Example Items. Pre-Calculus Pre-AP. First Semester Code #: 1221

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1 Eample Items Pre-alculus Pre-P Pre-alculus Pre-P Eample Items are a represetative set of items for the P. Teachers may use this set of items alog with the test blueprit as guides to prepare studets for the P. O the last page, the correct aswer, cotet SE ad SE justificatio are listed for each item. The specific part of a SE that a Eample Item measures is NOT ecessarily the oly part of the SE that is assessed o the P. Noe of these Eample Items will appear o the P. Teachers may provide feedback regardig Eample Items. () owload the Eample Feedback Form ad it. The form is located o the homepage of ssessmet.dallasisd.org. OR () To submit directly, click Eample Feedback after you logi to the ssessmet website. First Semester ode #:

2 P Formulas Pre-alculus/Pre-alculus PP Trigoometric Fuctios ad Idetities Pythagorea Theorem: a + b = c Special Right Triagles: Law of Sies: si si si a b c , 3, ,, Hero s Formula: ss as bs c Law of osies: a = b + c bc cos b = a + c ac cos c = a + b ab cos Liear Speed: v s t gular Speed: t Reciprocal Idetities: Pythagorea Idetities: Sum & ifferece Idetities: ouble-gle Idetities: si csc csc si cos ta sec cot sec cos cot ta si q + cos q = + ta q = sec q + cot q = csc q cos ( ) cos cos si si si( ) si cos cos si cos( ) cos cos sisi si( ) si cos cos si si si cos cos cos cos cos si cos si Sequeces ad Series The th Term of a rithmetic Sequece: Sum of a Fiite rithmetic Series: Sum of a Fiite Geometric Series: Sum of a Ifiite Geometric Series: a a ( ) d k a ( a a ) k a ( r ), The th Term of a Geometric Sequece: a ak r S k r a a r r a ar S a ( ) d a r, r r r r 0 r ab a b a b a b a b a b 0 0 iomial Theorem: Permutatios:! Pr ombiatios: ( r)! Projectile Motio r! ( r)! r! Vertical Positio: Vertical Free-Fall Motio: y tv si gt h 0 0 Horizotal istace: 0 tv cos ft m st () gt vt 0 s vt () gt v 0 0 g sec sec

3 P Formulas Pre-alculus/Pre-alculus PP oic Sectios ircle: Stadard Form: ( h) + (y k) = r Stadard Form: ( h) = 4p(y k) (y k) = 4p( h) Parabola: Ellipse: Focus: (h, k + p) (h + p, k) irectri: y = k p = h p Stadard Form: h y k h y k a b b a Foci: (h ± c, k) (h, k ± c) Hyperbola: a, b, c Relatioship: c = a b c = a b Stadard Form: h y k y k h a b a b Foci: (h ± c, k) (h, k ± c) b symptotes: ( y k) ± ( h) ( y k) ± a ( h) a b a, b, c Relatioship: c = a + b c = a + b Eccetricity: e c e c a a Epoetial Fuctios Simple Iterest: I = prt ompoud Iterest: Epoetial Growth or t r P N N r ecay: 0 t otiuous ompoud Iterest: otiuous Epoetial Growth or ecay: oordiate Geometry Pe 0 rt N N e kt istace Formula: d ( ) ( y y ) Slope of a Lie: Midpoit Formula: y y m y y M, Quadratic Equatio: a + b + c = 0 Quadratic Formula: Slope-Itercept Form of a Lie: y m b Poit-Slope Form of a Lie: y y m( ) a b b 4ac Stadard Form of a Lie: + y =

5 EXMPLE ITEMS Pre-alculus Pre-P, Sem The graph of f( ) is trasformed usig the give steps i the order show. Reflect across the -ais Vertically stretch by a factor of 3 Traslate uit right Traslate uits dow Which graph represets the trasformed fuctio? allas IS - Eample Items

