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# Coll Alg Bus MATH 1090

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This 15 page Class Notes was uploaded by Miss Noel Mertz on Monday October 26, 2015. The Class Notes belongs to MATH 1090 at University of Utah taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/229945/math-1090-university-of-utah in Mathematics (M) at University of Utah.

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Date Created: 10/26/15

Review Chapters 0 1 amp 2 Math 1090001 Spring 2001 Monday Feb 12 2001 1 0 Basic arithmetic If your grasp on arithmetic especially with variables is shaky I suggest you study for it as follows Make a table of all the rules contained in Chapter 0 Do or re do Problem Set 0 and perhaps some problems from Chapter 0 and at each step cite exactly which rule is used c Practise Long Division of polynomials Practise how to read o the dividend divisor quotient and remainder from a Long Division 0 Functions 7 Concepts regarding functions domain codmain range correspondence graphs etc i Know how to compute sums di erences products quotients and compositions of functions and when these operations are de ned 7 Know the Vertical Line Test for functionality Know how to locate the points at which a given function is unde ned by examining its formula This amounts to looking for divisions by zero even roots of negative quantities etc i Know the following types of functions linear quadratic rational Practise sketching each type Know the following terms gtk linear slope intercepts Parallel straight lines have equal slopes while slopes of non vertical perpendicular lines multiply to 71 gtk quadratic vertex axis of symmetry intercepts opening upward or downward discrimi nant 96 rational singularity intercepts horizontal vertical oblique asymptotes You will need to know how to do polynomial long division in order to sketch rational functions gtk The x intercepts of a function are also called the zeros of the function 7 Linear functions Know how to switch between the di erent forms of representing linear functions Quadratic functions Know how to nd the maximum or minimum of a given quadratic function Learn how to recognize you are being asked to nd one when doing word problems 0 Equations Solve single linear equations in one variable Solve single equations in one variable involving the absolute sign Solve single quadratic equations in one variable 7 by factoring by the Quadratic Formula Know how to determine the solution properties of an equation with its discriminant Solve systems of 72 linear equations in n unknowns n 23 by the method of Gaussian Elimination lf you7d like you are welcome to use matrix notation but you are not required to know it for Chapters 0 1 and 2 gtk Know the di erent solution possibilities to these systems unique solution in nitely many solutions or no solutions Know the geometry corresponding to each of these situations gtk Know how to properly express the solution of an in nitely many solution system with a parameter Solve systems of two equations 1 linear and 1 quadratic by the method of substitution 0 Applications Review Chapters 0 1 amp 2 Math 1090001 Spring 2001 Monday Feb 12 2001 2 7 Linear systems of equations Know how to translate information in a word problem into equations 7 Cost Revenue Pro t gtk Cost revenue pro t functions can be linear quadratic or rational gtk Break even point is simply the intersection of the cost and revenue functions gtk Total Cost Fixed Cost Variable Cost gtk Know how to work with cost per unit 7 Supply and Demand gtk Supply and Demand curves may be linear quadratic or rational Know the concept of market equilibrium Know the di erence between a demand function and quantity demanded Basically a demand function is the how quantity demanded depends on price Similarly for Supply gtk Know the e ect of a tax on suppliers on the supply function and consequently the market equilibrium gtk Know that when asked to nd the market equilibrium you are being asked to nd the intersection of the Supply and Demand curves j