exercise is to illustrate further the use of thebuttons on this page and to show you the most common way inwhich WeBWorK processes partially correct problems. Try en-tering incorrect answers in the answer fields below, to see whathappens. (This time WeBWorK will reject algebraic expressionssince I told it to expect a numerical answer.)

Type the number 4 here: .

Type the number 5 here: .

Correct Answers:

• 4• 5

5. (1 pt) 1010Library/set1 WebWork Demo/s1p3.pg

In the first few problems, now that you are familiar with thebasic mechanics of WeBWorK, you will be asked to evaluatesome arithmetic expressions and enter the answer as a numberinto WeBWorK. You may of course use a calculator. In laterproblems you will be able to enter the answer as an arithmeticexpression, but at present your answer must be a number suchas 4, -4, or 17.5.

Evaluate the expression4(5 + 9) = . (Remember that by conventiona missing arithmetic operator means multiplication .)

Correct Answers:

• 56

6. (1 pt) 1010Library/set1 WebWork Demo/s1p4.pg

Evaluate the expression9(3−3) = .

Correct Answers:

• 0

2

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7. (1 pt) 1010Library/set1 WebWork Demo/s1p5.pg

Evaluate the expression5/(4+6) = .Enter your answer as a decimal number listing at least 4 decimaldigits. (WeBWorK will reject your answer if it differs by morethan one tenth of 1 percent from what it thinks the answer is.)

Correct Answers:

• 0.5

8. (1 pt) 1010Library/set1 WebWork Demo/s1p6.pg

Evaluate the expression18− (9−8) = .

Correct Answers:

• 17

9. (1 pt) 1010Library/set1 WebWork Demo/s1p7.pg

Evaluate the expression8− (3−6) = .

Correct Answers:

• 11

10. (1 pt) 1010Library/set1 WebWork Demo/s1p8.pgThis problem illustrates the standard rules of arithmetic prece-dence:

Multiplication and Division precede Subtraction and Addition.Among operations with the same level of precedence, evalua-tion proceeds from left to right.However, expressions in parentheses are evaluated first.

Evaluate the expression6×6−3×6 =

Evaluate the expression6× (6−3)×6 =

Evaluate the expression6× (6−3×6) =

Correct Answers:

• 18• 108• -72

11. (1 pt) 1010Library/set1 WebWork Demo/s1p9.pgThis problem provides more illustrations of the use of parenthe-ses.

Evaluate the expression8−4−2−3 =

Evaluate the expression8− (4−2)−3 =

Evaluate the expression8− (4−2−3) =

Evaluate the expression8− (4− (2−3)) =

Correct Answers:• -1• 3• 9• 3

12. (1 pt) 1010Library/set1 WebWork Demo/s1p10.pgThe key idea in Algebra is to use variables in addition to num-bers. Sometimes we need to replace variables with specificnumbers. That’s called evaluating an algebraic expression.For example, if a = 2 then 3a = 6, and we say that we evaluatedthe expression 3a at a = 2. We’ll do this sort of thing all semes-ter long, and in this problem you get your first experience withevaluating algebraic expressions. Again, the emphasis in theseexercises is on understanding the rules of arithmetic precedence.

Let a = 11, b = 4, c = 13.Then a−b/c =and (a−b)/c =As usual, enter your answers as decimal numbers with at

least 4 digits.Correct Answers:

• 10.6923076923077• 0.538461538461538

13. (1 pt) 1010Library/set1 WebWork Demo/s1p11.pgLet r = 7.

Then 4/π∗ r =and 4/(π∗ r) =Correct Answers:

• 8.91267681314614• 0.181891363533595

14. (1 pt) 1010Library/set1 WebWork Demo/s1p12.pgLet a = 4, b = 7, c = 10, d = 12.

Then a−b/c−d = ,

(a−b)/(c−d) = ,a− (b/c−d) = , anda−b/(c−d) = .

3

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Correct Answers:

• -8.7• 1.5• 15.3• 7.5

15. (1 pt) 1010Library/set1 WebWork Demo/s1p13.pgThe next three problems are like the preceding three, except thatyou need to get all answers correct before WeBWorK will giveyou credit. This will be true for many problems in this class.The purpose of insisting on all answers being correct is to en-courage you to think about the whole context of the problemrather than the individual pieces.

Let a = 2.9, b = 5.7, c = 7.1.Then a−b/c =and (a−b)/c =Correct Answers:

• 2.09718309859155• -0.394366197183099

16. (1 pt) 1010Library/set1 WebWork Demo/s1p14.pgLet r = 8.3.

Then 4/π∗ r =and 4/(π∗ r) =Correct Answers:

• 10.5678882213019• 0.153402354787369

17. (1 pt) 1010Library/set1 WebWork Demo/s1p15.pgLet a = 4.1, b = 6.9, c = 7.9, d = 9.9.

Thena−b/c−d = ,

(a−b)/(c−d) = ,a− (b/c−d) = , anda−b/(c−d) = .

Correct Answers:

• -6.67341772151899• 1.4• 13.126582278481• 7.55

18. (1 pt) 1010Library/set1 WebWork Demo/s1p16.pgIn this and the following problems you will practice en-tering algebraic expressions into WeBWorK. Remember theRules of Arithmetic Precedence and use parentheses to makeyour meaning clear. Most of the difficulties students have withWeBWorK are due to not appreciating the precise rules that gov-ern the interpretation of what you enter. This is not just a matterof WeBWorK understanding what you are trying to say, Therules are used universally all over the world. Appreciating andapplying them properly is also crucial, for example, in computerprogramming. Make sure you understand what’s going in theseproblems. If you enter a wrong expression use the Preview But-ton to see what WeBWorK thinks you have entered.

We start simply. Enter here the expression a+b.Correct Answers:

• a+b

19. (1 pt) 1010Library/set1 WebWork Demo/s1p17.pgEnter here the expression

a+12+b

Enter here the expression

a+bc+d

If WeBWorK rejects your answer use the preview button tosee what it thinks you are trying to tell it.

Correct Answers:

• (a+1)/(2+b)• (a+b)/(c+d)

20. (1 pt) 1010Library/set1 WebWork Demo/s1p18.pgEnter here the expression

11a + 1

b

Enter here the expression

a+b+11+ 1

a+b

Correct Answers:

• 1/(1/a+1/b)• (a+b+1)/(1+1/(a+b))

21. (1 pt) 1010Library/set1 WebWork Demo/s1p19.pg

Enter here the expressionab + c

def + g

h.

Correct Answers:

• (a/b+c/d)/(e/f+g/h)

22. (1 pt) 1010Library/set1 WebWork Demo/s1p20.pg

The square x2 of a number x simply means the product of xwith itself. For example, 32 = 3∗3 = 9. You can enter a numbersuch as 32 as 3**2 . (An expression such as 32 or x2 is calleda power . We will learn a great deal more about powers duringthis semester.)

Enter here the expression x2

The square root√

x of a number x is a number whose squareequals x. For example

√25 = 5 since 52 = 5∗5 = 25.

4

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To enter square roots you can use the function sqrt . Forexample, to enter the square root of 2 you can type sqrt (2).

Enter here the expression√

aCorrect Answers:

• x**2• sqrt{a}

23. (1 pt) 1010Library/set1 WebWork Demo/s1p21.pgEnter here the expression

√a+b

Enter here the expressiona√

a+bEnter here the expression

a+b√a+b

Correct Answers:

• sqrt(a+b)• a/sqrt(a+b)• (a+b)/sqrt(a+b)

24. (1 pt) 1010Library/set1 WebWork Demo/s1p22.pg

Enter here the expression√x2 + y2

Enter here the expression

x√

x2 + y2

Enter here the expressionx+ y√x2 + y2

Correct Answers:

• sqrt(x**2+y**2)• x*sqrt(x**2+y**2)• (x+y)/sqrt(x**2+y**2)

25. (1 pt) 1010Library/set1 WebWork Demo/s1p23.pg

Enter here the expression

−b+√

b2−4ac2a

Note: this is an expression that gives the solution of a quadraticequation by the quadratic formula . We will learn much moreabout it later in the semester.

