AP Calculus Prerequisite Skills Summer Assignment 2016

Transcription

1 AP Calculus Prerequisite Skills Summer Assignment 2016 Dear AP Calculus Student, Welcome to the wonderful world of calculus! You ve worked hard (we hope) to achieve success in our previous math classes, and now ou re read to eperience the beaut, elegance, and challenge of calculus. Well, ou re almost read. Believe it or not, there aren t a lot of new concepts for ou to learn in calculus. (There are a couple of real biggies, though. The good news is that the biggest idea in Calculus involves slope. That s right, slope the same concept ou learned in Algebra 1! ). In an event, the most important thing at the outset of our calculus adventure is that ou have a solid foundation in algebra, trigonometr, and other pre-calculus skills. If ou are competent in these skills, we can focus on the calculus we will be learning and reall delve deepl in some nice applications. Therefore, to help ou prepare for net ear, we are giving ou some review work to do over the summer. I epect that this will take about 8 (or fewer) hours of our summer break to complete. (I predict we will have at least 8 hours of rain this summer, so to keep ou from becoming too bored, I have provided this work for ou. You can thank me later.) Make sure to check our answers. Do not despair if ou have difficult with some of the problems and have trouble coming up with the answer given. We will spend a few das reviewing these skills before having a test. Oh, eah, we re going to have a test on this stuff. Again, don t panic we will review when ou come back to school. It is ver important, however, that ou complete the packet, which means showing our work, checking our answers, tring again if ou got the wrong answer, and coming back to school knowing what it is that ou don t understand so ou can ask questions. Please bring our completed packets the first da of school and be read to ask questions about anthing ou did not understand. Have a great summer! Sincerel, Mr. Lundergan

2 -1- a tksuythac ZSZo4fMtqw7a6reW WL4LCz.b c 4AilllK qrgipglhjtqsn erfels2ervvpe8dh.k P fmjaqdwel 0wRiktbh0 LIbnSfjibnsi8t1e9 CAplRgoePbZrBaq X2.E Worksheet b Kuta Software LLC AP Calculus Name Prerequiste Skills Evaluate each function. 1) ) ; Find ) 2) f ( ) ; Find f () 3) ) ; Find ) 4) f ( a) a ; Find f ( a) 5) k( n)n n; Find k(a) 6) p( ); Find p( ) Write the standard form of the equation of the line described. 7) through: (, ), perpendicular to 8) through: (, ), perpendicular to 9) through: (, ), parallel to 10) through: (, ), parallel to

3 -2- g zk5uvtjav MSUo6fXtWwFanr8ep TL2L4C1.2 F XAKlrlF 9rRimgwhNtiss Qr8ejskeVrbvWe3dZ.P O JM5acdpeE zw3iktjh7 AI2nGfsiTnliktjem KA0lgZeKbarla6 A2C.L Worksheet b Kuta Software LLC Sketch the graph of each line. 11) 12) State the maimum number of turns the graph of each function could make. Then sketch the graph. State the number of real zeros. You should be able to figure this out without using our calculator. 13) f ( ) = 14) f ( ) = 15) Julia left the hospital driving toward the mountains 3.5 hours before Beth. Beth drove in the opposite direction going 1.5 mph faster then Julia for two hours after which time the were 576 mi. apart. How fast did Julia drive? 16) Jaidee left the science museum and drove toward the ferr office at an average speed of 21 km/h. Sarawong left 1.6 hours later and drove in the same direction but with an average speed of 29.4 km/h. How long did Jaidee drive before Sarawong caught up?

4 -3- k QKcuQt7aK 5SPoQfbtCw2aRrNe7 MLHLOCz.4 J KAVlslv MrJieg8hUtusd hrhejsoesrgv5esdm.o j RMSaXd8eE 5wIiMtYhI uimnafwiwnvi4tpe4 0ADlrgFe2bGrAan P2R.H Worksheet b Kuta Software LLC Solve each equation b factoring. 17) 18) a aa Solve each equation with the quadratic formula. 19) r rrr 20) a aa Perform the indicated operation. 21) f ( t)t t)t Find f ( )) 22) h( t)t t)t Find )h() 23) ) f ( ) Find f ( )) 24) h( a)a a)a Find ( gh)( a) Identif the domain and range of each. Then sketch the graph. 25) = log ( ) 26) = log ( )

