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Math 111 Final Exam Review A final review sheet is online, but you should also be looking through the old review sheets. WS 1-9: Information from graphs. 1. Know how and when to compute slopes form overall graphs. “Find ATS at …” (from the dist. Graph) “Find AC at …” (from the TC graph) “Find AVC at …” (from the VC graph) “Find overall rate of change at …” “Find AS from … to …” (from dist) “Find MR at …” (from TR) “Find MC at …” (from TC) “Find (incremental) average rate of change from … to …” 2. Be able to draw a reference line from a given slope and use it. “Find when ATS equals…” “Find when AC equals…” “Find when AVC equals…” “Find when overall rate of change equals…” “Find a …-minute interval when AS equals…” “Find when MR equals …” “Find when MC equals …” “Find an interval of length … when the average rate of change equals…” 3. Know what to do if the graphs of the slopes are given (i.e. graphs of VC, AVC, MC). And know how to read a table of incremental information. 4. Scenarios Understand the Dist/ATS/AS common questions. Understand the Reservoir common questions (greatest shortage, etc). Understand the TR/TC/VC common questions such as: “Draw TR when market price is …” “Find the quantity at which max profit occurs.” “Find the maximum profit.” “Find BEP” “Find the largest interval when positive profit is possible” “For which quantities is it possible to recover some fixed cost.” WS 10-16: Information from formulas. 1. Be able to answer all the questions from WS 1-9, but now with formulas. 2. Be able to work with functions and functional notation. “If D(t) = t2 – 3t, then what is ATS(t).” “If f(x) = 5x + x2, then what is f(x+1)-f(x).” 2. Know how to go between formulas for TC/VC and AC/AVC and MR/MC. 3. Know how to work with parabolas (quadratic formula and vertex formula) WS 17-23: Sequences/Bank Info. 1. Know how to work with additive and multiplicative sequences (test, explicit formulas, recursive formula, finding the 100th term, etc.) 2. Know the formulas and wording for bank information. a) “simple interest.” b) “annual rate, compounded n times a year” c) “annual rate, compounded continuously.” 3. Know the standard questions including: “Find the future value of …” “Find the present value of …” “How long …?”, “When …?”, “Find the time” “Find the rate …”, “Find r” “Find the interest earned from … to …” “Find the change in value from … to …” “Find the proportionate change from … to …” “Find the percentage change from … to …” “Find the factor by which … is multiplied to get …”