Correct Answers:

• (-b+sqrt(b**2-4*a*c))/(2a)

26. (1 pt) 1010Library/set1 WebWork Demo/s1p24.pgConsider the following expressions:

A = a+bc

and

B =a+b

cFor each of the WeBWorK phrases below write A if they de-

fine A and B if they define B.

You need to get all answers correct before obtaining credit.

a+b/c (This is the standard way to enter A, so enter A).

(a+b)/c (This is the standard way to enter B, so enter B).

((a+b)/c)

a+(b/c)

(a+(b/c))

Correct Answers:

• A• B• B• A• A

27. (1 pt) 1010Library/set1 WebWork Demo/s1p25.pgConsider again the formula for the solution of a quadratic equa-tion:

x =−b+

√b2−4ac

2aFor each of the WeBWorK phrases below enter a T (true) if

the phrase describes x, correctly, and a F (false) otherwise.

You need to get all answers correct before obtaining credit.

-b+sqrt(b**2-4*a*c)/2a

(-b+sqrt(b**2-4*a*c))/2a

(-b+sqrt(b**2-4*a*c))/(2a)

Correct Answers:

• F• F

5

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• T

28. (1 pt) 1010Library/set1 WebWork Demo/s1p26.pgMore of the same.

(-b+sqrt(b**2-(4*a*c)))/(2a)

(-b+(sqrt(b**2-4*a*c)))/(2a)

((-b+sqrt(b**2-4*a*c))/(2a))

(-b+(sqrt(b**2-4*a*c))/(2a))

(-b+sqrt(b*b-(4*a*c)))/(2a)

Correct Answers:

• T• T• T• F• T

29. (1 pt) 1010Library/set1 WebWork Demo/s1p27.pg

For each of the WeBWorK phrases below enter a T (true) ifthe two given phrases describe the same algebraic expressionand an F (false) otherwise. One way you can decide whether thephrases are equivalent is to substitute specific values for a, b,etc. If you get two different results the two phrases are certainlynot equivalent. If you get the same values there is small chancethis happened accidentally for just that choice of particular val-ues. In any case, pay close attention to when these phrases areequivalent and when they are not, it will help you tremendouslywith future WeBWorK assignments.

a+b b+a

a+b+ c a+(b+ c)

a−b− c a− (b− c)

Correct Answers:

• T• T• F

30. (1 pt) 1010Library/set1 WebWork Demo/s1p28.pg

More of the same.

a+b2 (a+b)2

a2 +b2 (a+b)2

a∗b∗ c a∗ (b∗ c)

a/b/c a/(b/c)

Correct Answers:• F• F• T• F

31. (1 pt) 1010Library/set1 WebWork Demo/s1p29.pg

In mathematics, lower and upper case letters mean differentthings. The letter a is not the same as the letter A. Keep that inmind when answering the questions below, using T or F as inthe preceding questions.

a a

a A

a+A A+a

Correct Answers:• T• F• T

32. (1 pt) 1010Library/set1 WebWork Demo/s1p30.pg

Much of this course will center around the manipulation ofalgebraic expressions, often with the goal of solving an equa-tion. This exercise is the first step in this direction. Again, indi-cated with T or F if the two expressions are equivalent.

a∗ (b+ c) a∗b+a∗ c

1/(a+b) 1/a+1/b

1/a/a 1/(a∗a)

Correct Answers:• T• F• T

33. (1 pt) 1010Library/set1 WebWork Demo/s1p31.pg

The reason why Mathematics is required for so many sub-jects is that it can be used to solve problems outside of mathe-matics, the dreaded word problems . There will be many wordproblems in this class, usually leading to a mathematical prob-lem of the kind we are discussing at the time. Students don’tlike word problems because they involve the extra layer of con-verting the word problem to a math problem. But keep in mind

6

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that math classes are the only kind of classes you take wheresome problems are not word problems!

This first word problem of this course can be solved by derivingand solving an equation, but it can also be solved essentially byguessing and modifying the answer until it fits, without any al-gebraic manipulation. We will revisit it in the future in a morecomplicated setting.

You buy a pot and its lid for a total of $ 11. The sales per-son tells you that the pot by itself costs $ 10 more than the lid.The price of the pot is $ and the price of the lid is $

.Correct Answers:

• 10.5• 0.5

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

7

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 7 is due : 11/03/2008 at 10:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set10 Polynomials and Factoring/s10p1.pgUse synthetic division to divide a polynomial with remainder.

x2 +2x+4 = (x−1)× ( )+( )Correct Answers:

• x+3• 7

2. (1 pt) 1010Library/set10 Polynomials and Factoring/s10p2.pgUse synthetic division to divide these two polynomials with re-mainder:

x2 +11x+32 = (x+5)× ( )+( )

x2 +5x+7 = (x+2)× ( )+( )Hint:

This is like the preceding problem.Correct Answers:

• x+6• 2• x+3• 1

3. (1 pt) 1010Library/set10 Polynomials and Factoring/s10p3.pgUse synthetic division to divide these two polynomials with re-mainder:

x2−8x−5 = (x−9)× ( )+( )x2−1x−37 = (x+6)× ( )+( )

Correct Answers:

• x+1• 4• x+-7• 5

4. (1 pt) 1010Library/set10 Polynomials and Factoring/s10p5.pgThis is like the preceding problems except that you divide by aquadratic term and obtain a linear remainder. Use long divisionto divide these two polynomials with remainder:

2x4 +11x3 +19x2 +x−29 = (x2 +4x+6)× ( )+()

Correct Answers:

• 2*x**2+3*x-5• 3*x+1

5. (1 pt) 1010Library/set10 Polynomials and Factoring/s10p6.pgUse long division to divide these two polynomials with remain-der:6x4 + 2x3− 3x2 + 20x− 22 = (3x2− 2x + 5)× ( )+ (

)Hint: This is exactly like the preceding problem.

Correct Answers:

• 2x**2+2*x-3• 4*x-7

6. (1 pt) 1010Library/set10 Polynomials and Factoring/s10p19.pgA boat travels at a speed of 20 miles per hour in still water. Ittravels 48 miles upstream, and then returns to the starting pointin a total of five hours. The speed of the current is miles perhour.Hint: Set up and solve a quadratic equation.

Correct Answers:

• 4

7. (1 pt) 1010Library/set10 Polynomials and Factoring/s10p20.pgThe speed of a commuter plane is 150 miles per hour slowerthan that of a passenger jet. The commuter plane travels 450miles in the same time the jet travels 1150 miles. The speed ofthe commuter plane is miles per hour and that of the jet is

miles per hour.Hint: Set up and solve a linear equation.

Correct Answers:

• 96.4285714285714• 246.428571428571

1

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8. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p8.pgLet the polynomial p be defined as in the preceding problem by

p(x) = 2x3−3x2 +4x−5

Suppose you evaluate the polynomial at x = 2 us-ing synthetic division (also called nested multiplication orHorner’s scheme). You obtain an array that has three rows,with four entries in the first and third rows, and three in the sec-ond. The entries in the first row are (from left to right):

, , , and ,The entries in the second row start in the second column, andare, from left to right:

, , and .The entries in the third row are from left to right:

, , , and .Correct Answers:

• 2• -3• 4• -5• 4• 2• 12• 2• 1• 6• 7

9. (1 pt) 1010Library/set9 Polynomials and Factoring/s9p1.pgRecall that the height h(t) at the time t of a rock tossed into theair at time 0 from a height h0 at an initial velocity v0 is given by

h(t) = h0 + v0t−16t2.

