QUIZ #1 will be on MONDAY 23 Sept --------------------------------- WHAT YOU WILL NEED ------------------ Pen. Name. ID Number. Scrap paper. You will not really need, but they might help: calculator, ruler, graph paper. Here is what quiz will cover. Actually it won't cover all these things since not enough time, but I'm not going to tell you which of the below will be on the quiz and which won't, so to be safest, know them all. The quiz problems are going to be a lot easier than the homework problems, more on the level of a COW problem. SUBJECTS COVERED ---------------- Limits: How to find them. Functions: Domain. Range. Composition. Inverse functions. Rational functions and polynomials. Precalculus (theoretically should have known this before class started... see my web page link to "prerequisites" subpage for quick review): Trig functions and their properties. How to solve triangles. Log and exponential functions and their properties. Lines. Their slopes. Recognize parallel and orthogonal lines. Easily go between coordinates and pictures, and equations, to describe the same stuff in 2 different ways. Be able to fit lines to data. Be able to solve systems of linear equations. Be able to solve quadratic equations. Coordinates. How to find coordinates of stuff in geometrical diagrams. Plotting functions. Method of induction. Sums. Algebraic manipulations of all kinds, able to manipulate equations to solve for stuff, to express A in terms of the other quantities in the equation (where A could be any letter in that equation). WHAT TO READ IN THE BOOK ------------------------ Unfortunately the book's coverage of precalculus review sucks - it has a random selection of subjects it covers, and in a weird order with some stuff entirely missing. Know: the GEOMETRIC FORMULAS in frontspiece of book. All of Chapter 1: functions, plotting, domain, range, rise, run, slope, increasing versus decreasing, concave-up and down, helf-life (what is T so that -a*T e = 1/2? Answer: T = ln(2)/a where ln is an abbreviation for log to the base e, and e=2.71828. This is really just a special case of the formula L e = x causes L = ln(x). Many calculators have e to the x buttons and ln(x) buttons.) composing functions. inverse functions. logs and exponents. The inverse of the function x F(x) = B is G(y) = log y B . x Then F(G(y))=y and G(F(x))=x. If B=e, these are F(x)=e and G(x)=ln(x) because "ln" means the same as "log to the base e." trig functions. polynomials. rational functions. power functions (or "monomials"). LIMIT concept: in chapter 2, end of section 2.1 and start of sec 2.2 on pages 60-69. --------------------------- Things I want you to know that are NOT in the book (or only in faraway places in the book): quadratic formula: page 561 how to solve systems of linear equations: not in book. (E.g. Gaussian "Elimination" technique discussed in class & homework & precalculus classes. See my "solutions to homework #2" on my web page, problem number 2.) Method of induction: not in book. Base of induction. N --> N+1 step in induction. Sum symbol: not really in book. Know what it means. See my web page useful notes on "sums and limits". How to sum arithmetic series by "pairing" method: What is the numerical value of 3+5+7+9+11+...+103? How would this problem be written in the compact "sum symbol" notation? Answer: 51 ----- \ > (2k+1) / ----- k=1 How to sum geometric series: see page 407-410 which is sec 9.1 of book. What is the binomial formula and the Pascal triangle? (not really in book.) 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 ? 4 What is (x+y) fully expanded out into a sum of monomials? Hints: 2 2 2 (x+y) = x + 2xy + y . 3 3 2 2 3 (x+y) = x + 3x y + 3xy + y . READING ------- Read book Frontspiece (1 page list of useful precalculus formulas), book ch 1, book ch 2 pages 60-69, and all the "useful notes" on my math75 web page.