Prerequiste Skills (Summer 2014)

Transcription

1 -1- X akqupttaa MSNogfItLwAaAr2eE xlhlkcy.k t jaelhlc DrNi8gJhlt8su 5r1eTslezrevqekdG.h E YMPa6ddeC nw0idtxhh iiknhfjihnlivtyey ianl6gselbjr9ak c2t.f Worksheet by Kuta Software LLC Honors Calculus Name Prerequiste Skills Summer 2014) Evaluate each function. 1) x) x ; Find ) 2) f x) x ; Find f ) 3) x) x ; Find ) 4) f a) a ; Find f a) 5) k n)n n; Find ka) 6) p x)x; Find p x) Write the slope-intercept form of the equation of the line described. 7) through:, ), perp. to yx 8) through:, ), perp. to y x 9) through:, ), parallel to y x 10) through:, ), parallel to yx Solve each equation. 11) b)b 12) x)xx 13) n)n 14) x)x Sketch the graph of each line. 15) xy 16) yx

2 -2- S 8KSuAtKas os3ovf3tlwnaorxeh WLxLyCi.q c vallsly ErSiwgGhot2sY rr5ehsaejrtvqeqdu.4 t OMNaKdKeM FwAiztuho KIEn4fZiOnmiStwe6 OAfl0guelbAr6aC t25.0 Worksheet by Kuta Software LLC 17) 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 they were 576 mi. apart. How fast did Julia drive? Solve each equation by factoring. 18) Jaidee left the science museum and drove toward the ferry 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? 19) k kk 20) m m 21) x xx x 22) n nn Solve each equation with the quadratic formula. 23) r rrr 24) a aa Perform the indicated operation. 25) h x)x x)x Find g h)) 26) x)x x f x)x Find g f )) 27) x)x f x)x x Find f x)) 28) h a)a a)a Find gh) a) Simplify each expression. 29) x x x 30) u u Solve each equation. Remember to check for extraneous solutions. 31) k k k k k k k 32) v v v v v 33) x x x x x x x x 34) v v v v v Solve each equation. 35) ) n ) n 36) x x

3 -3- s lkjuftrat 2SHoefDtMwpaNrdef NLCLQC2.S h EAGlhlp zr2ilgzhit4s9 CrReusYeCrAvgeodN.9 6 kmmagdnea swhiateh8 RIRn5friantiOtUel taxl0gmenbergae 72E.J Worksheet by Kuta Software LLC Solve each equation. Round your answers to the nearest ten-thousandth. 37) n 38) n 39) n 40) p 41) n 42) x 43) n 44) m 45) x 46) n Solve each equation. 47) log log x 48) log x)log xlog 49) log x )log 50) log log x) 51) log x)log xlog 52) log x )log 53) log x)log x 54) ln ln x) 55) log xlog x)log 56) log xlog x)log 57) ln xln 58) log x )log 59) p) p)p 60) n n) n) 61) v 62) b 63) n) 64) p) 65) v) 66) k Simplify. Your answer should contain only positive exponents. x y 67) xy ) x ) v v 68) v u v ) )

4 -4- r vkgu8tyaz wssowfktswjaqrpeo ml9l0ci.s b eaal9l6 jrxipgyhyt0s0 9rceDsDeUr0vReTde.x C IMraAdjeS NwriStohQ LIonHf4innCintpe5 FAdlGg7ejbTrEa0 P2d.W Worksheet by Kuta Software LLC ab 69) b a b ) Factor each completely. 70) m m nm ) 71) p p 72) b b 73) 2 ml of a saline solution was mixed with 5 ml of pure water to make a 4% saline solution. Find the percent concentration of the first solution. 74) Julia wants to make 16.5 ml of a 24% sugar solution by mixing together a 60% sugar solution and pure water. How much of each solution must she use? Simplify each expression. 75) nn ) n n) 76) x x x ) x x x ) Solve each system by elimination. 77) xy xy 78) xy xy Solve each system by substitution. 79) xy xy 80) xy xy Using radians, find the amplitude and period of each function. Then graph. 81) ycos ) 82) y sin )