Time is measured in seconds, height in feet, and velocity in feetper second. The positive direction is up, so if the rock is movingdown then its velocity is negative. The magic number 16 in thisequation is due to the mass and radius of earth and would bedifferent for example on Mars or on the Moon. The velocity ofthe rock at time t is given by

v(t) = v0−32t.

Suppose you throw a rock upward from a height of 64 feetwith an initial velocity of 48 feet per second. The rock will hitthe ground after seconds.Hint: Solve a quadratic equation.

Correct Answers:

• 4

10. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p1.pgSimplify the expression 15x+21

9x+15 = ( )/( ).Hint: Look for an integer factor that’s common to numeratorand denominator.

Correct Answers:

• 5x+7• 3x+5

11. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p3.pg

Simplify the expression x2+2xx2−x = ( )/( ).

Hint: If you are having difficulties with this problem it’ s prob-ably because you are looking for something that is much com-plicated than the actual answer. Think about the constant termin numerator and denominator.

Correct Answers:

• x+2• x-1

12. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p4.pgCancel common polynomial and integer factors. and fill in theblanks.x2+7x+12x2+9x+18 = (x+ ) /(x+ )For this identity to hold, x must not equal .Hint: If you have difficulties seeing how to factor the numeratorand denominator set them to zero, solve the resulting equation,and deduce the appropriate linear factors from the solution.Then cancel the common factor in numerator and denominator.

Correct Answers:

• 4• 6• -3

13. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p5.pgCancel common polynomial and integer factors. and fill in theblanks.x2−4x+3

x2−7x+12 = (x− ) /(x− )For this identity to hold, x must not equal .Hint: If you have difficulties seeing how to factor the numeratorand denominator set them to zero, solve the resulting equation,and deduce the appropriate linear factors from the solution.Then cancel the common factor in numerator and denominator.

Correct Answers:

• 1• 4• 3

14. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p7.pg

Simplify the expression x3+2x2−x−2x2+5x+6 = ( )/( ).

Hint: Find a linear factor that’s common to numerator and de-nominator. The denominator is easy to factor, set it to zero andsolve if you don’t see the factors. Then see if one of the twofactors is a factor of the numerator.

Correct Answers:

• xˆ2-1• x+3

2

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15. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p9.pg

1x+1 + 1

x+4 = ( )/( ).1

x+1 −1

x+4 = ( )/( ).1

x+1 ×1

x+4 = ( )/( ).1

x+1 ÷1

x+4 = ( )/( ).Hint: Rational expressions work just like fractions.

Correct Answers:• 2*x+1+4• (x+1)*(x+4)• 4-1• (x+1)*(x+4)• 1• (x+1)*(x+4)• x+4• x+1

16. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p11.pg

11x+15 + 7

x+12 = ( )/( ).11

x+15 −7

x+12 = ( )/( ).11

x+15 ×7

x+12 = ( )/( ).11

x+15 ÷7

x+12 = ( )/( ).Hint: Rational expressions work just like fractions.

Correct Answers:• (11+7)*x + 15*7+12*11• (x+15)*(x+12)• (11-7)*x -15*7+12*11• (x+15)*(x+12)• 11*7• (x+15)*(x+12)• 11*(x+12)• 7*(x+15)

17. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p16.pg

1x+1

+1

x+21

x+2+

1x+3

= ( )/( ).

Hint: Work on the numerator and denominator separately andthen divide the resulting rational expressions.

Correct Answers:• (2*x + 3)*(x + 3)• (2*x + 5)*(x + 1)

18. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p21.pgIn order for the identity

1x+1

+a

x−1=

−2x2−1

to hold for all x, a must equal .Hint: Simplify the left side of this equation and compare whatyou get with the right side.

Correct Answers:

• -1

19. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p25.pg(Note that most of your answers are algebraic expressions in-volving t.)A car starts on a trip and travels at a speed of 55 mph. Twohours later, a second car starts on the same trip and travels at aspeed of 65 mph.When the second car has been on the road for t hours, the firstcar has traveled miles and the second car has traveled

miles.At time t the distance between the first car and the second car is

miles.The ratio of the distance the second car has traveled and thedistance the first car has traveled is .The second car catches up with the first car hours afterthe departure of the first car. (Those are some determined dri-vers!)Hint: If you are having trouble with the last part of this problemreread the question carefully. It’s not my wording, and if it’sany consolation, I got hung up on it myself at first.

Correct Answers:

• 55*(t+2)• 65*t• -10*t+110• (65*t)/(55*(t+2))• 13

20. (1 pt) 1010Library/set11 Rational Expressions Equations and Functions-/s11p29.pgFinally, here is a real life word word problem. During the Fallof 2006, in Exam 2 of Math 1010-1 (our class), 199 people tookthe exam and received an average score of 62%. 84 people didnot pick up their exam, presumably because they did not attendclass on the day the exam was handed back. Those people hadan average score of 58%. Thus the people who did pick up theirexams, and presumably did attend class, had an average scoreof %. (Round your answer to the nearest integer.)

Of course, assuming attendance on a particular day is corre-lated with attendance in general, the moral of the story is that itpays to come to class. I would have liked to see this case mademore forcefully, but the above are the actual figures.

Correct Answers:

• 65

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

3

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 10 is due : 12/17/2008 at 06:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p1.pg

Simplify45−

23

12 + 3

7= /

Correct Answers:

• 28• 195

2. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p2.pg

The equation

6x−3 = 12−3(x−1)

has the solution x =Correct Answers:

• 2

3. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p3.pg

The equation x2 − 2x− 1 = 0 has two real solutions. Enterthe smaller here and the larger here

Correct Answers:

• -0.414213562373095• 2.41421356237309

4. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p4.pg

One solution of the equation x2−2x+3 = 0 is+ i

Correct Answers:

• 1• 1.4142135623731

5. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p5.pg

The equation1

x−2+

1x−3

+1 = 0

has two real solutions. Enter the smaller here andthe larger here

Correct Answers:• 0.381966011250105• 2.61803398874989

6. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p6.pg

The solutions of the inequality4−3x

2< 6

satisfyx .(Enter ”<” or ”>” and a rational number.)

Correct Answers:• >• -2.66666666666667

7. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p7.pg

Consider the polynomial

p(x) = (x2−1)(x+2)+3x+4.

Its degree is and its leading coefficient is .In standard form it can be written asp(x) = x3 + + x2 + x +

Correct Answers:• 3• 1• 1• 2• 2

1

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• 2

8. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p8.pg

Use long division with remainder to complete the blanks be-low. Remember that some of the coefficients may be negative.5x3 +x2−3x+1 = (x2−2x+1)×( x+ )+ x + .

Correct Answers:• 5• 11• 14• -10

9. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p9.pgFor this and the next two problems let

f (x) =x−4

x2−3x.

Two numbers not in the domain of f are and . (Enterthe numbers in increasing size.)

Correct Answers:• 0• 3

10. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p10.pgConsider the function from the previous problem and evaluatef (5) = .

Correct Answers:• 0.1

11. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p11.pgAgain, consider the function in the previous problem and evalu-ate f (2x+1) = .

Correct Answers:• (2x-3)/(4x**2-2x-2)

12. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p12.pgExpress the complex fraction below in standard form. Remem-ber that the real or the imaginary part may be negative.2+3i1+4i = + i.