Math1090 Final Review Exercises from old Final Exams 1A Find the inverse of the following matrix if possible If it s not possible then explain why 1 e 2i A 2 l 0 5 j 1 0 2i 18 For A 3 2 l 4 0 3 i matrix operations if possible If not possible explain why B53l dcw421 f h39 d quot1 2IJ an r 3 Slj perormtemdicate i 2 3 07 a AA g 3 Qt AA L is 3 lt2 E b BC 7 2amp2 1S BC W 8 1C Use GaussJordan Elimination to solve the following system 2X 4y 22 z 4 4x 9y 72 2 v2x4y43zz l0 ZA Given the arithmetic sequence xvii 3 Find the 100m term 100 h term g b Find the sum of the rst 100 terms Sum of rst 100 terms 11 a 5 a 28 How much would have to be invested at the end of each year at 6 interest compounded annually to pay off a debt of 80000 in 10 years s aelobl i i m 2C A lottery prize worth 1000000 is awarded in payments of 10000 ve times a year for 20 years Suppose the money is worth 20 compounded 5 times per year I a What is the interest rate i b What is the number of compoundings n n 90 c What is the formula used to nd the present value of this prize d What is the present value of this prize i 2V g 3A For fx17x and gxx2 a State the domain for both functions Domain for fX 4quot Domain for 300 X 5 E b Find gi f and state the domain of this new function Jag x 392 X domain X 4 1 c Find i M 8 VK f W X X SB Solve the equation 2x 1 5 2 3 3C Find the equation ofthe line passing through the points 1 1 and 2 3 4A Graph the Iinear inequality 4x lt 6y 4B Graph the system ofinequatities and shade the solution region Label ail vertices for the solution shaded region 446 C 3x4yZIZ K x v y 2 2 x S 6 ME 0 mic ECWtfh cueL0 NW Vertices 40 Find the maximum of the objective function 39x y 2xy subjected to the following constraints x 2 0 y 2 0 x y S 10 2x y 24 air I 5 3 3 3 xxx W Maximum value 2g at point 13 3 U 5A If the cost of production for a product is given by Xx x3 1 1x 84 and the revenue is given by RU 30x a Find the pro t function PM L Pm quotX 4 CBCS q b Find the breakeven pointst Breakeeven points U77 2 7 U l 58 if 100 feet offence is used to fence in a rectangular yard then the resulting area is given by Alxx50 x where x feet is the width of the rectangle and 50 e x feet is the length Determine the width and length that give the maximum area VVIdth for max area Length for max area Z 5 j 50 Let fx7xA34 a Solve x 0 to nd the x intercepts x intercepts lt3 6 Q to Find the vertex otthe parabola Vertex Iquot 2 3 Sketch the graph showing the vertex and wintercepts 6A Suppose that the population of Smalltown USA grows according to the formula Pl3200e 03quot where time t is measured in years a What is the initial population of the town at t 39 0 3 Initial population b How long will it take the population to double 3 is years c What is the population after 1 year 32 g GB Use the properties of logarithms and the fact that logo 2 2 03 logm 5 z 07 Iogm7085 to nd the values below a logiog 103m 8 Z 39 0 b logIO 35 c log 2 3 log52 6C Rewrite log2 32 2 x in exponential form and solve forx Exponentialform Z I 339 32 7 Given the matrices A B C and D perform the indicated operations or state that it39s not possible r 1 0 l 0 B 0 J l 7 1 SW7 l 1342 162M4 11 35 l2 3 Li 397 a A L 6 3r i er D b 2A773Igt WM do it uquot1 S 01 l l 3 f l d rquot 5 a W L e A 1 Mk 9055W i q to 8 Solve the following lgrfear system of equations if possible 3x7 2y 2 2 A xAytz SxHOyMSzilO 9 John makes a 1000 contribution at the end of each quarter to a retirement account for 10 years earning 7 interest After that he makes no additional contributions and no withdrawals and he leaves the money in the account for another 10 years a How much money is in the account after the 10 years of contributions 3 S 2 2 3 3 I b How much money is in the account at the end of 20 years it i l Li S Y i so 4 l D 10 For fxquotxe2 and glxx2l Statethedomain forboth functions XZL 1 X 6R Find ifggt5 JE 74 Find Urgllxl m 11 Solve the equation 3x 1 3 6 3 w w A X Z 2 10 2 N 12 Find the equation of the line parallei to y 2X1 and passing through the point 4 5 ZXtB 13 Angela buys a car After a down payment she still owes 20000 She