Review Midterm 2 •
The midterm will cover sections 3.2, 3.3, 3.5, 3.6, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, and Appendix D. •
You will have 80 minutes to take the exam in class on March 7th. •
You will be allowed to use 4x6 index card with hand written notes on both sides. Make sure it is truly a 4x6 index card and not something that closely resembles a 4x6 index card. •
You will NOT be allowed to use a calculator (or other electronics), notes, textbook, or your neighbor. •
You must show your work to receive credit. (You work should be organized and legible.) •
Scratch paper will be provided; scratch work will not be graded. •
Bring your student ID and a pencil & eraser. Functions (Covered in chapters 3 and 4) • Polynomials • Rational • Radical • Exponential • Logarithmic You should be able to… • Rewrite a Quadratic equation in vertex form or standard form. • Find the maximum or minimum of a function (especially a quadratic function) o Set up an optimization problem from a “story”, write the equation of the function (in one variable) to maximize or minimize. • Divide Polynomials o Synthetic Division o Long Division o Remainder Theorem • Analyze functions o Identify Domain o Identify x-­‐intercepts & y-­‐intercepts o Identify asymptotes  Vertical  Horizontal (only for rational and exponential functions)  Slant (only for rational functions) o Identify end-­‐behavior o Identify critical values o Identify intervals where function positive/negative – construct sign line o Identify turning points (given a sign line or graph) o Identify intervals where function increasing/decreasing •
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o Identify inflection points (given a sign line) o Identify intervals where function concave up/down Graph the functions and transformation of functions from chapters 3 & 4 Explain the relationship between roots and factors of a polynomial function. Explain the relationship between zeros and intercepts of a polynomial function. Find Zeros of a Function o For Polynomials, know how to use each test  (1) Rational Zeros Theorem  (2) Upper and Lower Bound Theorem  (3) Conjugate Pair Theorem  (4) Descartes Rule of Sign  Fundamental Theorem of Algebra (# of zeros)  Leading Coefficient Test (end behavior)  Multiplicity of Roots (even vs. odd)  Root Location Theorem (related to Intermediate Value Theorem) Use the binomial theorem to expand a binomial Calculate n choose r. Use the properties of exponents to simplify exponential expressions. Use the properties of logs to expand/contract logarithmic expressions. o Including the change of base formula. Evaluate logarithmic and exponential expressions. Use definition of logarithms to rewrite exponential and logarithmic equations. Solve. (Know when solutions are extraneous.) o Polynomials equations o Rational equations o Radical equations o Logarithmic equations o Exponential equations Practice Problems: Ch. 3: p. 214 (Self-­‐Test) #1, 2ab, 3-­‐10all p. 214-­‐215 (Practice for Calculus) #1-­‐6all, 9, 15, 23 3.2 #46, 47, 50, 52, 53, 56 3.3 #16, 18, 22 Appendix D #12, 18, 25, 31, 32, 38, 39, 40, 42, 46 Ch. 4: p. 277 (Self-­‐Test) #1-­‐9all p. 278-­‐279 (Practice for Calculus) #1, 3, 6, 25, 26, 31, 33-­‐41all, 43-­‐45all, 49-­‐57all, 59