6 EXMPLE ITEMS Pre-alculus Pre-P, Sem if Which graph represets f( ) ( 4) if 3? 6if 3 3 lake is purchasig a ew car for $3,000. If the value of the car decreases at a rate of 9% per year, approimately how may years will it take for the value of the car to reach $5,000? 5.90 years 6.7 years 8.03 years 8.79 years allas IS - Eample Items

7 EXMPLE ITEMS Pre-alculus Pre-P, Sem 4 The first three terms of a sequece are show. 83, 79, 75, What is the sum of the first 5 terms of this sequece? Record the aswer ad fill i the bubbles o the grid provided. e sure to use the correct place value. 5 Polly was give a ratioal fuctio. 3 f( ) 4 6 What discotiuities did Polly discover upo her ivestigatio of this fuctio? The graph of f() has a ifiite discotiuity at = ad a removable discotiuity at = 3. The graph of f() has a ifiite discotiuity at = 3 ad a removable discotiuity at =. The graph of f() has a ifiite discotiuity at = 4 ad a removable discotiuity at = 3. The graph of f() has a ifiite discotiuity at = 0. 6 What is the sith term i the epasio of 0 ( y)? 3,440 4 y 6 8,064 5 y 5 8,064 5 y 5 3,440 4 y 6 allas IS - Eample Items

EXMPLE ITEMS Pre-alculus Pre-P, Sem 4 5 7 Which graph represets the fuctio f( )?

8 EXMPLE ITEMS Pre-alculus Pre-P, Sem Which graph represets the fuctio f( )? 3 8 Which list represets all possible ratioal zeros of f ( ) ? 3, 8,, 7, 7, 3, 3 7, 8 3, 3, 7 3, 7, 3, 7 3 allas IS - Eample Items

9 EXMPLE ITEMS Pre-alculus Pre-P, Sem 9 The aual growth rate for a ivestmet is foud usig the fuctio r P l t P 0 where r is the aual growth rate, t is the time i years, P 0 is the iitial ivestmet, ad P is the preset value. Five years ago, Hele ivested $5,000 at a aual growth rate of 3.7%. What is the preset value of Hele s ivestmet? $5, $5,88.47 $6,06.09 $3, Which equatio represets a slat asymptote for the graph of the fuctio f( ) 5? y 7 y 3 y 4 y 6 Newto s Law of oolig models the temperature, T, of a object over time, t, i miutes, usig the fuctio Tt () T ( T T) e m 0 m kt where T 0 is the iitial temperature of the object, T m is the temperature of the surroudig medium, ad k is a costat for that particular medium. cookie was take from the ove ad placed o a coolig rack with a surroudig air temperature of 0. fter five miutes, the cookie cooled to 48. If k = 0.35, what was T 0, the iitial temperature of the cookie? bout 5 bout 60 bout 8 bout 76 allas IS - Eample Items

EXMPLE ITEMS Pre-alculus Pre-P, Sem polyomial fuctio of degree four is graphed as show. y 000 800 600 400 00 f() -0-4 6 8 0-00 00 00 00-000 ased o this graph, which statemet is true?

10 EXMPLE ITEMS Pre-alculus Pre-P, Sem polyomial fuctio of degree four is graphed as show. y f() ased o this graph, which statemet is true? f () has a total of four roots ad three local etrema. f () has a total of two roots ad three local etrema. f () has a total of two roots ad five etrema. f () has a total of four roots ad five etrema. 3 ball is dropped from a height of 6 feet, ad the retur bouce is 8% of the previous height. How far has the ball traveled whe it hits the groud for the sith time? Roud the aswer to the earest teth of a foot. Record the aswer ad fill i the bubbles o the grid provided. e sure to use the correct place value. allas IS - Eample Items

11 EXMPLE ITEMS Pre-alculus Pre-P, Sem 4 The umber of dowloads of a ew sog grows at a cotiuous epoetial rate durig the first week after the sog s release, as show i the table. ays, t 0 5 Number of dowloads, N(t),00 9,900 Which fuctio is used to fid Nt ( ), the umber of dowloads after t days? Nt ( ),00(.55) t Nt ( ),00(.40) t Nt (),00e Nt (),00e.55t.40t 5 Matthew ad some frieds are goig to a cocert. They hire a car service for $75 to drive them to a restaurat for dier ad the to the cocert. They divide the $60 cost of the dier equally. However, sice Matthew s dad provided cocert tickets for the group, the frieds agree that Matthew does t have to help pay for the car service. The frieds divide this cost equally amog themselves. If each fried speds a total of $5, how may frieds wet to the cocert with Matthew? If f( ) ad g ( ) 3, what is f( g( ))? allas IS - Eample Items