sets up a 5 year loan with monthly payments due at the end of each month with an interest rate of 6 a How much wrll each monthly payment be 33K g b if Angela decides to pay off the loan after 3 years how much money should she pay then g 3 Erie t 1439 For the following system of inequalities x 339 2x Zys 10 x20 2 y 0 a Sketch and shade in the solution region defined by the inequalities Y r z E V t b Find the maxim um of the obj ctive function xi J lZX subjected to the above constraints Maximum value lg at point g i3 15 The total costs for a company to produce and sell x units of a product are given by th50050xxZ in dollars The sale price for one item is 250 3 Find the revenue function RlYl l 7quot 133x 1 VA b Find the pro t function PM P t x x 200 X BUO c Find the breakveven points 2 3 a Ht 4 quot 78 Q d Find the number of items sold to get the maximum profit log 16 The population of Mathville was 12000 in 1960 and 21000 in 1980 The population growth of the city follows the formula 1 Poem where t is the number of years after 1960 3 Determine Po and h t Po J long A a Q QLWCIK to Estimate the population of Mathville in the year 2000 7 tom 0 How many years after 1960 will the population grow to be 34000 V 3 7 uid 17 Let x24x3 3 Find the vertex of the parabola LZ vl b Tell if its a minimum or maxrmum pornt W 1 c Solvey 0 to nd the xvintercepts if there are any 5 c quota Q d Sketch the graph showing the vertex and xintercepts 18 Solve for the exact value of x a 335 log3x42log353 x l9 Solve for x 34013 x 3 LE vii 20 The Utah Company manufactures a certain product that has a selling price of 40 per unit Fixed costs are 1600 and variable costs are 20 per unit Determine the least number of units that must be sold for the company to have a profit of no less than 5000 All work must be shown the guess andtest method is not acceptable V Es 153 21 A rectangular plot of land has an area of 18000 square feet lf its length is ve times its width how much fencing would be required to surround the property 32 22 For the following functions answer the specified questions fltx 26 r q 39 X 7x 3x 20x25 g i m A quotFigquot 3 What is the domain of flxl X alga x 43 E is b What is the domain of gm 7 X 602 c New C t a d 110 3953 e lt gllt2gt 73 23 Graph the function er 21 I and determine the x and yintercepts R Xintercept o l l lt3 yintercept O t 24 The students at a university buy 3000 graphing calculators per year when they cost 50 each and they buy 2000 calculators per year when they cost 100 each Let P be the price per calculator and Q be the quantity of calculators sold Assuming the relationship between P and Q is linear give an equation expressing P in terms on P a 3 Q rm 25 Find the value for x which maximizes the quadratic function xlex71ix 24 it 26 Solve the following equations a lnt2x770 3 7 J b 19 y 7 1 c logx10g32 X locz 3 27 Jeremy wants to make one savings deposit today so that in 7 years he will have 16000 Given an interest rate of4 compounded semiannually twice a year how much money should Jeremy deposit y Q Lll 28 Brittany is 25 years old and she plans to retire when she turns 60 When she retires she would like to have 1 000000 of savings She is going to achieve the savings by contributing to a sinking fund between now and her retirement with equal monthly payments paid at the end of each month Assume the interest rate is 6 per year compounded monthly How much should her monthly payments be i i Q 29 Given the matrices A and B perform the indicated operations or state that it39s not possible if it39s not possible explain why F 0 I 1 1415 M 810 i 2 3 0 2 1 0J M s at 2 Lave sr mcs M Mr evle tres as 5 t A b BA x 39 t C BquotI You mustdo this by hand using rowoperations no calculatorsil Pf J 39t 2 30 Determine if the system of equations below has any solutions it a solution exists nd it Show all work y z 6 r quot x 2y32 14 3223 2x y 22 10 II It 31 Maximize the objective function 2 4x 3y subject to the constraints XZ yZO Xy 4 3x2y2 6 y xx Maxier value ofz i 5quot at the point 0 2 13 C

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