Example Items. Pre-Calculus Pre-AP

Size: px

Start display at page:

Download "Example Items. Pre-Calculus Pre-AP"

Wilfrid Jennings
5 years ago
Views:

1 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 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 Example Item measures is NOT ecessarily the oly part of the SE that is assessed o the P. Noe of these Example Items will appear o the P. Teachers may provide feedback regardig Example Items. () owload the Example Feedback Form ad it. The form is located o the homepage of the ssessmet website (assessmet.dallasisd.org). OR () To submit directly: Logi to the ssessmet website. Uder News i the left-had colum, click o Sem Example Items owload. bove the subjects, click o Example Feedback Form. Secod 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 x, x 3,x x, x, x 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: si csc csc si cos ta sec cot sec cos cot ta si θ + cos θ = + ta θ = sec θ + cot θ = csc θ cos ( ) cos cos si si si( ) si cos cos si cos( ) coscos sisi si( ) si cos cos si ouble-gle Idetities: six si x cos x cos x cos x cos x cos x si x cos x si x Projectile Motio Vertical Positio: Vertical Free-Fall Motio: Horizotal istace: x ( v cos ) t 0 y gt ( v0 si ) t y0 ft m st () gt vt 0 s vt () gt v 0 0 g sec sec oic Sectios Parabola: (x - h) = 4p(y - k) (y - k) = 4p(x - h) ircle: x + y = r (x h) + (y - k) = r Ellipse: Hyperbola: x h y k x h y k a b b a x h y k y k x h a b a b

3 P Formulas Pre-alculus/Pre-alculus PP Expoetial Fuctios Simple Iterest: I = prt ompoud Iterest: Expoetial Growth or t r P N N r ecay: 0 t otiuous ompoud Iterest: otiuous Expoetial Growth or ecay: Sequeces ad Series Pe 0 rt N N e kt 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 k a ( a a ) k a a k a ( r ), r r a r r The th Term of a Geometric Sequece: S a ar a ar, r r iomial Theorem: Permutatios: a b a b a b a b a b P r! ombiatios: ( r)! r! ( r)! r! oordiate Geometry istace Formula: d ( x x ) ( y y ) Slope of a Lie: Midpoit Formula: y y m x x x x y y M, Quadratic Equatio: ax + bx + c = 0 Quadratic Formula: x a b b 4ac Slope-Itercept Form of a Lie: y mx b Poit-Slope Form of a Lie: y y m( x x) Stadard Form of a Lie: x + y =

5 EXMPLE ITEMS Pre-alculus Pre-P, Sem hyperbola has vertices at (, 5) ad (, 3). The slope of oe asymptote is equatio of the hyperbola?. What is the ( y ) ( x ) 6 64 ( y ) ( x ) 6 64 ( x ) ( y ) 6 8 ( x ) ( y ) 6 8 ellipse cetered at the origi has a vertical major axis of uits ad a eccetricity of 0.5. What is the equatio of the ellipse? x y x y x y 9 36 x y What are the polar coordiates of the poit (, )? 7 4, 4 4,,, allas IS - Example Items

6 EXMPLE ITEMS Pre-alculus Pre-P, Sem 4 Which graph represets the curve give by the parametric equatios x t ad y t 3 over the iterval t? 5 If a plae itersects a double-apped coe parallel to the slat height of the coe, what type of coic sectio is formed? Parabola ircle Ellipse Hyperbola allas IS - Example Items

7 EXMPLE ITEMS Pre-alculus Pre-P, Sem 6 Poit P is rotated 0 couterclockwise aroud a circle with a diameter of 0 meters. If the ceter of the circle is at the origi, which coordiates represet the locatio of P relative to the ceter? ( 5 3, 5) ( 0 3, 0) ( 0, 0 3) ( 5, 5 3) 7 What is the rectagular form for the curve give by the parametric equatios x t 5t ad y t? x y y x y y x y y x y y If a = 6,, 9, b =, 6, 8, ad c = 8, 4, 3, what is a 3 b c? 3 5, 0, 4 57, 48, 30 4, 8, 0, 4, 4 allas IS - Example Items

8 EXMPLE ITEMS Pre-alculus Pre-P, Sem 9 kicker i a football game attempts a field goal 50 yards from the goal post. The ball is o the groud ad is kicked with a iitial velocity of 8 ft/sec at a agle of 66. The height of the crossbar o the goal post is 0 feet, as show i the diagram. For the field goal to be good, the ball must pass over the crossbar ad betwee the uprights. ssumig the kick is straight ad passes betwee the uprights, which coclusio is true? The ball hits the groud before reachig the goal post, so the field goal is o good. The ball passes uder the crossbar, so the field goal is o good. The ball passes over the crossbar, so the field goal is good. The ball hits the crossbar, so it caot be determied if the field goal is good. 0 What is the exact value of 4π ta, if it exists? Udefied allas IS - Example Items

EXMPLE ITEMS Pre-alculus Pre-P, Sem I, m 3, m 0 ad side c 750. What is the approximate legth, to the earest hudredth, of side a? Record the aswer ad fill i the bubbles o the grid provided.

