1 1 1 p q p q. 2ln x x. in simplest form. in simplest form in terms of x and h.
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1 NAME SUMMER ASSIGNMENT DUE SEPTEMBER 5 (FIRST DAY OF SCHOOL) AP CALC AB Dirctions: Answr all of th following qustions on a sparat sht of papr. All work must b shown. You will b tstd on this matrial somtim during th first wk of school. PART I: ANSWER ALL QUESTIONS WITHOUT USING YOUR CALCULATOR. Dtrmin if ach of th following ar tru. If not, plain why not. Assum all prssions ar dfind for all ral numbrs in th domain. k k h h p q p q y y d. a a b b. a b a b c b f. a b a b. Simply ach of th following prssions 5. Solv for y : y y y. Solv for ln ln ln ln Writ an quation of th lin that passs through, and has a slop of.. What ar th coordinats of th point at which th lin passing through th points (, ) and (, ) intrsct th y ais? 7. If f, thn find f f in simplst form. 8. If f, thn find f h f h in simplst form in trms of and h. 9. Find th domain of ach of th following functions (us intrval notation): g 8 h 5 p d. yln. Writ an prssion for th ara of an quilatral triangl whos sid is rprsntd by.
2 . Sktch th graph of ach of th following functions: f f f d. f. f,, f. f ln g. f h. f i. f,,,. Sktch f. Dscrib th ffct that ach of th following would hav on f() without th us of a graph. f() f( ) f( + ) d. 5f( + ). f() f. f(). Givn f and g, writ ach of th following in simplst form in trms of. f g g f f f. Answr ach of th following for f : Sktch th graph of f(). Dtrmin if f has an invrs function. Sktch th graph of f d. Writ an quation for f.. 5. Simplify using only positiv ponnts. Do not rationaliz th dnominator. y y. Writ an prssion for th surfac ara of a bo givn th ach of th following conditions: Th dimnsions of th bas ar and y and th hight is h. Th dimnsions of th bas ar and y and th hight is h, but th bo dos not hav a top. Th bo has a squar bas and no top, and th sid of th bas is and th hight is h. 7. A svn foot laddr, laning against a wall, touchs th wall y ft abov th ground. Writ an prssion (in trms of y) for th distanc from th foot of th laddr to th bas of th wall. 8. Writ an prssion for th ara of a smicircl whos diamtr is rprsntd by.
3 9. Solv ach of th following systms of quations: a + b = 7 + y = 7 a + b = 8y =. Copy and complt th chart θ sin θ cos θ tan θ. Solv ach of th following for all valus of in th intrval sin sin sin sin tan sc. Which of th following prssions is not quivalnt to th othr two prssions? A. cos B. cos C. cos. Which of th following prssions ar quivalnt? A. sin B. Arcsin C. sin D. sin. Solv for ln ln ln ln ln 5. Solv for th valu of k whn = and y =. ln 5 ln ln y k y k PART II: ANSWER ALL QUESTIONS USING YOUR CALCULATOR. Answr th following basd on th graph of y : Dtrmin if th points (, ) and (, ) ar on th graph. Is th function vn, odd or nithr? Eplain. Find th -intrcpts and y-intrcpt. 7. Find th points of intrsction of th following systm of quations: yln y
4 ANSWER KEY AP CALC AB SUMMER ASSIGNMENT 8. NO NO YES d. NO. NO f. NO ln ln ln ln ln y y y y y y.. y i 8,,., 5. y h h h h h h h h h h h h h d., 7 5. A. Chck your sktchs with a calculator. shift down units shift right units rflct ovr th -ais, thn shift lft d. stpr graph, shift lft. grow slowr f. part of graph that is blow th -ais is (looks narrowr) (looks widr) rflctd ovr th -ais...d. f 5. y y y y. A y h yh A y h yh A h 7. 9 y 8. r A 8
5 9.. θ sin θ cos θ tan θ a, b 8. sin cos sin, y sin sin sin cos,,,. C. AD,. ln ln ln sin sin 5,, tan tan tan tan tan 5, ln 5 ln =,, but >, so NO SOLUTION 5. 9 k k. (, ): NO (, ): YES ODD bcaus th function is symmtric with rspct to th origin. -intrcpts:,, y-intrcpt: 7..59,.8, 5.,.
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