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# Fundamentals of Math MATH 1300

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This 17 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 1300 at University of Houston taught by Staff in Fall. Since its upload, it has received 64 views. For similar materials see /class/208409/math-1300-university-of-houston in Mathmatics at University of Houston.

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Date Created: 09/19/15

Math 1300 Intermediate Algebra Name Final Exam Review This review is comprehensive but should not be the only material used to study for the nal exam It should not be considered a preview of the nal exam It does not substitute for studying previous tests quizzes homework class notes text discussions etc There may be questions on the nal exam unlike questions on this review and vice versa No question on this review will be exactly duplicated on the nal exam This review is longer than the nal exam You may obtain help working the review sheet in the Math Lab located in 925N 1 Factor each expression completely 1 27a2b3c l8ab2c2 2 x2 2x 15 3 xa b 8a b 4 a2 81b2 5 52 6303 9y2 6 6112 41y 2x 7 1 25x2 8 8x2 2606 15 9 mm my nw ny 10 8m3 32x 11 x2 73 10 12 4x2 11x 3 13 x2 3x 7 14 6x2 17a 14 2 Write each fraction in lowest terms 4333 2x Zlmn3 m n 1 2 3 2cm2 35m2n n m 3a21 a2b2 5m5y4xy 4 5 6 a28a7 ab x2xy 3 Perform the indicated operations and simplify 333253122 x23as2 x3 3 3x x2 152 696 3m9 562 4 acZ x392x 2 2x9 x2 2 ac3 7 5 6 41132 49 902 49 x1x2x 2t3t 7 3 2 395 2 8 a2 9 a2 4 2a 4 56 3 n4 m2w 12 a25a6 a24a3 39 a1 4 Simplify each complex fraction 3 b 7m 3 1 T 2 T 14m Solve each equation 1x24 2c 23x2 11x0 2 4 35 4x2 360 5 135x 1 6 2x2 32x 15 8 4 ac8 7gtx3 3m WEH O 9 3x2x 10 39 10 Vm12zx 3 x x1 10 11 c3 2w3 12 a 3 13 3132 5x 2 13 1 14 Solve the equation for x 63 5 5 What IS the value of ac 10 Express each phrase as a ratio in lowest terms with units of measure canceled 1 4 inches to 3 feet 2 1 pound to 8 ounces 3 3 quarters to 3 dollars 4 3 days to 2 weeks Perform the indicated operations and simplify Assume all variables represent positive numbers In problems 6 and 13 you must rationalize the denominator 1 2 fol O 3 W 4 2523112 5 2x xE2a xB 6 7 V9 16 8 win6 V3 9 x200x7y5 10 xE xZis 11 71 12 mt32x M50563 xl8ac as 2 i4 13 72 14 1 10 11 12 14 15 16 Simplify as much as possible making all exponents positive Assume all variables represent positiVe numbers 2 16 9x4y2 i 1 125 3 32 x 5 mod 1 Change 2 5y to an exponential expression 1 2 Change W to an exponent1alexpress1on x Graph each equation on a rectangular coordinate system 1 3x5y 15 3 2 2 g 2y 2 4 x 331 Find the slope of the line that passes through each pair of points 1 3 1 6 2 0 8 quot395 0 3 Are these two lines either parallel or perpendicular Find the slope of the line determined by each equation 13x24y 2 2y 4 3 a 6 Find the distance between the two points P and Q 1 P59Q8 13 2 P36Q1 2 Does the point 3 1 fall on the line with equation 3x 2y 2 11 Find the ac and y intercepts of the following lines 12x 4y28 23x2y44 Find the midpoint of the line segment joining each pair of points 1 8 5 2a 3 2 0a 4 0 5 17 18 Use the graphing method to solve the following systems of equations 30 1 E y 3 1 y5 2 2 9quot 2ac4y8 Use the substitution method to solve the following systems of equations y2x1 3 4x 3y 5 3w y7 4 2x3y1 Use the addition method to solve the following systems of equations 4x34 y 2m5y 2 5 2y43 x 6 4x3y10 For each stated problem write symbols for the variable or variables translate the words into an equation or equations and then solve the problem 1 If an even number is squared the result is four more than three times the number What is the number 2 A truck can go 180 miles on 12 gallons of gas How far can the truck go on 15 gallons 3 A school board has determined that there should be 3 