5 -5- B xk4u3t6ad USBolfEtLwraYrkeO eltl9c0.s 9 VA0lclT 1rNiBgChftysB MrFeXs5eMrHvmeodU.x p ymga2dneu Qw3iZtMhC MI7n8fliRnFiDtnex JAplagUeNbWrZay i2j.7 Worksheet by Kuta Software LLC Find the measure of the indicated angle to the nearest degree. 83) 18 10? 84) 35? 11 85)? )? 8 4 Solve each equation for. 87) cos 88) cos 89) sin 90) tan 91) sin 92) tan 93) sin 94) cos Find the measure of each side indicated. Round to the nearest tenth. 95) C x 34 A 96) C A 16 in B 13.9 in B 49 x

6 -6- P YKPuItfau ESVobfrtywRairQeb 2LmLxCB.N L EAhl2l4 Or4i1gUhLtrs3 KrXeksheTrPvieOdL.e E CMfaAdieG rwqiptshf KIWnTfPi1nriat2eY CA6logdeKbzrZaj r2m.r Worksheet by Kuta Software LLC 97) 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, Rx), to give the income as a function of the number, x, of customers. b. Write a function, Cx), to give the cost versus the number, x, of customers. 98) The following table shows the trend in worldwide grain production wheat, rice, and corn, primarily), in millions of tons: Year: Amount a) Use your 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 year 0 = c. What is the income if Susan had 5 customers? d. What is the cost if Susan had 5 customers? e. How many 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 roughly linearly while the population is growing roughly exponentially. 99) A population of fruit flies, initially numbering 100, becomes 150 in 3 days. Determine the population of fruit flies after 10 days. 100) The number of students enrolled in a Pre Calculus refresher course is given by the function Nt)=1000/1+999e^-0.3t)), where t is time in days. a) How many students were enrolled at t = 0 days? b) How many were enrolled at t = 10 days? c) How long will it take for 500 teachers to enroll?

7 A vkcuwtiac JSmoNfWtvwBaBrReS LLRLvCF.p b BANlflp Jreidg2hqt6sd 2r5eKsDe2rUvQeldw.D 5 3MPaPdTeQ wweigtdhi 3ITndfZiVnTiqtaeq KA3lwgWesbgrqa9 m2x.n -7- Worksheet by Kuta Software LLC Answers to Prerequiste Skills Summer 2014) 1) 2) 3) 4) 5) a a 6) x 7) y x 8) y x 9) xy 10) xy 11) 12) 13) 14) 15) a 16) 17) 76.4 mph 18) 5.6 hours 19), 20), 21), 22), 23), 24) i, i 27) x x 28) a 31) 32), 35) 36) 25) 26) 29) x x 30) u u 33), 34), 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 48) 49), 47) 51) 52), 53) 50) 54) 55) 56) 57) 59) 60) 61), 62) e e e 58), 63) 64) 65) 66) 67) y v a 70) n m 68) 69) u b 71) p) 72) b b) 73) 14% p

8 T XKFuDtNa0 ss4odfptxwtalriex LLALBCw.q j hailglv TrHiagZhktEs6 brmefsnearyvjelde.c J sm8aidtet RwRi8tahK iiqnzflianuivtbe0 LAfltg2ebbbrJau 622.y -8- Worksheet by Kuta Software LLC 74) 6.6 ml of 60% solution, 9.9 ml of pure water 75) n n 76) x x x x 77), ) 78) Infinite number of solutions 79), ) 80), ) 81) Amplitude: Period: 82) 83) 29 84) 18 Amplitude: Period: 85) 17 86) 27 87), 88), 89) 90), 91),,,,, 92) 93),,,,,,, 94),,,,,,, 95) 23.7 in 96) 21.2 in 97) Rx) = 500x; Cx) = x; $2500; $3250; 8 98) a) y = 24x b) about 2396 milliion tons billion) c) around the middle of 2003 d) if grain production is linear while population growth is exponential, food shortages could occur 99) 385 k =.135) 100) a) 1 student b) about 20 students c) about 23 days