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# Algebra with Calculus for Bus MAT 1033

UTSA

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This 14 page Class Notes was uploaded by Miss Cloyd Cronin on Thursday October 29, 2015. The Class Notes belongs to MAT 1033 at University of Texas at San Antonio taught by Edward Esparza in Fall. Since its upload, it has received 48 views. For similar materials see /class/231333/mat-1033-university-of-texas-at-san-antonio in Mathematics (M) at University of Texas at San Antonio.

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Date Created: 10/29/15

MAT 1033 Test 1 Review Name Solve on separate paper and select the best answer MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question Simplify the expression Write answer with positive exponents Variables are positive real numbers 1 MW 7 A 13349 B 13107 C b3 D 1317 2 16k4m814 A 3 B amp C 2ka D 4ka m2 m2 Write the rational exponent expression as an equivalent radical expression 3 awU3 3 A 3 B 1 C L D 3 J 3 3 3 I 3x 3x Simplify the expression 3 4 4 26 3 A 2 B 4 26 C 8 D 4 5 IE 6x43 2 A 10 245 643 12 B 3 10 12 CI10 12 D llO 4 E 12 Solve the equation 6 4lty4 5lty 5 A 41 B 9 C 9 D 41 Solve the equation 2 1 7 7 gx gx3x1 27 9 1 9 A E B I C E D E Solve the equation 8 5 39 0 x1x 1 A6 B C1 1 D 11 Solve the formula for the speci ed variable 9 A lhb1 b2 for b1 2 b 2A h hb 2A Ab1 Bb1 2A hb A hb Solve the equation 10 1 5x 4 1 3 7 1 7 1 A 5 B 1 7 C 5 5 D 5 Solve the problem 11 Roberto invested some money at 6 and then invested 2000 more than twice this amount at 11 His total annual income from the two investments was 3860 How much was invested at 11 A 2800 B 6000 C 28000 D 26000 12 Chuck and Dana agree to meet in Chicago for the weekend Chuck travels 378 miles in the same time that Dana travels 354 miles lf Chuck39s rate of travel is 4 mph more than Dana39s and they travel the same length of time at what speed does Chuck travel A 70 mph B 56 mph C 63 mph D 59 mph Use factoring to solve the equation 13 x2 x 42 A 6 7 B 1 42 C 6 7 D 6 7 Solve by the square root property 14 r 42 13 A EAE B 9 C4J 4 V D 4J 4 V Use the quadratic formula to solve the equation Give both exact and approximate answers 15 6x2 10x 1 A 5 11319 4053 078 B 3910i6quot119 094 2393 c 5 2 31 0095 1761 D 6 19 41101156 Solve the problem 16 A ball is thrown downward from a window in a tall building lts position at time t in seconds is s 16t2 32t where s is in feet How long to the nearest tenth will it take the ball to fa1153 feet A 18 sec B 09 sec C 11 sec D 12 sec Solve the equation for the indicated variable 17 A rtr2 for r Ar E 8r3 quot Cr3 An Dr i n A 371 Find the x intercepts and y intercepts of the graph of the equation 18 y x2 7 A X intercept 7 0 no y intercepts B y intercept 0 7 no x intercepts C y intercept 0 7 X intercept 7 0 D y intercept 7 0 no x intercepts Decide whether the pair of lines is parallel perpendicular or neither 19 3x 2y 12 2X 3y 9 A Parallel B Perpendicular C Neither Write an equation in standard form for a line passing through the pair of points 20 2 6 and 5 8 A 2gtlt 7y 46 B 2x 7y 46 C 4x 13y 124 D 4gtlt 13y 124 Solve the problem 21 Assume that the sales of a certain appliance dealer are approximated by a linear function Suppose that sales were 6500 in 1982 and 64500 in 1987 Let x 0 represent 1982 Find the equation giving yearly sales Sx A Sx 58000x 6500 B Sx 11600x 64500 C Sx 58000x 64500 D Sx 11600x 6500 22 Let Cx 100 80X be the cost to manufacture X items Find the average cost per item if50 items are made A 113 B 94 C 82 D 288 Solve and graph the inequality Give answer in interval