5 -4- k XK8uotOaT 7S3odfctQwma6rSeM nlglac6.r famlli pr0i9gmhmtssn troehssearvvke5d.h l kmasdwen FwiRt2hI EIunjfViHnRi6t3ej 2AzlJgceVbrma Worksheet b Kuta Software LLC Sketch the graph of each function. 27) 28) Find the inverse of each function. 29) )( ) 30) ) Solve each equation. 31) 32)

6 -5-7 mkufthal uspo9f6tiwpayrbej ZLRL3CJ.h 3 waql8lw 0rHi6gzhgtPs1 0r4ebsLerrpvDeCda.o n hmpawdaek Vw7ivthhZ uianqfgibnuihtnem JAolSgVetbvrYa4 P22.Q Worksheet b Kuta Software LLC Graph each equation. 33) 34) Simplif each epression. 35) 36) u u Solve each equation. 37) ( ) n ( ) n 38) Solve each equation. Round our answers to the nearest ten-thousandth. 39) k 40) Solve each equation. 41) log log ( ) 42) log log 43) log log log 44) log log

7 -6-3 IKouDtUap pszoof5t7wsa4reev XLpLICq.O Z wa5ltla rqingnhct7s5 8r8eIsBeQr0voeJdW.R O AM1abdFej TwNiptAhO VI2nhfiwnYistBez UAhlZgceBbmr9as 52q.6 Worksheet b Kuta Software LLC 45) ( p) ( p)p 46) n( n)( n) 47) n 48) v Simplif. Your answer should contain onl positive eponents. ( 49) ( ) ) ( v v ( 50) v u v ) ) ( ab 51) b a b ) 52) m ( nm ) m Factor each completel. 53) 54) 55) 56) p p 57) b b 58) 2 ml of a saline solution was mied with 5 ml of pure water to make a 4% saline solution. Find the percent concentration of the first solution. 59) Julia wants to make 16.5 ml of a 24% sugar solution b miing together a 60% sugar solution and pure water. How much of each solution must she use? Simplif each epression. 60) ( nn )( n n) 61) ( )( ) Describe the end behavior of each function. You should be able to do this without looking at a graph. 62) f ( ) = 63) f ( ) =

8 -7- U LKRu1tDah sscozfit9wwaarteo LULXCP.T D DAXlJlc hrjifg6hstos0 1rdezsNeYrvfePda.g Q 4MaaSdqez kw8izthi CIFnKfEiSnEi3tQeR 3AlEgjelb6r7ak 221.U Worksheet b Kuta Software LLC Find the area of each sector. 64) 65) 13 in 12 ft Solve each sstem b elimination. 66) 67) Solve each sstem b substitution. 68) 69) Solve each sstem b graphing. 70) 71) Convert each degree measure into radians and each radian measure into degrees. 72) ) 700

9 -8- o PKnuItTaZ QSAozfItMwJaQrBeF LLrLXC0.X g UAPl2lb 8rFiVgKhKt0sz Oresiesr5vseLdN.8 l YMtaZdpeq Qw8itHhU 1INn2fIienhibtuet LA6lDgkeObRrMak b2a.h Worksheet b Kuta Software LLC Find a coterminal angle between 0 and ) 75) Find the eact value of each trigonometric function. 76) csc 77) tan 78) cot 79) cos Use the given point on the terminal side of angle to find the value of the trigonometric function indicated. 80) tan 81) csc (, ) (, ) Solve each triangle. Round our answers to the nearest tenth. 82) 83) ma30, mc61, c B A 23 d 91 C 26 d Find the measure of the indicated angle to the nearest degree. 84) 18 10? 85) 35? 11 86)? )? 8 4

10 -9- a zkmukt8a7 JSUonfbtNwNa1r6eg glflfca.t L 8Aglllh orri7gpht0s3 7rbeQs6eXrgveQdg.m o MGadduez Dwki4tVhj HIqnmfTi2nHist3ep FA2lzgembzrUa2 j2c.9 Worksheet b Kuta Software LLC Solve each equation for. 88) sin 89) tan 90) tan 91) cos Solve each triangle. Round answers to the nearest tenth. 92) C 93) B A 49 4 ft B 15 d C 5 d A In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. 94) b2 km, ma68 95) b3 m, c6 m