teachers for every 45 students How many teachers are needed for an enrollment of 300 students 4 The singles court in tennis is four yards longer than it is wide If its perimeter is 44 yards then what are the length and the Width 5 Josh opened a parking meter and removed 30 coins consisting of dimes and nickels If the value of these coins is 230 then how many of each type does he have 6 The product of two consecutive positive odd numbers is 143 Find the numbers 7 A number is 4 less than a second number Four times the first number is 6 more than twice the second number Find the numbers 8 The length of a rectangle is one inch less than twice the width The area is 45 square inches What is the length of the rectangle 9 Find the length of the longest straight line that can be drawn in a 3 inch by 4 inch rectangle 10 Jill walked diagonally across a rectangular eld that measured 1000 feet by 2400 feet Determine how far she walked 4 ANSWERS 1 1 9abzc3ab 4 2c 2 cc 5x 3 3 a b as 8 r 4 Prime 5 cc 332 6 230390 231 1 7 1 5x1 5x 8 4w 32a 5 9 a ym n 10 85656 2c 2 11 c 5x 2 12 4x 1m 3 13 Prime 14 3a 22a 7 2y 1 3172 2 1 2 5 m 3 1 1 4 a 1 5 In lowest terms 6 36 10512 L a 1 6 1 3 3o 1 9 2 3x 6 3 F 4 x 7 5 9 6252 7 4 a 3 6 3t 7 x 3 8 2a 6 4 1 6 7712 2 b3 n 2 5 1m 1iE 2ac0c 13l 3x6 4x 6ac6 54 6w 7 x 12 8 No solution 9 a 2 so 1 10 as 4 11 No solution 12 m 13m2x 14 9 1 1 3 6 1 5 2 2 3 Z 4 a 9 7 1 7 2 T6 3 4 4 5x23 5 4x2 5 6 M 7 5 8 10 20 9 10933112 2563 10 45 11 1 12 3V2 x 2m 13 mg 2 14 not a real number 8 1 5 2 i 3 x11 4 3w2 5 i 39 64 y 30 9 lt1 2 5W 2 lt4xquot 10 11 12 13 14 15 16 17 18 1 2 z N 3 4 I u quot0 4 4 1 8 1 2 g 3 Neither parallel nor perpendicular 3 1 Z 2 0 3 Unde ned 1 5 2 2V1 Yes 1 the cintercept 40 the yintercept 0 2 4 2 the clntercept g 0 the ylntercept 02 1 5 1 2 0 1 x 2 y 3 2 No Solution 6 w4y 2 4 w2y 1 1 4 2 225 miles 3 20 teachers 4 L 13 yds W9 yds 5 16 dimes 14 nickels 6 11 and 13 7 7and 11 8 9in 9 5 inches 10 2600 ft Exercise Set 11 Numbers State whether each of the following numbers is prime composite or neither If composite then list all the factors of the number 1 a 8 b 5 c 1 d 77 e 12 2 a 11 b 76 c 15 d 0 e 72 Answer the following 3 In ae use long division to change the following fractions to decimals a b C d e Nate Notice the pattern above and use it as a shortcut in Om to write the following fractions as decimals Without performing long division 7 WIS f i g h i i i i k 1 g m N016 4 Use the patterns from the problem above to change each of the following decimals to either a proper fraction or a mixed number a 071 d 12 b 07 e 43 c 25 1 78 State whether each of the following numbers is rational or irrational If rational then write the number as a ratio of two integers If the number is already written as a ratio of two integers simply rewrite the number 5 a 07 b J5 c g d 75 e R t 03 g 12 h i e i 7J5 k 004004000400004 Math 1300 Fundamentals quathernctIics The University of Houston 6 a J77 13 d E g 31 7 I b 08 c E e 7 t 7J5 h 710 i 0 k 003003000300003 Circle all of the words that can be used to describe each of the numbers below 7 79 Even Odd Positive Negative Prime Composite Natural Whole Integer Rational Irration al Real Undefined 0 7 Even Odd Positive Negative Prime Composite Natural Whole eger Rational Irration al Real Undefined 42 Even Odd Positive Negative Prime Composite Natural Whole Integer Rational Irration al Real Undefined Even Odd Positive Negative Prime Composite Natural Whole Rational Irration al Real Undefined Answer the following 11 Which elements of the set 78 721 702 0 J7 7r 5 12 belong to each category listed below a Even AeAaw Evavv z E E m Undefined b Odd d Negative f Composite h Whole i Real 1 Irrational Chapter 1 Inn oductaty Information andReview Exercise Set 11 Numbers 12 Which elements of the set 7625 74 73 7J3 71 g 1 2 10 belong to each category listed below a Even b Odd c Positive