notation 23 11x 75 12x 11 Solve the inequality 24 Fantastic Flags lnc finds that the cost to make x flags isC 9X 14542 while the revenue produced from them is R 41X C and R are in dollars What is the smallest whole number of flags X that must be sold for the company to show a profit A 455 B 465344 Determine whether the following rule de nes y as a function of x 25 yx3 A Function State the domain of the given function 26 fgtlt 1 W A W m C m 7 or 7m 27 fx x 6 A 6 w B w 6l Evaluate the function 28 Find f3 when fgtlt 2x2 2x 4 A 19 B 28 29 Given that fx x 7 find f 4 A n 26458 B 3 a 17321 Graph the piecewise linear function 30 x 7 4 x 2 1 F 2 x xlt1 C 291 B Not a function C 6 m D 727100 D W6l Solve the problem 31 At a manufacturingplant the total cost in dollars to produce x items is Cx 032x 2510 What is the marginal cost per item A 032 13 2510 C m 032 D 251032 x 32 A house was purchased for 90000 After 9 years the value of the house was 126000 Assume that the appreciation in value is given by a linear equation Find the equation A y 90000 9x B y 90000 4000x C y 4000x D y 126000 Determine the vertex of the parabola 33 yx 426 A 6 4 B 4 6 C 6 4 D 4 6 Find the x and y intercepts Ifnu x intercepts exist state so 34 fx x2 2x 18 A 76 0 0 18 B No X intercep ts 0 18 C No X intercepts 0 18 D 76 0 0 18 Find the rule of a quadratic function whose graph has the given vertex and passes through the given point 35 vertex 4 6 point 8 22 A fxx426 B fxx 426 C fx2x426 D fxx 42 6 Solve the problem 36 At a manufacturingplant the total cost in dollars to produce x items is Cx 478x 24000 What is the total cost to produce 1400 items A 32192 B 2400478 C 6692 D 30692 Graph the function 37 fx2x 4 Solve the problem 38 The total revenue from the sale of x CDs is the function 2 x RX 7 90X Find the number of CDs that will produce maximum revenue A 250 B 310 C 270 D 540 39 Suppose the supply and demand price functions for a certain videotape are given by supply p q2 demand p q2 44 where p is price and q is quantity Find the equilibrium price A 22 13 26 C 21 D 24 MAT 1033 Test 3 Review Name Solve on seEarate Eager and select the best answer MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question For the given function findw 1 fx x2 8x A2x 8h B2X8h 2 C2Xh D2gtlthh 8h 16x h 2 2 3 2Fmd 11m 3Xl391 3Xh h 4h hao h A 3x2 4 B Does not exist C 0 D 3x2 3xh2 Find the point from those given that has the given property 3 The point where the slope of the tangent line is the least B 22 C 26 Solve the problem 4 The total cost to produce x handcrafted wagons is CX 90 2X X2 2X3 Find the marginal cost when x 5 A 232 B 142 C 235 D 325 Find the derivative 5 y 13x2 15x3 2x A 26x 1 45x2 B 26x 3 45x2 2 C 26x 3 45x2 D 26x 1 45x2 2 Solve the problem 2 6 The revenue generated by the sale of x bicycles is given by RX 5000x Find the marginal revenue when x 1300 units A 3700umt B 6300unit C 2600umt D 5000unit Find the derivative 7 fx 5x4 8x3 5 A 4x33x2 B 4x33X2 7 C 20X324x2 7 D 20X324x2 2 4 8yxx 4 4 4 4 A 391 B 391 C 391 D 39 y X2 y X2 y X y XX2 Find the derivative of the function 9 fx 6x 54x 1 A f39x 48x 26 B f39gtlt 48x 14 C f39x 24x 14 D f39gtlt 48x 7 Use the quotient rule to nd the derivative 10 t t2 g Fm t2 22t t2 22t 22t t2 39t B 39t C 39t D 39t g t 112 g t 112 g t 112 g t 112 Find the equation of the tangent line to the curve when x has the given value 11 fx 7 X3 x 2 x 1 x Ay7 7X28 By7 7x 9 Cy7 E Dyiz1 Find the derivative 12 6x 16x 6 x 2 2 2 2 2 A 36x 144x 78 B 108x 228x 90 C 108x 228x 90 D 36x 144x 78 X22 x 2 X22 x 2 Let fx 8x2 5x and gx 7x 9 Find the composition 13 fg3 A 1212 B 408 C 7050 D 618 14 fgk A 56k2 35k 9 C 392k2 973k 603 