Correct Answers:• 0.823529411764706• -0.294117647058824

13. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p13.pgSolve the linear system

4x −y = 22x +y = 4

x = and y = .Correct Answers:

• 1• 2

14. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p15.pgThe line that passes through (1,1) and has slope−1 can be writ-ten in general form asy+ x - = 0.

Correct Answers:

• 1• 2

15. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p16.pgThe distance between the point (−1,2) and the originis

Correct Answers:

• 2.23606797749979

16. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p17.pgIf 125x = 25, then x = .

Correct Answers:

• 0.666666666666667

17. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p18.pgThe rational function

r(x) =1

x−1+

1x−2

+2

x−3

can be written in standard form asr(x) = ( )/( .

Correct Answers:

• 4xˆ2-15x+13• (x-1)(x-2)(x-3)

18. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p19.pgYou have a backyard that’s three times as long as it is wide.Within one yard of its boundary you plant shrubs and flowers,and the remainder you cover with 340 square yards of lawn. Thewidth of your lawn is yards and its length is yards.

Correct Answers:

• 10• 34

19. (1 pt) 1010Library/set math1010fall2005-90/setFinal/p20.pgIt takes you 6 hours to dig a hole. It takes your brother 8 hours todig the same hole. Your younger sister takes 12 hours. It takesthe three of you hours to dig that hole.

Correct Answers:

• 2.66666666666667

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

2

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number Final is due : 12/18/2008 at 08:33pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set14 Review/s14p1.pgThe key to algebra is that algebraic expressions work just likearithmetic expressions. In particular, rational expressionswork just like fractions.

That is why it is so important to understand fractions. The prob-lem on this page summarizes the four basic arithmetic opera-tions with fractions, i.e., addition, subtraction, multiplication,and division. Your answer should be a simple fraction, with nocommon factors in numerator and denominator. Don’t botherwith mixed numbers.

Simplify35 + 1

334 −

25

= /

Correct Answers:

• 8• 3

2. (1 pt) 1010Library/set14 Review/s14p2.pg

An important task in algebra is to solve an equation. Thismeans we find a value, or values of the variable, or variablesthat make the equation true.

A type of equation that occurs particularly frequently arelinear equations. The equation in this problem is of that type.

The equation

15x−2 = 85−4(x−2)

has the solution x =Correct Answers:

• 5

3. (1 pt) 1010Library/set14 Review/s14p3.pgAnother major type of equation are quadratic equations. Asyou go on in mathematics you will solve many more qua-dratic equations. You can use the quadratic formula but it ishard to remember reliably. An alternative is the technique ofcompleting the square. It is based on the binomial formulaswhich you should have used so often in this class that you can’thelp remembering them. If in fact you do not remember them,look them up and do so many exercises involving them that youwon’t be able to forget them if you tried.

Occasionally it is obvious how a quadratic expression or polynomialcan be factored and if so you look for when the individual fac-tors are zero.

The equation x2− 4x− 2 = 0 has two real solutions. Enter thesmaller here and the larger here

Correct Answers:• -0.449489742783178• 4.44948974278318

4. (1 pt) 1010Library/set14 Review/s14p4.pgHere is another quadratic equation. It has aconjugate complex pair of solutions.The solution of the equation x2−8x+20 = 0 is

± iCorrect Answers:

• 4• 2

5. (1 pt) 1010Library/set14 Review/s14p5.pgQuadratic Equations do not always occur in standard form..When they occur in disguise you apply the fundamental princi-ple of equation solving:figure out what bothers you and get rid of it by doing thesame thing on both sides of the equation.If you understand and fully appreciate that principle you havegrasped more than half of Math 1010!

1

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Sometimes the process of converting an equation to a quadraticequation introduces spurious solutions. They solve the quadraticequation but not the original equation. That makes it doubly im-portant that you check your answers. You check not just to makesure you didn’t make a mistake, but also to make sure you iden-tify only the solutions of the original equation.

Even if you can guess the answer to the equation below, fig-ure out how to solve it properly anyway, and check the solutionsfor two alternative approaches when the set closes.

The equationx+2

√x−3 = 0

has the real solutions x = .Correct Answers:

• 1

6. (1 pt) 1010Library/set14 Review/s14p6.pgInequalities are solved like equations, by figuring out whatbothers us and getting rid of it by doing the same thing on bothsides of the inequality. The only difference is that when multi-plying with a negative factor we reverse the inequality. Thuswe replace < with >, ≤ with ≥, etc.

The solutions of the inequality

5−2x3

< 7

satisfyx .(Enter ”<” or ”>” and a rational number.)

Correct Answers:

• >• -8

7. (1 pt) 1010Library/set14 Review/s14p7.pgPolynomials are functions or expressions that can be evaluatedin a finite number of additions, multiplications, and subtrac-tions. However, they require no division for their evaluation.(Fractions are considered constants in this context). Polynomi-als have a whole language associated with them that you need tounderstand. You also need to be able to manipulate polynomialexpressions to obtain their standard form.

Consider the polynomial

p(x) = (x2 +1)(x−2)−3x−1.

Its degree is and its leading coefficient is .In standard form it can be written asp(x) = x3 + x2 + x + .Note that some of these answers may be negative.

Correct Answers:

• 3• 1• 1• -2

• -2• -3

8. (1 pt) 1010Library/set14 Review/s14p8.pgRational Functions of Expressions are ratios (or quotients)of polynomials. They are processed exactly like fractions.

Polynomials in standard form are sums of powers of the vari-able. Numbers in decimal representation are sums of powers of10. Polynomials are processed much like numbers, except thatyou cannot trade some powers of x for a higher power of x. Thusthe manipulation of polynomials is in some ways actually easierthan the corresponding manipulation of decimal numbers!

An example for this fact is provided by long division.

Use long division with remainder to complete the blanks below.Remember that some of the coefficients may be negative.2x3 +2x2 +5x−5 = (x2−x+2)×( x+ )+ x + .

Correct Answers:

• 2• 4• 5• -13

9. (1 pt) 1010Library/set14 Review/s14p9.pgPerhaps the most central concept in all of mathematics is thatof a function. You need to understand the concepts of rule,domain, and range, and what it means to evaluate a function ata number or an algebraic expression that may itself be definedby a function.

For this and the next two problems let

f (x) =x+1

x2−5x+6.

Two numbers not in the domain of f are and . (Enterthe numbers in increasing size.)

Correct Answers:

• 2• 3

10. (1 pt) 1010Library/set14 Review/s14p10.pgConsider the function from the previous problem and evaluatef (−2) = .

Correct Answers:

• -0.05

11. (1 pt) 1010Library/set14 Review/s14p11.pgAgain, consider the function in the previous problem and evalu-atef (x−1) = .

Correct Answers:

• x/(x*x - 7*x + 12)

2

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12. (1 pt) 1010Library/set14 Review/s14p12.pgThe Number System is built in stages to facilitate the four ba-sic operations. It is extended to complex numbers to facilitatethe computation of square roots of negative real numbers. Allyou need to remember to work with complex numbers is thatthey work exactly like algebraic expressions of the form a + biwhere a and b are real numbers, except that

i2 =−1.

There is a trick related to dividing complex numbers: you mul-tiply numerator and denominator with the conjugate complexof the denominator. This makes the denominator real, andthe standard form of the complex number follows from thedistributive law.

Express the complex fraction below in standard form. Re-member that the real or the imaginary part may be negative.1−3i2+ i

= + i.Correct Answers:

• -0.2• -1.4

13. (1 pt) 1010Library/set14 Review/s14p13.pgLinear systems of equations arise frequently in applications.They are usually solved by Gaussian Elimination and Back-ward Substitution. When working by hand it is cru-cial to organize the computation in a clear way that letsyou check your calculations so far. A linear systemmay have none, one, or infinitely many solutions.

