IYIIII ( ) % =D. ons ( 1) 94 ) ( (

Transcription

1 C tz (5 Math 60 Exam #1 Review This is a preview of the test Any questions from the homework are possible on the exam i) Please practice every problem on this review two or three times, ii) Find problems like them in the homework and practice those iii) Create your own exam using homework problems, place two hours on a timer, and take the exam iv) Practice the problems you missed and find ones like them to practice v) Create a new exam and take it Repeat if needed 1 a) Simplify (4pts) b) Simplify (5pts) 4 5 ons : 3 % =D c) 3(5 8) ( 3) 3 d) (6 4) IYIIII 3C 3) C 3) XD > ) 9 7 ) ( ) a) Evaluate b) Evaluate use 9 b c+ a ( 1) ) ( +49 ) +( ) 94 ) ( ) ; use a = 7, b = 1, and c = 380 1

2 x 3 a) Simplify b) Simplify: 5 y 6z 8 y 8z 3 tgl/+@ * mm c) Simplify: ( z z 10) d) Simplify: 10(5a ) 4(5 a) 41 50ato 54 o*4a e) Simplify: 9 x+ 9 5 x x+ 3 5 f) Simplify: 3 x 4 x y x y # 5x s , arm # 63, g 7y 4 a) Solve: b) Solve: 41 =F if =34, y= T

3 c) Solve: 4x 5 7 d) Solve: 1x 59 6 x 5 5L ' =3, E #= 1 e) Solve: x x f) Solve * =[5 5,155 x±}}=3x=±d +sx# = }y ' I9g=t _ or xiof to " g) Solve: " x x h) Solve: 7 14 ( M ) [ I ] *+4= Ex3# 47=5+3 ( h t 14?tfiis death 1) ± t = n= O 5 a) Solve: b) Solve: *s# Kt_g8g or 3148= = I g3 s 13+74=10 K@ or 7m=±g It 3t7m=lo t 3

4 6 a) Solve: for x b) Solve for z b= a =CaI ) (X+3 =10y t3z=loy x= O 15 * c) Solve for p #=P@, =io O 7 a) Solve: 4x 6 x 4$ # b) Solve: 4x 8 4 3*5 ) # t Xz z X< 3 Answer Interval notation: C a, 3 ) 3 Answer Interval notation: 30 ) c) Solve: n 4 6n 9f3+t3nn=8 4N attesiee L Answer ] # Interval notation: C a, ] 7ns 7 4 he #

5 8 Translate the phrase into an algebraic equation Do not solve a) 5 less than twice a number is seven more than the number = 7 + X ~ 5=7+6 b) The product of six and a number is 30 times the difference of 14 and the number 11=30 ( 14 x ) 9 A piggy bank contains 9 coins in quarters and nickels The have a value of $505 Find the number of each coin type a) Express in terms of x: # qgenar dimes X # nickels 9 X # quarter Quarters 5 5 Nicked Number Value Total Quarks Dimes X 505 Nickels 9 X S 9 X S x 145 Total sx=sos =505 = c) # Make dimes 11 # quarters Turtle and Vince sell reptiles Specifically, they sell tortoises and lizards They have 8 more lizards than tortoises, and the total value of the reptiles is $60 The value of a lizard is $5 and the value of a tortoise is $3 How $5 many of each type of reptile do they have? a) Express in terms of x: # tortoises # lizards LizardsTortoises 5 stt 3 t t > t 611=30441 o = 360 t = 5 Tortoises Lizards Total 8th Number Value SX Total t 3 3T 8th 5 4o+st 8t# X g check : 11+18= =505 = 5 Chcckitmurelizuib 3 > t= 185 t=5 5) 3( +543=5 c) # tortoises 5 # lizards 13 5

6 11 16ft steel beam is to be cut into two pieces so that one piece is 1 foot longer than twice the other Find the length of each piece =L + z X a) Express in terms of x: One of the pieces ltzx The other piece Gft It = Zx t X 16 3x=Is check : 11+5=6 $ 3 1t3 =/s # =s 54+1=11 3 = IS 1+61= =4 c) One of the pieces The other piece 1 A mountain cabin on 1 acre of land costs $30,000 If the land cost 4 times as much as the cabin, what was the cost of each? 4C a) Write in terms of x: The cost of Land:, The cost of the Cabin: C C Check : 4 ( t C = 30, tooo,ou=3o,ow SC = =4 ooo, 30,000 t s d) Answer: C = 6,000 The cabin costs $6,000 and the land costs $4,ou 13 The sum of three consecutive odd integers is 189 What are the integers? a) Write in terms of x: 1st integer, nd integer, xtz 3rd integer xt4 Xtxtztxt 4= =183 3 = 3 +6 lgy 6T 11= c) 1st integer, nd integer, 3rd integer check : =189 6

7 = X + t Find three consecutive even integers such that the sum of the least integer and the greatest integer is 1 more than the middle integer + Xtz a) Write in terms of x: 1st integer, nd integer, Xtz 3rd integer xt4 + Xt4= xt 4=14 Check : c) 1st integer, 10 nd integer, 1 3rd integer A total of $9000 is invested, part of it at 10% and the rest at 1% The total interest after one year is $1030 How much was invested at each rate? a) Fill in the table d) 1% 16 A total of $7000 is deposited into two simple interest accounts On one account, the annual simple interest rate is 10%, and on the second account, the annual simple interest rate is 15% How much should be invested in each account so that the total annual interest earned is $800? a) Fill in the table +4=1/+14 = / +4=14 Account 1 Account Total Account X=10 Principle Rate Interest X / X good 1030 Principle Rate Interest 10+14=1+1 4=4 Check : soot6sou=9oa , =10 0 ozx= Su =1030 # In 0, =1030 X= =0,0 Zx = so $500 $6500 X Check : Vzocotsoouilooo Account NX ioso oisx Total W =800 tlu#cdtolsfao)=8w0l0xt/0soio1sx=8oo ( oso toso 0,0=50 * to = Sooo }d $5000 $000 c) 15% 7

8 17 Two planes start at the same time from the same point and fly in opposite directions The first plane is flying 100 mph faster than the second plane In 3 h, the two planes are 1050 mi apart Find the rate of each plane a) picture Pi R ( heck : distance 1050 for plane I d= (5 3)=675 miles dptnnce for plane 100A dz=@5) (3) ' 375mL 1050 miles X 3 3X Bike c) Answer: Zhonrheadsht 18 A bicyclist traveling 15 mph heads out at 8 AM At 10 AM a motorcyclist heads out in the same direction traveling 45 mph At what time will the motorcyclist pass the bicyclist? a) picture d, + diluso =1050 3co3G = > SO X= 15 to =5 Planet is flying at zzsmph and plane is traveling at 15 mph Bike Motorcycle time 15 ttz 1st +30 HZ h 8am +3=11 an Mta 't yg + yst I h loamtl = 11am 1St +30=45 E t\t_t Check ; Bike dp= 1567=4 smile = 3% 1 =t t Mdwcyok dm=4s(d=4smilg c) Answer: The motorcyclist will pass the bike at 11am 8