Find fgx and gfx 15 fx 5x 9 gx 4x 7 A fgx 20x 26 gfx 20X 29 B fgx 20x 29 gfx 20x 26 Find the derivative of the function 16y l4x2 2 1 A 39 B 39 y 4X2 y 4x2 17 fx 4x3 74x7 3 A f39x 160x9 196x6 36x C f39x 16x9 196x6 36x 18f ltx M34 A f39x i B f39x 5 2x 35 42x 33 Find the derivative 19 y 10e6X A 10xe60X B 10e60x 20 y 4egtlt2 A 8xeX2 B Bxe4x2 Find the derivative of the function 21yln2x 1 1 A 3393 22yln9gtlt2 2 2x A B X x29 B 392k2 973k 603 D 56k2 35k 9 C fgx 20x 29 D fgx 20x 26 gfx 20x 26 gfx 20x 29 C y39 4 D y39 8 m m B f39x 16x9 196x6 36x2 D f39x 160x9 196x6 36x2 40 5 C W D W 2x 33 82x 35 C 60xe6x D 609 6X C BerX D 8xe 1 1 C D E 1 18 C 2X 9 D 7 Find the derivative 23 fx eX In x x gt 0 x x x Aelnxx B39e Cexlnx1 DeXnX x x x Solve the problem 24 Suppose that the amount in grams of a radioactive substance present at time t in years is given by At 670e 57t Find the rate of change of the quantity present at the time whent 6 A 125 grams per year B 303 grams per year C 125 grams per year D 303 grams per year 25 Suppose that the population of a certain type of insect in a region near the equator is given by Pt 20 In t 8 where t represents the time in days Find the rate of change of the population whent 3 A 18 insectsday B 37 insectsday C 25 insectsday D 67 insectsday Determine the location of each local extreman of the function 26 fx x3 75x2 12x 3 A Local maximum at 4 local minimum at l B Local maximum at 1 local minimum at 4 C Local maximum at 4 local minimum at 1 D Local maximum at 1 local minimum at 4 Find the open interval where the function is changing as requested 27 Increasing fx lXZ ix 4 2 A w 1 B M 0 C 1 m D 1 1 Solve the problem 28 Find the acceleration function at if st 6t3 4t2 2t 7 A at 36t 2 B at 36t 8 C at 18t22t 8 D at 18t2 8t2 Evaluate f quot1 29 x i Af 1 32 Bf 1 56 Cf 1 7 Df 1 44 Find all critical numbers for the function State whether it leads to a local maximum alocal minimum or neither 30 fx x3 6x2 12x 1 A Local maximum at 2 B Local maximum at 2 local minimum at 2 C Local minimum at 2 D No local extrema Find 3911 Incz nn nf nu bxnlul minimumfm 3911 function 31 A Nuns C 75 D D 3 VA mm mammaum ammmmmmupmm am 32 x x3 7 3x2 7 D5A A 2 7A a 2 75 c A 7A D A 75 Snlv 1h pxnblun WW m meycandybamumsmmmmmmy A m candy m a m mm mm C m candy m D m mm mm Find 3911 magnum 3A f 3x 3dx 3 A C EZXZC C 3C D 35 fDAydy A W C B My C CeAY C D gm C 35 ICXBJXLAW 7 7 x9 xA x x9 xA x As A A C E9 3 A C 1 7 1 7 7x9 xA x 7x9 xA x C 3 3 A C D 3 A A C Findthninlngul a uszqu A6x1o1x Z C E6xzrllnxoC CZAgtltZ 1gtlt Z C D mtumxmc Snlv 1h pxnblun 38 graph nd m2 equam mm graph Afx x3 7 m amx x378xzolfbltol Cfxlx3 lxlqmos Dfxlx378xz lfblto5 3 z 3 3 Asmmg uman 8mm AE 75mrzcloAn EE 5mrzclo136 cE 5mrAcloAn DE 5mrzcloaa Evduatuhzingul 4 MI x2x5dx 73 AZA33 E1517 c1A5 Wm M f 5x zdx 1 Ayal mam cps D375 Find an m nfth mmangm 41 17 OT mT A3 x 1mm 1 m 5 98 A B c m7 Solve the problem 44 A certain comp any has found that its expenditure rate per day in hundreds of dollars on a certain type oi job is given by E39X 6X 5 where X is the number of days since the start of the job Find the expenditure if the job takes 4 days A 2900 B 68 C 6800 D 29 45 A company is considering anew process The savings rate St from this new process is St 500 t2 where t is the number of years the process has been in use Find the total savings during the first 5 years A 3500 B 11250 C 6750 D 5000 46 For the same new process described in the previous question how long will it take to break even if the initial cost to imp lent the new process is 15000 A 82 years B 75 years C 60 years D 55 years

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