11 -10-8 DKuuMtPaf JSDonf5tdwTaLrIeq VLvLcCU.9 l VAdlulX Zrki3gUhhtusd trexsceprkvgende.k v RMXaWddew 4wEi9tBhe QI3nCfNiPnJi2t7eo 2A1lpgde3bUrcaS 42f.I Worksheet b Kuta Software LLC 96) Susan has decided to design web sites. She believes it will cost her $2500 for equipment to start her business plus she plans to spend $150 per customer to individualize the web site. She will charge $500 per customer. a. Write a function, R(), to give the income as a function of the number,, of customers. b. Write a function, C(), to give the cost versus the number,, of customers. 97) The following table shows the trend in worldwide grain production (wheat, rice, and corn, primaril), in millions of tons: Year: Amount a) Use our calculator to find the linear model that best fits these data (use STAT/EDIT to enter data, and STAT/CALC LINREG to find the equation). Let ear 0 = c. What is the income if Susan had 5 customers? d. What is the cost if Susan had 5 customers? e. How man sites will Susan have to design to make a profit? b) What does the model predict for the amount of grain produced in 2020? c) When does the model predict that the total amount of grain produced will reached 2000 million tons (2 billion tons)? d) Describe the implications of the fact that grain production is growing roughl linearl while the population is growing roughl eponentiall. 98) A population of fruit flies, initiall numbering 100, becomes 150 in 3 das. Determine the population of fruit flies after 10 das. 99) The number of students enrolled in a Pre Calculus refresher course is given b the function N(t)=1000/(1+999e^(-0.3t)), where t is time in das. a) How man students were enrolled at t = 0 das? b) How man were enrolled at t = 10 das? c) How long will it take for 500 teachers to enroll?

12 -11- m JK6uDtFaj 6S0oQf7tVwFaErne SLVLLCw.E f CAVl1lA srviegkhrt2si JrqeEsVe4r8vXeEdr.M a 3MRardae6 MwuiktLha TI5nnf3iwnpietae3 OABlUgKebKrCaz F2j.7 Worksheet b Kuta Software LLC Answers to Prerequiste Skills 1) 2) 3) 4) 5) a a 6) 7) 8) 9) 10) 11) a 12) 13) Ma # Turns: 2 # Real Zeros: 3 14) Ma # Turns: 2 # Real Zeros: 3 15) 76.4 mph 16) 5.6 hours 17), 18), 19) 21) 22), 20) i, i 23) 24) a 25) Domain: Range: All reals 26) Domain: Range: All reals

13 -12- O wk2u6tmag QSQoIfOt2wcanre2 LILwCL.a v samlkl3 srkitgohbtqsz wrhesmeertvwedn.q J MZaEdBeo Ew3iCtthH gi8nrfli7nmihtuel 5AClkgweebqrcaX 2f.N Worksheet b Kuta Software LLC 27) 28) 29) g ( ) 30) 33) g ( ) 31), 34) 32), 35) u 39) 36) 40) 41) No solution. 42), 43) 44) 45) 46) 47), 48) 49) v a 50) 51) u 37) 38) 52) n m 53) ( )( ) 54) ( )( ) 55) ( ) 56) p( p) 57) b ( b) 58) 14% 59) 6.6 ml of 60% solution, 9.9 ml of pure water 60) n n 61) 62) f ( ) as 63) f ( ) as f ( ) as f ( ) as 64) ft² 65) 66) (, ) in² 67) Infinite number of solutions 68) (, ) 69) (, ) 70) (, ) 71) (, ) 72) 73) 74) 75) 76) Undefined 77) 78) 79) 80) 81) 82) ma41, mb48, c35 d 83) mb89, a, b 84) 29 85) 18 86) 17 87) 27 88), 89), 90), 91), 92) ma41, b3 ft, a2.6 ft 93) mb19.5, ma70.5, a14.1 d u b

14 -13- c UKGu5t3aH SS4oSfmt0wzaerEeS LPLNCM.8 X TAulklT 4rkimgFhmtJsS bruecsqegrvvfendn.k n hmjaedeeb 0wuiEtChI bi5niffinnyihtdeo PAQlBgPeZbmrBaX b2d.5 Worksheet b Kuta Software LLC 94) mb22, a5 km, c5.4 km 95) mb30, ma60, a5.2 m 96) R() = 500; C() = ; $2500; $3250; 8 97) a) = b) about 2396 milliion tons (2.396 billion) c) around the middle of 2003 d) if grain production is linear while population growth is eponential, food shortages could occur 98) 385 (k =.135) 99) a) 1 student b) about 20 students c) about 23 das