Study guide for final exam, Math 1090 - College Algebra for Business and Social Sciences This guide is meant to be a help on studying what I think is most important important that you learn form this exam, as well as a synthesis of the most important things you will need in the final. I think a good way to review the material (except for doing as many problems as you can from the book) is to have a look at Kelly MacArthur s notes on her webpage (www.math.utah.edu/ macarthu/past.html here you find two pages from 2011 and 2012, which contain material which might be useful for you). Also, the tutoring center will be working at least untile the week before finals. Everyone has his own method of studying, and the method really depends on the subject and on the person. I can tell you what I would do for this kind of exam. Review the theory of one chapter (meaning: read it carefully, and repeat it out loud, maybe with some scratch paper in front of you, WITHOUT looking at the book when you repeat), and do some problems from it, then pass to the following. Take the problems without going back to look up the theory. Save some of the problems for the couple of days before the exam, when the review of the theory is complete and you just have to get faster at solving problems. Googling College algebra problems can provide you with a practically infinite amount of problem to practice (the ones from the book are preferable, since they will be similar to the problems on the final). CHAPTER 1: and 2 How to handle and solve a linear equation (what s a linear equation?) Linear inequalities. What are they? In which sense are they similar/different from linear equations? (when I time both sides by a negative term, I need to switch the sign, the solution set is given by more than just one value of x) How to draw the solution set for a linear inequality A linear equation in two variables is the equation of a line. What is the meaning of the slope, the y,x intercepts. 1
How to translate informations about a line in symbols: how to get the slope? How to write the equation of a line passing through a point with given slope/given points/etc.. how to graph a line from the equation linear systems: substitution and elimination methods what is a function, what is domain and range, vertical line test The concepts of Revenue, Cost, Profit, Break-even point The concepts of demand and supply equations, equilibrium point how to solve problems as these with linear systems Section 7,8 How to solve a linear system of inequalities and graph the solution How this relates to optimization problems, and how to solve these with a linear system of inequalities and optimizing a profit/objective function CHAPTER 2:,2 what is a matrix, scalar, entry, zero matrix, transpose. The dimension of the matrix Sum of two matrices, when is it possible Product of two matrices, when is it possible and how does it work elementary row operations solving the linear system Ax=b by manipulating (A b) Gauss-Jordan elimination 2
inverse matrices. When are they possible? How to find them, manipulating (A I) the problems labeled as investments, or ticket sales CHAPTER 3: quadratic equations: how to solve them quadratic formula quadratic equations in two variables, parabolas how to describe them: concavity, vertex, axis intercepts how to graph a parabolas same concepts as.6, with different equations polynomial functions: terminology (degree, leading coefficients, roots) how to transform a graph: inner and outer transformations and their effects: shifts, reflections, stretches/shrinks Section 7 arithmetic operations with functions (sum, difference, product, quotient) composition 3
CHAPTER 4 definition of an inverse function injectivity: when does an inverse exists how to compute it exponential functions: graph, behaviour depending on the base,4 logarithmic functions, definition and graph the domain of a logarithmic function, what is a vertical asymptote PROPERTIES OF LOGARITHMS how to solve a logarithmic equation, and an exponential equations change of base formula exponential growth/decay (we anticipated here the formula for compound interest) CHAPTER 5: what are geometric and arithmetic sequences, the advantages of this sequences when we sum some terms Interest: simple, compounded periodically, compounded continuously. Meaning and formulas Annual percentage yield 4
what is an annuity (ordinary, due) Future value of an ordinary annuity Future value of an annuity due what is a sinking fund, sinking fund payment formula What is a deferred annuity present value of an annuity (ordinary) present value of an annuity due present value of a deferred annuity Concept of installment payment and amortization amortization formulas: periodic payment of amortized loan, total interest paid, loan payoff amount There is a page at the beginning of the book, called Tips for taking math exams. I agree with the suggestions you find there, and it might be worth the couple of minutes it takes to go through them. Of course the investment of time and serious study are fundamental ingredients to succeed in a subject like math, hence the work you did throughout the semester will be the bulk of your preparation for the final. But remember that the final exam is just a performance of few hours: it is important to take it in the best condition you can. Get enough sleep and (try to) be relaxed and concentrated. 5