Solve the linear system

4x −y = 32x +y = 5

x = and y = .Correct Answers:

• 1.33333333333333• 2.33333333333333

14. (1 pt) 1010Library/set14 Review/s14p15.pgA major tool in elementary mathematics is the graphing of equa-tions in the rectangular (or Cartesian) coordinate system.The interplay between algebra and geometry can be exploitedto gain insights that would otherwise be much harder to ob-tain. Particularly important are equations whose graphs arestraight lines.

The line that passes through (1,3) and has slope 2 can be writtenin general form asy− x - = 0.

Correct Answers:

• 2• 1

15. (1 pt) 1010Library/set14 Review/s14p16.pgTo compute the distance between two points we simply applythe Pythagorean Theorem.

The distance between the points (2,−3) and (1,1)is

Correct Answers:

• 4.12310562561766

16. (1 pt) 1010Library/set14 Review/s14p17.pgPowers and radicals provide a beautiful illustration of howmathematics starts from simple beginnings and then expands ina consistent manner until it reaches results and concepts (likeanything non=zero to the power zero equals one) that aren’t ob-vious and may seem strange at first.

If 32x = 18 , then x = .

Correct Answers:

• -0.6

17. (1 pt) 1010Library/set14 Review/s14p18.pgThe key to manipulating rational functions and expressions isthat they work exactly like fractions.

The rational function

r(x) =x+1x−1

+2x+3x−2

can be written in standard form asr(x) = ( )/( ).

Correct Answers:

• 3xˆ2-5• (x-1)(x-2)

18. (1 pt) 1010Library/set14 Review/s14p19.pgThere are some basic procedures for solving word problemssuch as: use common sense, draw a picture, introduce a vari-able, set up and solve an equation, have expectations, checkyour answers. Word problems are unpopular with students sincethey add a layer of complexity, remember that you are study-ing mathematics precisely because it enables you to solve wordproblems.

The length of a rectangle is 4 inches more than its width. Itsarea is 96 square inches. The length of the rectangle isinches and its width is inches.

Correct Answers:

• 12• 8

19. (1 pt) 1010Library/set14 Review/s14p20.pgIt takes you 8 hours to dig a hole. It would take you and yourbrother 5 hours to dig that same hole together. If your brotherwas to dig the hole by himself it would take him hours.

Correct Answers:

• 13.3333333333333

3

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20. (1 pt) 1010Library/set14 Review/s14p21.pgThe rational Equation

1x+1

− 2x−1

= 3.

has two solutions. The smaller is and the larger is .Correct Answers:

• -0.333333333333333• 0

21. (1 pt) 1010Library/set14 Review/s14p22.pgIf you write the following expression(

x−3x2

x3x−2

)2

as a single power of x then the exponent isCorrect Answers:

• -4

22. (1 pt) 1010Library/set14 Review/s14p23.pgIf you write the following expression(

x−1/3x1/6

x1/4x−1/2

)−1/3

as a single power of x then the exponent isCorrect Answers:

• -0.0277777777777778

23. (1 pt) 1010Library/set14 Review/s14p24.pgWrite the following expression

x+5x−6

+x+2x−1

−1

in the standard form of a rational expression:Correct Answers:

• (x*x+7*x-23)/(x-6)/(x-1)

24. (1 pt) 1010Library/set14 Review/s14p25.pgThe number x such that

8x =14

equals x =Correct Answers:

• -0.666666666666667

25. (1 pt) 1050Library/set13 Review/1050s13p1.pgEquations of straight lines and graphs of linear equations.Know how to obtain an equation of a straight line given twopieces of information, for example, two points, or a point andslope. Intercepts lead to special cases of points.

Let L be the line through the points (1,−2) and (−2,−3).The slope of L is . Using x and y as the variables as usual,its equation in slope intercept form is y = .

The x-intercept of L is x = .Correct Answers:

• 0.333333333333333• 1/3*x-7/3• 7

26. (1 pt) 1050Library/set13 Review/1050s13p2.pgQuadratic Equations. Know how to solve quadratic equa-tions, by completing the square, or applying the quadratic for-mula.

The equation2x2 +3x−3 = 0

has two real solutions. The smaller is , and the larger is.

Correct Answers:• -2.18614066163451• 0.686140661634507

27. (1 pt) 1050Library/set13 Review/1050s13p3.pgQuadratic Equations. Quadratic Equations don’t always looklike such. To obtain one you may have to carry out some sort ofsubstitution or manipulate expressions suitably.

The equation2x−5

√x+2 = 0

has two real solutions. The smaller is , and the larger is.

The equation2x4−5x2 +2 = 0

has two positive real solutions. The smaller is , and thelarger is .The equation

1x−1

− xx+1

−2 = 0

has two real solutions. The smaller is , and the larger is.

Correct Answers:• 0.25• 4• 0.707106781186547• 1.4142135623731• -0.720759220056126

4

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• 1.38742588672279

28. (1 pt) 1050Library/set13 Review/1050s13p4.pgFunctions. Understand the concepts of domain, range, andinverse of a function, and know how to evaluate and composefunctions.

Let

f (x) =x+5x+2

.

Then the domain of f is the set of all real numbers except, and its range is the set of all real numbers except .

Moreover,f (2) = ,f (t +1) = , andf ( f (t2)) = .This is hard to do in WeBWorK, but you should also be able todraw the graph of f , showing clearly all intercepts and asymp-totes.

Correct Answers:

• -2• 1• 1.75• (t+6)/(t+3)• (2t**2+5)/(t**2+3)

29. (1 pt) 1050Library/set13 Review/1050s13p6.pgRules of Exponents. Understand how to combine powers.

(6y2)2(2y3)−1 = ayb

where

a = andb = .

Correct Answers:

• 18• 1

30. (1 pt) 1050Library/set13 Review/1050s13p7.pgSimplifying Rational Expressions. Understand how to ma-nipulate rational expressions. They work just like fractions!

x−5x2−25

− 3x+5

=AB

where A and B are polynomials of degree as low as possible andthe leading coefficient of B is 1.A = andB = .

Correct Answers:

• -2• x+5

31. (1 pt) 1050Library/set13 Review/1050s13p8.pgGraphing. Understand the interplay between algebra and ge-ometry when graphs are shifted horizontally and vertically.

For example, the graph of

f (x) = ex−2−3

is the graph of the exponential y = ex shifted units hor-izontally and units vertically. (Distinguish left and rightand up and down with the appropriate signs of the shift. Youshould also draw the graphs of the original and the shifted ex-ponential in one coordinate system.)

Correct Answers:• 2• -3

32. (1 pt) 1050Library/set13 Review/1050s13p10.pgLogarithm Rules. Understand the rules for logarithms. Youshould be able to write logarithms as sums, differences or multi-ples of logarithms when appropriate, or expressions int terms ofseveral logarithms in terms of single logarithms. For example,

log2 32(a+1)−4 = A+B log2(C) where A = andB = are numbers andC = is an expression in terms of a.

Correct Answers:• 5• -4• a+1

33. (1 pt) 1050Library/set13 Review/1050s13p11.pgMore Logarithm Rules. Similarly

ln(x+1)− ln(x2) = ln(C)

whereC = is an expression in terms of x.