d Negative e Prime 1 Composite g Natural h Whole i Integer i Real k Rational l Irrational m Undefined Fill in each of the following tables Use Y for yes if the row name applies to the number or N for no if it does not 13 Answer the following If no such number exists state Does not exist 15 1 a H gt1 18 Find a number that is both prime and even Find a rational number that is a composite num er Find a rational number that is not a whole num er Find a prime number that is negative Math 1300 Fundamentals quafheman39cs The University of Houston p A G N O p A N 5 Find a real number that is not a rational number Find a whole number that is not a natural number Find a negative integer that is not a rational umber Find an integer that is not a whole number Find a prime number that is an irrational number Find a number that is both irrational and odd Answer True or False If False justify your answerj N N N N N 5 6 O Equot N W 1quot All natural numbers are integers No negative numbers are odd No irrational numbers are even Every even number is a composite number All whole numbers are natural numbers Zero is neither even nor odd All whole numbers are integers All integers are rational numbers All nonterminating decimals are irrational numbers Every terminating decimal is a rational number Answer the following 3 3 5 9 UI P l GW List the prime numbers less than 10 List the prime numbers between 20 and 30 List the composite numbers between 7 and 19 List the composite numbers between 31 and 41 List the even numbers between J5 and List the odd numbers between J5 and 123 Chapter 1 Inn oducmiy Information andReview Exercise Set 11 Numbers UI W Fill in the appropriate symbol from the set lt gt Find the multiplicative inverse of the following numbers If undefined write undefined a 3 b 4 C 1 41 7 7 J d e 2 59 Find the multiplicative inverse of the following I numbers If undefined write undefined 43 7 7 a 72 b g c 0 3 44 73 7 5 d 1g e 1 45 M 9 60 Find the additive inverse of the follow1ng numbers If undefined write undefined 46 75 75 a 72 b c 0 7 d 1 e 1 53 47 53932 E 61 Place the correct number in each of the following blanks 48 L 0 07 a The sum of a number and its additive 39 100 if 39 inverse is F ill in the correct number 49 l l b The product of a number and its 39 3 4 multiplicative inverse is F ill in the correct number 50 l l 6 5 62 Another name for the multiplicative inverse is the 51 71 fl 3 4 Order the numbers in each set from least to greatest 52 1 and plot them on a number line Hint Use the approximations J H 141 and 53 75 4 13 173 54 7 J5 63 71 743 04 g 7 4049 64 741310653713Jo64 56 l5 5 3 Answer the following 5 I Find the additive inverse of the following numbers If undefined write undefined a 3 b 4 C 1 d e 2 Math 1300 Fundamentals quathernan39cs The University of Houston Chapter 1 Introducmiy Information andReview Exercise Set 17 Interval Notation and Linear Inequalities For each of the following inequalities Write each of the following inequalities in interval a Write the inequality algebraically notation b Graph the inequality on the real number line c Write the inequality in interval notation 1 xis greaterthan 5 2 1 0 1 2 3 4 5 2 x is less than 4 3 xislessthanorequalto3 1 2 3 4 5 6 4 x is greater than or equal to 7 5 xisnotequaltoZ 1 2 3 4 5 6 6 x is not equal to 75 26 7 xislessthan fl 3 2 1 0 1 2 3 A 8 x is greater than 76 27 9 x is greater than or equal to 74 3 2 1 0 1 2 3 4 10 x is less than or equal to 72 28 11 xisnotequalto 78 4 3 2 1 0 1 2 E 12 x is not equal to 3 13 x is not equal to 2 and x is not equal to 7 GiVen the set S 2 4 r 3 use Slletitlltion t0 determine which of the elements of S satisfy each of 14 x is not equal to 74 and x IS not equal to 0 the following inequalities 29 2x 5 g 10 Write each of the following inequalities in interval 30 4x 2 gt 714 notation 31 72x 1 gt 77 15 x gt 3 32 73x 12 