12 EXMPLE ITEMS Pre-alculus Pre-P, Sem 7 If 3 f( ) 8, which graph represets y 0 f ( )? y y 0 y What is the domai of the fuctio f( ) 3 (, 3) ( 3, ) (, 3] [ 3, ) (, 3] [ 3, 0) (0, ) (, 3) ( 3, 0) (0, ) allas IS - Eample Items

13 EXMPLE ITEMS Pre-alculus Pre-P, Sem 9 The formula to calculate the level of soud itesity i decibels (d) is 0 log I I 0 where is the umber of decibels, I is the soud itesity i watts per square meter (W/m ) of ay soud, ad I 0 = 0 W/m, which is the itesity of the faitest soud audible to the huma ear. The pai threshold for the huma ear is 0 d. What is the itesity, I, of this soud? 0 0 W/m 0 W/m 0 0 W/m 0 W/m 0 Which fuctio has a removable discotiuity at? 3,, f( ) f( ) 9 f( ) 4 f( ) 8 0 What is the sum of the arithmetic series 5k? k 3 allas IS - Eample Items

14 EXMPLE ITEMS Pre-alculus Pre-P, Sem The graph of the fuctio, h(), is show. Which graph represets the trasformatio g ( ) h ( 5) 6? allas IS - Eample Items

15 EXMPLE ITEMS Pre-alculus Pre-P Key, Sem Item# Key SE SE Justificatio P.G Graph fuctios, icludig epoetial, ad their trasformatios, icludig af(), f() + d, f( - c), f(b) for specific values of a, b, c, d i mathematical problems. P.F Graph piecewise defied fuctios. 3 P.N alyze situatios modeled by fuctios, icludig epoetial fuctios, to solve real-world problems P.5 alculate the th partial sum of a arithmetic series i mathematical problems. 5 P.L etermie various types of discotiuities i the iterval (-, ) as they relate to fuctios. 6 P.5F pply the iomial Theorem for the epasio of (a + b) i powers of a ad b for a positive iteger, where a ad b are ay umbers. 7 P.F Graph ratioal fuctios. 8 P.5J Solve polyomial equatios with real coefficiets by applyig a variety of techiques i mathematical problems. 9 P.N alyze situatios modeled by fuctios, icludig logarithmic to solve real-world problems. 0 P.I etermie the key features of ratioal fuctios such as asymptotes. P.5I Solve epoetial equatios i real-world problems. P.I alyze the key features of polyomial fuctios such as relative maimum, relative miimum, zeros P.5E alculate the th partial sum of a geometric series. 4 P.5I Geerate epoetial equatios i real-world problems. 5 P.N alyze situatios modeled by fuctios icludig ratioal to solve real-world problems. 6 P. Represet a give fuctio as a composite fuctio of two fuctios. 7 P.E etermie a iverse fuctio for a give fuctio over its domai ad represet the iverse usig multiple represetatios. 8 P.I alyze the key features of ratioal fuctios such as domai. 9 P.5H Solve logarithmic equatios i real-world problems. 0 P.L etermie various types of discotiuities i the iterval (, ) as they relate to fuctios. P.5 Evaluate fiite sums writte i sigma otatio. P.G Graph trasformatios, icludig f() + d, f( - c), for specific values of c, ad d, i mathematical problems.

Example Items. Pre-Calculus Pre-AP

Example Items. Pre-Calculus Pre-AP Example Items Pre-alculus Pre-P Pre-alculus Pre-P Example Items are a represetative set of items for the P. Teachers may use this set of items alog with the test blueprit as guides to prepare studets for