Correct Answers:• (x+1)/xˆ2

34. (1 pt) 1050Library/set13 Review/1050s13p12.pgLogarithmic Equations. Understand how to solve equationsinvolving logarithms. For example, the solution of the equation

ln12− ln(x−1) = ln(x−2)isx =

Correct Answers:• 5

35. (1 pt) 1050Library/set13 Review/1050s13p13.pgExponential Equations. Understand how to solve equationsinvolving exponentials. For example, the largest solution of theequation

2x2−5x+9 = 8isx =

Correct Answers:• 3

5

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Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

6

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 8 is due : 12/16/2008 at 11:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set math1010fall2004-2/set21/p1.pgEvaluate the radical expression if possible. If not, write ”unde-fined”.

a)(

3√−6)3

=

b)

√(35

)2

=

c)√−122 =

d)(82)3/2

=

e)(−23)5/3

=Answer:Correct Answers:

• -6• 3/5• undefined• 512• -32

2. (1 pt) 1010Library/set math1010fall2004-2/set21/p2.pgRewrite the expression using rational exponents.

a) t5√

t2 = ta where a =b) NOTE. In this problem y≥ 0:

y 4√

y2 = yb where b =

c)3√x4√

x3= xc where c =

d) 5√

z3 · 5√

z2 = zd where d =Answer:Correct Answers:

• 7/5• 3/2• -1/6• 1

3. (1 pt) 1010Library/set math1010fall2004-2/set21/p3.pgSimplify the expressions.

a)(−2u3/5v−1/5

)3= k

ua

vb where k= , a= , b=

b)

(3m1/6n1/3

4n−2/3

)2

= kmanb where k= , a= , b=

c)3√√

2x = (kx)c where k= , c=

d)5√

3√

y4 = yk where k=

e)(a−b)1/3

3√

a−b= C1aC2 bC3 where C1= , C2= , C3=

f)(3u−2v)2/3√

(3u−2v)3= (C1u+C2v)C3 where C1= , C2= ,

C3=Correct Answers:

• -8• 9/5• 3/5• 9/16• 1/3• 2• 2• 1/6• 4/15• 1• 0• 0• 3• -2• -5/6

4. (1 pt) 1010Library/set math1010fall2004-2/set22/p1.pgSimplify the radical expressions.

a)√

0.25 =b) 3√0.000027 =c)

√125u4v6 = a f (u,v) where a= and

f (u,v)=d) 5√160x8 = axb where a = and b =e) 5

√96x5 = a f (x) where a= and f (x)=

1

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NOTES:In a and b you must enter a decimal number.

Correct Answers:

• 0.5• 0.03• 5*sqrt(5)• uˆ2*(abs(v))ˆ3• 2*(5)ˆ(1/5)• 8/5• 2*(3)ˆ(1/5)• x

5. (1 pt) 1010Library/set math1010fall2004-2/set22/p2.pgSimplify the radical expressions.

a)

√15

=ab

where a= and b=

b)12√

3= a√

b where a= and b=

c)

√4x3 = a

f (x)g(x)

where a= , f (x)= , and

g(x)=

d)5√8x5

= af (x)g(x)

where a = , f (x) = , and

g(x) =

e)

√20x2

9y2 = af (x)g(y)

where a= , f (x) = , and

g(y) =Correct Answers:

• sqrt(5)• 5• 4• 3• 2• sqrt(x)• xˆ2• 5*sqrt(2)/4• sqrt(x)• xˆ3• sqrt(20)/3• abs(x)• abs(y)

6. (0 pts) 1010Library/set math1010fall2004-2/set23/p1.pgCombine the radical expressions.

a) 4 3√

y+9 3√

y = a f (y), a= , f (y)=b) 15 4

√s− 4

√s = a f (s), a = , f (s)=

c) 8√

2+6√

2−5√

2 = a√

b, a = , b=d) 9 3

√17 + 7 3√2 − 4 3

√17 + 3√2 = a 3√b + c 3√d, a= ,

b= , c= , d=NOTE: b > d.

e) 4 4√

48− 4√

243 = a 4√b, a= , b=f) 4

√y+2

√16y=a f (y), a= , f (y)=

g) 3√16t4− 3√54t4 = f (t) 3√

g(t), f (t)= , g(t)=h) 4

√3x3−

√12x= f (x)

√g(x), f (x)= , g(x)=

i)√

9x−9 −√

x3− x2= f (x)√

g(x), f (x)= ,g(x)=

j) x 3√

27x5y2 − x2 3√

x2y2 + 2 3√

x8y2 = f (x) 3√

g(x,y),f (x)= , g(x)=

Correct Answers:

• 13• yˆ(1/3)• 14• sˆ(1/4)• 9• 2• 5• 17• 8• 2• 5• 3• 12• sqrt(y)• -t• 2*t• 4*x-2• 3*x• 3-x• x-1• 4*xˆ2• xˆ2*yˆ2

7. (0 pts) 1010Library/set math1010fall2004-2/set23/p2.pgPerform the addition or subtraction.

a) x√3x

+√

27x = a f (x), a= , f (x)=

b) 8x2√

5x+ x

√5x = a f (x), a= , f (x)=

c)√

43x3 +

√3x3 = f (x)

√g(x), f (x)= ,

g(x)=Correct Answers:

• 10/3• sqrt(3*x)• 13/5• x*sqrt(5*x)• (2+3*xˆ3)/(3*xˆ2)• 3*x

8. (0 pts) 1010Library/set math1010fall2004-2/set24/p1.pgMultiply and simplify.

a)√

3(4+

√3)

= a+b√

3, a= , b=

b)√

10(√

5+√

6)

= a√

2+b√

15, a = , b=

c)( 3√

9+5)( 3√5−5

)= 3√45 + a 3√5 + b 3

√9 + c,

a = ,b = ,c =d) (16

√u−3)(

√u−1) = au+b

√u+c, a = ,b = ,

c =e)(7−3

√3t)(

7+3√

3t)=a+bt, a = ,b =

f) 4√

8x3y5(

4√

4x5y7− 4√

6x7y6)

=a 4√2x2 |y|3 +bx2y2 4√

3x2y3,a = ,b =

Correct Answers:2

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• 3• 4• 5• 2• 5• -5• -25• 16• -19• 3• 49• -27• 2• -2

9. (0 pts) 1010Library/set math1010fall2004-2/set24/p2.pgMultiply and simplify.

a) 10√9+√

5= a√

9+b√

5, a= , b=

b) 8√7+3

= a√

7+b, a= , b=

c) 9√3−√

7= a√

3+b√

7, a= , b=

d)(5−

√3)÷(3+

√3)

= a+b√

3, a= , b=e) z√

u+z−√

u = a√

u+ z+b√

u, a= , b=Correct Answers:

• 5/2• -5/2• -4• 12• -9/4• -9/4• 3• -4/3• 1• 1

10. (1 pt) 1010Library/set math1010fall2004-2/set26/p1.pgPerform the operation(s) and write the result in standard form.

a)√−25−

√−9 = a+ ib, a = , b =

b)√−24

(√−9+

√−4)

= a+ ib, a = , b =Correct Answers:

• 0• 2• -10*sqrt(6)• 0

11. (1 pt) 1010Library/set math1010fall2004-2/set26/p2.pgSolve for a and b.

(2a+1)+(2b+3) i = 5+12i

a = , b =Correct Answers:

• 2• 9/2

12. (1 pt) 1010Library/set math1010fall2004-2/set26/p4.pgPerform the multiplication and simplify.

a) (3+5i)(2+5i) = a+bi, a = , b =b) (3−2i)3 = a+bi, a = , b =Correct Answers:

• -19• 25• -9• -46

13. (1 pt) 1010Library/set math1010fall2004-2/set26/p6.pgAdd and simplify.