9 EXMPLE ITEMS Pre-alculus Pre-P, Sem I, m 3, m 0 ad side c 750. What is the approximate legth, to the earest hudredth, of side a? Record the aswer ad fill i the bubbles o the grid provided. e sure to use the correct place value. airplae flies east for 00 miles before turig 60º south ad flyig for 00 miles. What are the magitude ad the directio of the airplae from its startig poit? Magitude: 73. miles irectio: E 9. S Magitude: 64.6 miles irectio: E 9. S Magitude: 73. miles irectio: E 30 S Magitude: 64.6 miles irectio: E 30 S 3 Which agle has a egative sie value ad a egative cotaget value? π 7 5π 8 4π 3 9π 5 allas IS - Example Items

10 EXMPLE ITEMS Pre-alculus Pre-P, Sem 4 From the top of a 550-foot cliff, a hiker looks dow at a river below. Her agles of depressio to the ear ad far baks of the river are 70 ad 50 respectively, as show i the picture. ased o this iformatio, approximately how wide is the river? 6. feet 00. feet 6.3 feet 46.5 feet 5 Two forces act upo a object as show. What is the approximate magitude of the resultat force?. pouds 4.8 pouds 30.9 pouds 48. pouds allas IS - Example Items

11 EXMPLE ITEMS Pre-alculus Pre-P, Sem 6 The co-vertices of a ellipse are at (, ) ad (8, ) ad the eccetricity is. What is the 3 equatio of this ellipse? ( x 3) ( y ) 69 5 ( x 3) ( y ) 5 69 ( x 3) ( y ) 5 69 ( x 3) ( y ) urig a scoutig exercise, dres leaves camp ad hikes miles orthwest. He the turs ad hikes 3 miles due orth. Felicia leaves camp ad plas to hike o a direct path to dres ew positio. What are the directio ad distace Felicia should hike? irectio: 07.7 istace: 3.6 miles irectio: 87.7 istace: 3.6 miles irectio: 87.7 istace: 4.6 miles irectio: 07.7 istace: 4.6 miles 8 If 7 cos ad ta 0, what is the value of csc? allas IS - Example Items

12 EXMPLE ITEMS Pre-alculus Pre-P, Sem 9 Julissa wats to fid the measure of i. She uses the Law of osies to work the problem as show. Step : cos x Step : 30 6 cos x Step 3: 9 6 cosx Step 4: Step 5: I which step did Julissa make a mistake? Step Step Step 3 Step 4 9 cos x 6 x cos Which polar equatio produces a Spiral of rchimedes? π 3 r cos r si r allas IS - Example Items

What is the approximate measure, to the earest degree, of the agle betwee the path from Owe s house to the

13 EXMPLE ITEMS Pre-alculus Pre-P, Sem Owe s house is blocks from the library ad 8 blocks from the school. The library is 9 blocks from the school. What is the approximate measure, to the earest degree, of the agle betwee the path from Owe s house to the library ad the path from Owe s house to the school? Record the aswer ad fill i the bubbles o the grid provided. e sure to use the correct place value. allas IS - Example Items

14 EXMPLE ITEMS Pre-alculus Pre-P Key, Sem Item# Key SE SE Justificatio P.3I P.3H Use the characteristics of a hyperbola to write the equatio of a hyperbola with ceter (h, k). Use the characteristics of a ellipse to write the equatio of a ellipse with ceter (h, k). 3 P.3 overt betwee rectagular coordiates ad polar coordiates. 4 P.3 Graph a set of parametric equatios. 5 P.3F 6 P.4 etermie the coic sectio formed whe a plae itersects a double-apped coe. etermie the relatioship betwee the uit circle ad the defiitio of a periodic fuctio to evaluate trigoometric fuctios i mathematical problems. 7 P.3 overt parametric equatios ito rectagular relatios. 8 P.4J Represet the additio of vectors ad the multiplicatio of a vector by a scalar symbolically. 9 P.3 Use parametric equatios to solve real-world problems. 0 P.4 etermie the relatioship betwee the uit circle ad the defiitio of a periodic fuctio to evaluate trigoometric fuctios i mathematical problems P.4G Use the Law of Sies i mathematical problems. P.4I Use vectors to model situatios ivolvig magitude ad directio. 3 P.4 Represet agles i degrees based o the cocept of rotatio. 4 P.4E Solve problems ivolvig trigoometric ratios i real-world problems. 5 P.4K pply vector additio i real-world problems. 6 P.3H 7 P.4K Use the characteristics of a ellipse to write the equatio of a ellipse with ceter (h, k). pply vector additio ad multiplicatio of a vector by a scalar i real-world problems. 8 P.4E etermie the value of trigoometric ratios of agles. 9 P.4H Use the Law of osies i mathematical problems. 0 P.3E Graph polar equatios by plottig poits ad usig techology. 49 P.4H Use the Law of osies i real-world problems.

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

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