0 16 x 2 75 2 17 xgiz 33 x llt10 18 x lt 7 34 l g 2 x 5 19 3 lt x g 5 For each of the following inequalities 20 7 3 x 3 2 a Solve the inequality b Graph the solution on the real number line 21 x i 7 c Write the solution in interval notation 22 x159 35 2xlt10 36 3x 2 24 Math 1300 Fundamentals quatheman39cs The University of Houston Chapter 11mroducmiy Information andReview Exercise Set 17 Interval Notation and Linear Inequalities 37 75x230 38 74xlt40 39 2x752711 40 3x4gil7 41 873xgt20 42 107xgt0 43 4xilllt7x4 44 579xg3x77 45 10x7722x6 46 874xlt675x 47 578x24xl 48 x1028x79 49 7345xlt7277x 50 74372x7x20 51 iix x5 a 52 xgt7107x 53 7103x2lt8 54 79lt2x73ltl3 55 74377x l7 56 il9lt574x i3 57 l lt 3Hquot lt A u u 3 572 5 58 Tgt 6 gt 3 Which of the following inequalities can never be true 59 a 5x9 b 9x5 c 73ltx7 d 752xgt73 Math 1300 Fundamentals quafheman39cs The University of Houston 60 a 3gtxgt5 Answer 6 a 1 a W 1quot b 78 xltl c 72ltx78 d 772xgt710 the following You go on a business trip and rent a car for 75 per week plus 23 cents per mile Your employer will pay a maximum of 100 per week for the rental Assume that the car rental company rounds to the nearest mile when computing the mileage cost 21 Write an inequality that models this situation b What is the maximum number of miles that you can drive and still be reimbursed in full Joseph rents a catering hall to put on a dinner theatre He pays 225 to rent the space and pays an additional 7 per plate for each dinner served He then sells tickets for 15 each 21 Joseph wants to make a profit Write an inequality that models this situation b How many tickets must he sell to make a profit A phone company has two long distance plans as follows Plan 1 495month plus 5 centsminute Plan 2 275month plus 7 centsminute How many minutes would you need to talk each month in order for Plan 1 to be more cost effective than Plan 2 Craig s goal in math class is to obtain a B for the semester His semester average is based on four equally weighted tests So far he has obtained scores of 84 89 and 90 What range of scores could he receive on the fourth exam and still obtain a B for the semester Note The minimum cutoff for a B is 80 percent and an average of 90 or above will be considered an Chapter 1 Introducmiy Information andReview Exercise Set 15 Order of Operations Answer the following 1 In the abbreviation PEMDAS used for order of operations a State what each letter stands for wgtpgww A 5quot V If choosing between multiplication and division which operation should come first Circle the correct answer Multiplication Division Whichever appears first A n V If choosing between addition and subtraction which operation should come first Circle the correct answer Addition Subtraction Whichever appears first 2 When performing order of operations which of the following are to be viewed as if they were enclosed in parentheses Circle all that apply Absolute value bars Radical symbols Fraction bars Evaluate the following 3 a 345 b 345 c 3745 d 3745 e 3745 t 3745 4 21 10767 b 10767 c 1067 d 1067 e 77106 t 77106 5 a 7377 b 773 c 7377 d 773 6 a 725 b 725 I275 w25 Math 1300 Fundamentals quatheman39cs The University of Houston A n V C a a 72775 b 72775 727775 d 727775 720475 t 27757 767274 b 767274 76724 d 7672x741 27764 t 274762 2 1 1 2 1 1 n2 0 gig 2 1 1 EH 3 5 0 Slab 3 5 3 5 1 3 1 5 54772 b 71772 571477 d 7741752 752712 t 75712 72732 b 723732 72314 d 723143 2H32 1 232 20210 b 20210 7201072105 24 472 b 24 4 7 2 24724272 10252 b 10522 210275275 3934 b3934 37973743 set er see mgr 59 set Chapter 1 Inn oducmiy Information andReview Exercise Set 15 Order of Operations 19 774151 35 7457243272 36 7924 37 742 121752 743 Z Z 23 1L 7 j 3s 7J1445 726 4123 2 3 4 J49 3722 24 3 3 10 39 39 737539 3J5 J25 40 3149722 25 533 3449 26 16 4916712 39 7 4 41 3 2 16 45 27 2734ZH tlz 28 244441 42 W 29 273J 43 I727SZI75Y 