11−2i

+4

1+2i= a+bi

a = , b =Correct Answers:

• 1• -6/5

14. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p1.pg

Let u = 3 + 6i and v = 5 + 4i. Enter the real and imaginaryparts of the following expressions in the appropriate boxes.u+ v = + iu− v = + iu× v = + iu÷ v = + iHint: If you do not know how to handle these problems youneed to study complex numbers. Treat u and v like algebraicexpressions, but remember that

i2 =−1.

Correct Answers:

• 8• 10• -2• 2• -9• 42• 0.951219512195122• 0.439024390243902

15. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p2.pgThis problem is like the preceding one. Let u = 4 + 3i andv = 2+3i. Thenu+ v = + iu− v = + iu× v = + iu÷ v = + iHint: If you do not know how to handle these problems you

3

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need to study complex numbers. Treat u and v like algebraicexpressions, but remember that

i2 =−1.

Correct Answers:

• 6

• 6• 2• 0• -1• 18• 1.30769230769231• -0.461538461538462

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

4

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 9 is due : 12/16/2008 at 11:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p14.pgIn the first few problems, fill in the blanks to make aperfect square. For example, in

x2 +6x+ = (x+ )2

fill in 9 and 3 since

x2 +6x+9 = (x+3)2.

x2 +14x+ = (x+ )2.x2−8x+ = (x− )2.x2−20x+ = (x− )2.

Correct Answers:

• 49• 7• 16• 4• 100• 10

2. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p15.pgThis is like the preceding problem, except that your answersmay be fractions.

x2 +3x+ = (x+ )2.x2−5x+ = (x− )2.x2 + 1

3 x+ = (x+ )2.Correct Answers:

• 2.25• 1.5• 6.25• 2.5• 0.0277777777777778• 0.166666666666667

3. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p16.pgThis is like the preceding problem, except that your answersmay be negative

x2 + 73 x+ = (x+ )2.

x2− 57 x+ = (x+ )2.

x2 + 23 x+ = (x+ )2.

Correct Answers:

• 1.36111111111111• 1.16666666666667• 0.127551020408163• -0.357142857142857• 0.111111111111111• 0.333333333333333

4. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p27.pgQuadratic equations do not always occur in standard form.Sometimes they have to be converted to standard form usingour basic principle of doing the same thing on both sides to getwhere we want to go.

The equation

x+1x

= 2

has only one solution. It isx = .Hint:When you see the solution you will say ”of course”. As a firststep, multiply with x on both sides.

Correct Answers:

• 1

5. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p28.pgThe equation

1− xx

= x

1

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has two real solutions solution. They arex = ± .Hint:Begin by multiplying with x on both sides.

Correct Answers:• -0.5• 1.11803398874989

6. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p29.pgThe equation

x−12x+1

=x+1x−1

has two real solutions. Enter the smaller one here and thelarger one here .Hint:Begin by multiplying with 2x+1 and x−1 on both sides.

Correct Answers:• -5• 0

7. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/p14.pgThe equation √

x+√

2x = 1has the solutionx = .Hint: using the methods discussed in class this gives rise to aquadratic equation with two solutions. Only one of those solu-tions works in the original equation.

Correct Answers:• 0.17157287525381

8. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p21.pgIn the next few problems of this set you are asked to solvequadratic equations. These are of the form

ax2 +bx+ c = 0.

There are usually two solutions that are either of the formr ± s or of the form r ± si where i2 = −1, and r and s arereal numbers. Enter r and s. Also enter ”i” if the solution is aconjugate complex pair of numbers, ”1” if both solutions arereal, or ”0” if there is only one real solution. In the last case,also enter s = 0.

For example, the equation

x2 + x+1 = 0

has the solution

x =−1/2±√

32

i.

Enter −1/2, sqrt(3)/2, and i here:x = ± here.The equation

x2 + x−1 = 0

has the solution

x =−1/2±√

52

.

Enter −1/2, sqrt(5)/2, and 1 here:x = ± here.The equation

x2 + x+14

= 0

only has the solutionx =−1/2.

Enter −1/2, 0, and 0 here:x = ± here.

Correct Answers:

• -0.5• 0.866025403784439• i• -0.5• 1.11803398874989• 1• -0.5• 0• 0

9. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p22.pgThe equation

x2−1x−12 = 0

has the solution x = ± .Correct Answers:

• 0.5• 3.5• 1

10. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p23.pgThe equation

x2−10x+50 = 0

has the solution x = ± .Correct Answers:

• 5• 5• i

11. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p24.pgThe equation

x2−4x+4 = 0

has the solution x = ± .Correct Answers:

• 2• 0• 0

2

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12. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p30.pgThe equation

x4−10x2 +9 = 0has four solutions. Enter them in increasing order:x1 =x2 =x3 =x4 =Hint: Begin by thinking of x2 as the unknown.

Correct Answers:• -3• -1• 1• 3

13. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p31.pgThe equation

x−√

x−2 = 0has the solutionx = .Hint: Begin by thinking of

√x as the unknown.

Correct Answers:• 4

14. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p34.pgThe height of a triangle is 8 inches less than its base. The areaof the triangle is 192 square inches. The height of the triangle is

inches and the base of the triangle is inches.Hint: The area of a triangle equals one half of base times height.

Correct Answers:• 16• 24

15. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p35.pgThe height of a triangle is 25 inches greater than its base. Thearea of the triangle is 625 square inches. The height of the trian-gle is inches and the base of the triangle is inches.Hint: The area of a triangle equals one half of base times height.

Correct Answers:

• 50• 25

16. (1 pt) 1010Library/set8 Quadratic Equations Functions and Inequalities-/s8p36.pgYou are approaching the island of Hawaii in a small boat. Thehighest point on Hawaii is Mauna Loa at 13,677 feet. You seeit just barely above the horizon. The radius of Earth is 3,963miles. Ignoring atmospheric effects, you figure that you are

miles in a straight line from the top of Mauna Loa.Hint: Draw the triangle whose vertices are the top of MaunaLoa, your boat, and the center of the earth. Apply thePythagorean Theorem. A mile has 5,280 feet.

Correct Answers:

• 143.300383809674

17. (1 pt) 1010Library/set math1010fall2004-2/set29/p2.pg

Use the descriminant to determine if the solutions are real orcomplex.

a) x2 + x−1 = 0

• A. complex• B. real

b) 10x2 +5x+1 = 0

• A. complex• B. real

c) 3x2−2x−5 = 0

• A. complex• B. real

NOTE: You only get TWO chances to answer all parts of thisproblem.

Correct Answers:

• B• A• B

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

3

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 11 is due : 12/16/2008 at 11:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) Library/ma112DB/set9/sw6 1 5.pgFor the function f (x) =

( 15

)x, calculate the following function

values:f (−3) =f (−1) =f (0) =f (1) =f (3) =

Correct Answers:

• 125• 5• 1• 0.2• 0.008

2. (1 pt) Library/Rochester/setAlgebra28ExpFunctions/pexp.pgStarting with the graph of f (x) = 7x, write the equation of thegraph that results from

(a) shifting f (x) 2 units downward. y =

(b) shifting f (x) 9 units to the right. y =

(c) reflecting f (x) about the x-axis. y =Correct Answers:

• 7ˆx - 2• 7ˆ(x - 9)• -7ˆx

3. (1 pt) Library/Rochester/setAlgebra28ExpFunctions/srw4 1 11.pgFind the exponential function f (x) = ax whose graph goesthrough the point 3,1/125.a = .

Correct Answers:

• 0.2

4. (1 pt) Library/Rochester/setAlgebra28ExpFunctions/c4s1p13 18-/c4s1p13 18.pgMatch the functions with their graphs. Enter the letter of thegraph below which corresponds to the function.

