ALGEBRA FOR CALCULUS Topics List for Chapters 3 and 4 Exam Spring 2013 Section 3 1 and 3 2 Complex Numbers and Quadratic Functions All calculations with complex numbers like the homework on pp 239 240 Be sure to review powers of i like 79 88 on p 240 Be able to use complex numbers while solving a quadratic equation or finding zeros of quadratic functions 43 44 47 71 72 on p 254 Be able to solve a quadratic equation by completing the square like 29 36 on p 254 Be able to solve a quadratic equation by using the quadratic formula like 37 56 You will definitely be given one in which you need to simplify the radical like 45 All answers must be given in exact form no decimal approximations Be able to solve quadratic type equations like 79 94 on pp 254 255 Section 3 3 Graphs of Quadratic Functions Be able to complete the square on a quadratic function and put it in vertex form 11 16 on p 266 Use the shortcut formula for finding the vertex of a given quadratic function 31 40 on p 268 Also identify domain range whether it has a max or min and the intervals over which function is increasing or decreasing Find max or min value in a real world scenario given the quadratic function 41 44 49 51 Be able to write a quadratic function given a real world scenario You definitely will have one of these most likely an area problem like 46 53 on pp 268 69 and also those on the worksheet or a profit function like 50 52 Section 4 1 Section 4 2 Section 4 3 326 Be able to classify the types of polynomial functions 1 10 on p 306 Be able to determine end behavior of the graph of a polynomial function given its function rule like 11 18 on p 306 Be able to determine whether or not a given function is a polynomial and why why not Given a polynomial function give its zeros and the multiplicities of those zeros 27 42 on p 306 Given a polynomial function be able to indicate its end behavior zeros and their multiplicities construct a sign chart and a rough sketch WITHOUT the use of your calculator Like the quiz Good problems to look at are 13 36 on pp 318 19 Given the graph of a polynomial function be able to determine whether its degree is even or odd and if its leading coefficient is positive or negative Given the graph of a polynomial function be able to write a possible function rule for the function Use long division to divide two polynomials Use synthetic division to divide two polynomials Use synthetic division to find function values and be able to explain why this works 23 30 on p Use synthetic division to determine whether or not a number is a zero of a polynomial 31 38 on p Spring 2013 327 Section 4 4 List all the possible rational zeros of a polynomial 49 54 on p 338 Find all the zeros of a polynomial including imaginaries 55 70 on p 338 You need to show all these steps in order to obtain full credit This problem will be worth approximately 15 points 1 Use the Rational Zero Test to list all the possible rational zeros 2 Use your graphing calculator to narrow your choices 3 Use synthetic division to test your choices 4 5 List the factored form EACH TIME YOU FIND A ZERO List all linear factors and all zeros write a polynomial given its zeros 1 16 on pp 337 338 MyLabsPlus has a set of practice HW problems under the homework tab and a practice exam under the Test and Quizzes tab The more problems you do the better prepared you will be Also working through the MLP practice exam will simulate the time pressure of the real thing Study hard THE FOLLOWING SECTIONS WILL BE INCLUDED ON A SEPARATE IN CLASS 25 POINT QUIZ NO GRAPHING CALCULATORS WILL BE PERMITTED ON THE QUIZ Section 4 5 Rational Functions Be able to identify the vertical and horizontal asymptotes of a rational function 1 20 on p 357 Be able to sketch by hand a rational function 33 51 55 57 61 65 67 on p 358 showing all steps x and y intercepts vertical and horizontal asymptotes domain sign chart No graphing calculators will be permitted on this quiz Section 4 6 Polynomial and Rational Inequalities Be able to solve a polynomial or rational inequality using a sign chart You need to show your sign chart to receive points for the problem 29 46 and 53 71 on p 369 70