30 273441 2824 31 24344 12 4739327539 44 m 32 2734 2 33 2lt21gt2 Ji2 z 34 5727 E2 V2322 il3i3zl 7 46 1 Mi az 13 14m Math 1300 Fundamentals of Mathematics The University of Houston Chapter 11mroducmiy Information andReview Exercise Set 15 Order of Operations Evaluate the following expressions for the given values of the variables 47 mi forP5r71andk7 48 l for x4y73andz8 y z 49 ibc I2786 for 174 and 072 50 m for a7lb3andc18 211 Math 1300 Fundamentals ofAIathematics The University of Houston Chapter I 39 Introductory Information andReview Exercise Set 14 Exponents and Radicals Write each of the following products instead as a base and exponent For example 66 6 1 Fill in the appropriate symbol from the set lt gt a 777 b 1010 c 888888 d 3333333 a 999 1 44444 c 5 555 d 1717 772 0 9quot 0 86 0 786 0 7102 7102 7103 40f Evaluate the following 9 11 12 a 31 b 32 c 33 d 31 e 32 t 33 g 731 h 732 i 33 0 3 k 3 I 3 m 3 n a o 3 a 5 b 50 c 50 d 51 e 51 t lt51 g 52 h 62 i lt52 i 53 k 63 I lt53 m 54 n 754 o 75 a 052 b 2 2 c a 0032 b Math 1300 Fundamentals quatheman39cs The University of Houston Write each of the following products instead as a base and exponent Do not evaluate simply write the base and exponent No answers should contain negative exponents 13 a 5256 b 5456 14 a 3835 b 3835 69 69 15 a 6 2 h 67 79 79 16 a 7 5 h 77 47 43 411 473 17 a 48 b 4845 812 874 89 1839 a b a 736 b 52quot3 a 324 b 2354 Rewrite each expression so that it contains positive exponents rather than negative exponents and then evaluate the expression a 5 1 b 5 2 c 5 3 a 3391 b 3 2 c 3393 a 2 3 b 2 5 a 72 b 104 a b if a 7 a 752 b b 5 a 78V b 78 2 Chapter 1 Imroducrmy Information andReview Exercise Set 14 Exponents and Radicals Evaluate the following 42 co 7 do 0 723 2 2 05d 29 3 T 13 T6 2 2 3 6 72 43 7 3 b 5 1 751 21153122 30 a 5 2 h 573 72 2 3 0 2 1 72 44 5 f 31 a 23 b 253 76a b 32 a 3 1 22 b 3 2 10 Write each of the following expressions in simplest radical form or as a rational number if appropriate If it is already in simplest radical form say so Simplify the following No answers should contain negative exponents 45 a 36 b J7 c J 33 a 3x3y4 3 b 33c3y z2 3 46 a JE b JE c 32 34 a 6x 5y3z42 b 6x 5y3z4 2 47 a 50 b J17 c x73x74x7671 35 x77 L 16 4s a 192 b E c J55 2 r3 4 36 amp x4x7171 49 a J b J5 c 27r 37 k3m2 50 a 45 b JR c M k71 r2 3 m 51 a J5 b 80 c J5 4 r3 4 7 3s a b c 52 a M b M c 84 a3b7569 72 4w 1 if 2 39 471079 53 a 5 b 4 c 7 r7 0 2 40 735276264 54 a b E c 0 0 7 41 a H 55 a ab0 J3 1 ll E 13 c 2 l 3 b E c E 56 a J5 Math 1300 Fundamentals quatheman39cs The University of Houston Chapter 11222206114010131 Information andReview Exercise Set 14 Exponents and Radicals b 378 c 7 b 4781 0 745 W 45 65 a 61000000 b 1000000 c 41000000 57 a s35 b lx4ysz7 63 a 58 a 27 ms11212905 Evaluate the following a a A 5 V n N A 5quot V 7 U N c 45 c 11 c 731 a 02 01quot m 06 ex l A 1 v s SIH A 5quot v s l SIH 60 a W b 54 9 my 68 a u A 5quot V a l G A 5 V A 5quot V 7 V o o v o o 5 4 100000 We can evaluate radicals other than square roots With square roots we know for example that c 7V5 1001000 J5 7 since 72 49 and 4 49 is not a real number There is no real number that when squared 70 a 31 b 5 71 c 731 gives a value of 49 since 72 and 72 give a value of 49 not 49 The answer is a complex number which will not be addressed in this course In a similar fashion we can compute the following Cube Roots J3 125 5 since 53 125 J3 125 5 since 53 125 Fourth Roots 0000 10 since 104 10000 l 10 000 is not a real number Fifth Roots 2since 2532 J5 32 2 since 25 32 Sixth Roots 6 since G 64 5 is not a real number Evaluate the following If the answer is not a real number state Not a real number 61 a M b m 0 la 62 a J3 b J3 c 43 Main 1300 Fundamentals quafhenan39cs The University ofHausmn Chapter I 39 Introductory Information andReview

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