1. f (x) = 5−x

2. f (x) = 5x+1−43. f (x) = 5x +34. f (x) = 5x−3

5. f (x) = 5x

A.

B.1

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C.

D.

E.

Correct Answers:

• C• A• B• E• D

5. (1 pt) Library/ma112DB/set9/sw6 2 27.pgCertain radioactive material decays in such a way that the massremaining after t years is given by the function

m(t) = 100e−0.015t

where m(t) is measured in grams.(a) Find the mass at time t = 0.Your answer is(b) How much of the mass remains after 40 years?Your answer is

Correct Answers:• 100• 54.8811636094026

6. (1 pt) Library/Rochester/setAlgebra28ExpFunctions/sw6 2 11.pgIf 19000 dollars is invested at an interest rate of 8 percent peryear, find the value of the investment at the end of 5 years forthe following compounding methods.(a) Annual:Your answer is(b) Semiannual:Your answer is(c) Monthly:Your answer is(d) Daily:Your answer is(e) Continuously:Your answer is

Correct Answers:• 27917.2334592• 28124.6414134485• 28307.0684577305• 28343.4269578864• 28344.6692551841

7. (1 pt) Library/Rochester/setAlgebra28ExpFunctions/srw4 1 5.pgFor the function f (x) = 4ex, calculate the following functionvalues:f (−3) =f (−1) =f (0) =f (1) =f (3) =

Correct Answers:• 0.199148273471456• 1.47151776468577• 4• 10.8731273138362• 80.3421476927507

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

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Hsiang-Ping Huang math1010fall2008-4WeBWorK assignment number 12 is due : 12/16/2008 at 11:00pm MST.The

(* replace with url for the course home page *)for the course contains the syllabus, grading policy and other information.

This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.

The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are makingsome kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you arehaving trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor forhelp. Don’t spend a lot of time guessing – it’s not very efficient or effective.

Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,you can if you wish enter elementary expressions such as 2∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e∧ (ln(2)) instead of 2,(2+ tan(3))∗ (4− sin(5))∧6−7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.

You can use the Feedback button on each problem page to send e-mail to the professors.

1. (1 pt) 1050Library/set8 Exponential and Logarithmic Functions-/1050s8p19.pg

The Figure above shows the graphs of five functions, listed be-low. Match the functions with the colors, using b for blue, r forred, g for green, p for purple, and y for yellow.

: f (x) = x.: f (x) = ex.: f (x) = 5x.: f (x) = ln(x).: f (x) = log5(x).

Hint: You know the graphs of the exponential functions, andyou that the logarithms are the inverses of the exponential func-tions.

Correct Answers:

• y• r• b• g• p

2. (1 pt) 1050Library/set8 Exponential and Logarithmic Functions-/1050s8p20.pg

The lessons we learned about shifting graphs apply to loga-rithmic functions just as they apply to any other functions.

The Figure above shows the graphs of five logarithmic func-tions, listed below. Match the functions with the colors, using bfor blue, r for red, g for green, p for purple, and y for yellow.

: f (x) = ln(x).: f (x) = ln(x−1).: f (x) = ln(x+1).

1

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: f (x) = ln(x)−1.: f (x) = ln(x)+1.

Hint: Look where the graph intersects the x-axis, and whereit has a vertical asymptote.

Correct Answers:

• p• g• r• b• y

3. (1 pt) 1050Library/set8 Exponential and Logarithmic Functions-/1050s8p21.pgBefore calculators were widely available people used logarithmtables to simplify multiplication and division, using the fact thatthe logarithm of a product equals the sum of the logarithms andthe logarithm of the quotient equals the difference of the loga-rithms.

These tables were constructed by computing laboriously andcarefully the logarithms of a few selected numbers and thencombining the logarithms using the rules just mentioned.

This exercise suggest how the process may have worked.

Let

L(x) = loga(x)

where we don’t know the base a. However, we do know that

L(2) = 0.3204 and L(3) = 0.50783.

Use this information to compute

L(6) = .L(9) = .L(12) = .L( 2

3

)= .

L(310)

= .L(1) = .

Correct Answers:

• 0.82823• 1.01566• 1.14863• -0.18743• 5.0783• 0

4. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p1.pgYou can compute the following logarithms with your basicknowledge of powers.

For example, since

23 = 8

we know thatlog2 8 = 3.

log5 25 = .log6 36 = .log3 27 = .log10 10,000 = .log10 0.001 = .logπ 1 = .

Hint: To get started observe that 52 = 25.Correct Answers:

• 2• 2• 3• 4• -3• 0

5. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p2.pgMore logarithms:

log2 4 = .log9 81 = .log2 1024 = .log3 81 = .

Correct Answers:

• 2• 2• 10• 4

6. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p13.pgThe following few problems ask you to solve exponential equa-tions of increasing complexity. Your answer needs to be a deci-mal number with at least four digits. The first problem is easy:

2

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The solution of the equation

5x = 100

is x = .Correct Answers:

• 2.86135311614679

7. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p14.pgThe solution of the equation

3×5x +25 = 100

is x = .Correct Answers:

• 2

8. (1 pt) set9 Exponential and Logarithmic Functions/1050s9p18.pgThe equation

ln(x+1)− ln(x−2) = lnx

has the solution x = .Hint: First use the properties of logarithms, then apply the ex-ponential on both sides.

Correct Answers:

• 3.30277563773199

9. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p19.pgFor the following statements write T if they are true, and F ifthey are false. To avoid cumbersome sentences it is tacitly un-derstood that logarithms have the same base, and are applied tothe appropriate terms. We also assume that all logarithms areevaluated at positive numbers.For example, a more precise version of the first sentence wouldbe: The logarithm with a certain base of the product of two pos-itive numbers equals the sum of the logarithms with the samebase of those two numbers.

The logarithm of a product equals the sum of the loga-rithms.

The logarithm of a quotient equals the difference of thelogarithms.

The logarithm of a power equals the product of the expo-nent and the logarithm of the base (of the power).

Correct Answers:

• T• T• T

10. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p27.pgThe remaining problems are true/false questions concerninglogarithmic and exponential identities. You don’t need to mem-orize these, they all flow from two facts:

Logarithms and Exponentials are inverses of each other.(Of course they need to have the same base.)

Exponential functions are just powers and logarithms arejust exponents.

For the following proposed identities enter T if they are true,and F if they are false. We assume that the expressions involvedmake sense. For example any base is positive and not equal to1, and logarithms are taken only of positive numbers.

loga(uv) = loga u+ loga v.loga(u+ v) = (loga u)(loga v).loga

( uv

)= loga u− loga v.

loga(u− v) = loga uloga v .

loga (uv) = (loga u)(loga v).loga (uv) = u(loga v).loga (uv) = v(loga u).

Correct Answers:

• T• F• T• F• F• F• T

11. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p28.pgFor the following proposed identities enter T if they are true,and F if they are false.

eln(x−1) = x−1.e(lnx)−1 = x

e .ln((x−1)(x−2)) = ln(x−1)+ ln(x−2).lnx2 = 2lnx.

Correct Answers:

• T• T• T

3

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• T

12. (1 pt) 1050Library/set9 Exponential and Logarithmic Functions-/1050s9p30.pgFor the following proposed identities enter T if they are true,and F if they are false.

lnex = xln((ex)2

)= x2.

ln((ex)2

)= 2x.

ln(

1ex

)=−x.

ln(eu + ev) = u+ v.ln(eu + ev) = uv.ln(eu + ev) = eu+v.

Correct Answers:• T• F• T• T• F• F• F

Generated by the WeBWorK system c©WeBWorK Team, Department of Mathematics, University of Rochester

4