ZZ - Advanced Math Review 2017

Transcription

1 ZZ - Advnced Mth Review Mtrix Multipliction Given! nd! find the sum of the elements of the product BA First, rewrite the mtrices in the correct order to multiply The product is BA hs order x since B is sized x nd A is sized x BA! Now, dd the sum of the elements to get choice E, 99 Mtrix Multipliction Which mtrix product is undefined?!!!! M nd N re oth order x, so MN nd NM cn oth e found P is order x nd R is order x, so PR nd RP cn oth e found MP cn lso e found, ut since N is x nd R is x, NR is undefined The correct choice is K, NR Eqution of n Ellipse Find the focus points for the ellipse! using the formul! Since > for ellipses, this ellipse hs verticl mjor xis with the eqution Now clculte! 6 + c! c, with c ± Since the ellipse hs verticl mjor xis, the foci re on the y-xis with coordintes (, ) nd (, ), which is choice B! Eqution of Prol Find the distnce etween the focus of the prol! nd its directrix using the formul! A B B A M N P 8 R 6 + y x c + + y x c + ) ( ) ( + x x f p!

2 ZZ - Advnced Mth Review y ( x h) + k Compring the given eqution to! p, we see tht! p so p! 8 The distnce etween the focus p nd the vertex is therefore!! 8 This must e douled to find the distnce etween the focus nd the directrix, so the correct choice is J,! Eqution of Hyperol ( y ) ( x ) Wht re the slopes of the symptotes for the hyperol! 9 6? ( y k) ( x h) With formul!, we see tht nd y ± x ± Asymptotes for hyperol with verticl trnsverse xis re found y using!, with slopes! Since is pired with y nd is pired with x, represents the verticl chnge nd represents the horizontl chnge of the hyperol s fundmentl rectngle ± The correct choice is C,! 6 Arithmetic Sequences A cross country tem runs one hlf of mile on the first dy of prctice nd increses the distnce y the sme mount ech prctice session If 8 miles re run on the st dy of prctice, how much ws the distnce incresed ech dy? 8 + ()d n d Use the formul! n + ( )!!! d! The correct choice is H,! mile Geometric Series If ll is dropped from height of feet nd it lwys reounds 8 of the distnce tht it flls, pproximtely how fr does it trvel efore coming to rest? S The ouncing ll represents n infinite geometric series Use the formul! r to find the totl distnce trveled The series is represented y Use the formul with nd r 8 to find the reound totl distnce only Then doule this sum nd dd to find the totl sum S S! r!! 8! S Now dd + + feet The correct choice is E, feet 8 Asymptotes of Rtionl Function!

3 ZZ - Advnced Mth Review x + x + Find the equtions of ll symptotes for! x x + ( x + ) x + This rtionl function fctors s! ( x )( x + ) nd reduces to! x with hole when x The verticl symptote is x nd the horizontl symptote is y The correct choice is G, x, y, hole when x 9 Conditionl Proility ( ) Find the proility tht student plys in mrching nd, given tht the student performed in the spring ply Student Activities Plys in Mrching Bnd Plys in Orchestr Does not Ply n Instrument In the Spring Ply In the Fll Ply 6 Not in Ply 8 By using the word given, this is conditionl proility question The smple spce consists of the 9 students who performed in the spring ply Of these, students ply in mrching nd The correct choice is D,! 9 Permuttions If students re rndomly selected from clss of to serve s president, vice-president, tresurer, nd secretry, wht is the proility tht the youngest students in the clss re selected? This is permuttion question since the order mtters for the students who serve s president, vice-president, tresurer, nd secretry Clculting P gives, permuttions Of these, only one permuttion includes the four youngest students in the clss The correct choice is F,! Comintions If locl pizz resturnt hs toppings ville, how mny different pizzs re ville if the customer cn choose ny numer of different toppings etween nd? Assume tht the order of the toppings does not mtter This is comintion question since the order of the toppings does not mtter The long wy to solve this prolem is dding 8 different comintion clcultions eginning with C nd ending with C However, since this is inomil sitution, ech topping is either included or not included This gives choices for ech of the toppings Therefore, simply clculte, The correct choice is D, Amplitude of Trigonometric Function!

4 ZZ - Advnced Mth Review sin(x π ) Wht is the mplitude of the function!? Using the eqution! sin( x c) + d, the mplitude is! The correct choice is F,! Vectors Wht is the mgnitude of the vector (6, 8)? Use the Pythgoren Theorem to find the mgnitude Mgnitude! 6 + 8! The correct choice is C, Terminl Sides If (, ) is point on the terminl side of the ngle! θ, find cos! θ A reference ngle is the smllest ngle tht the terminl side of given ngle mkes with the x-xis In Qudrnt II, the reference ngle is 8! θ Consider the ( - -) reference right tringle in qudrnt II, where sin θ >, cos! θ <, nd tn! θ < The correct choice is H,! Coterminl Angles Wht is the mesure of the smllest negtive ngle tht is coterminl with degrees? To find negtive ngle coterminl with given ngle, sutrct 6 6! The correct choice is A,! 6 Best Fit Line dj Since cos! θ! hyp, this gives cos! θ! Use the grphed dt points to predict the numer of cses sold for populr soft drink in the yer The line etween 99 nd is the etter predictor, since it gives more recent sles dt!

5 ZZ - Advnced Mth Review!! 8 9 The slope of tht line is m 99 If the yer is considered yer, llowing x for yer yields! 9 Add this to the strting point of 8 million cses in yer for totl of million cses The correct choice is J, million cses Modeling If! were clculted, it would hve 9 digits Wht would the digit frthest to the right e (the ones digit)? Strt y noticing the pttern: Clculting! ends in Clculting! ends in 9 Clculting! ends in Clculting! ends in Clculting! ends in Since 9 keeps repeting in groups of four,! would end in nd! would end in 9 The correct choice is E, 9 8 Domin of Function Find the domin of the inverse function for f(x)! x The rnge of the originl function ecomes the domin of the inverse of tht function [ ) [ ) Since the originl function hs rnge!,, the domin of the inverse of tht function is lso! If the inverse is clculted, it would e f (x) + ut only when x >, which is written in intervl nottion s x [ ) [ ) The correct choice is J,!!