y = x 5 ( ) + 22 at the rate of 3 units per second.

Transcription

1 C 4-6,8 Review Pre-Calculus Name Period THEME 1 Parametric Equations Refreser notes: 1) Maggie moves at constant speed of 6 m/s. Se starts at te point (12,3) and eads towards te y-axis along te line y = 1 3 x 1. a) Give Maggie s parametric equations of motion. b) Give an expression for te distance from Maggie s location to te origin, t seconds after se starts moving. 2) Fran and Zoe live in te coordinate plane. At midnigt, Fran starts out from te point (35,0). Se moves at a constant speed along a straigt line and will pass troug te point (0,18) after 5 seconds. At midnigt, Zoe starts out from te point (5,22) and eads toward te fourt quadrant along te line y = x 5 ( ) + 22 at te rate of 3 units per second. a) Find parametric equations for Fran s location t seconds after midnigt. b) Find parametric equations for Zoe s location t seconds after midnigt. c) Find and simplify an expression tat represents te distance between Fran and Zoe at any time t. THEME 2 Writing Linear Equations from a Situation: 3) On a certain island, tere are goats and kangaroos. You visit te island for te first time and find 150 goats and 260 kangaroos on te island. Ten years later, you return and find 280 goats and 300 kangaroos. Suppose te number of goats is a linear function of t, te number of years since your first visit. Also, suppose te number of kangaroos is a linear function of t. Wen will te number of goats be twice te number of kangaroos? (Give your answer in years since your first visit.) 4) Suppose te number of rabbits in a certain park is a linear function of time. In 1980, te park ad 300 rabbits. In 1994, te park ad 1000 rabbits. Te number of goldfis in te park s pond is also a linear function of time. In 1988, te pond ad 100 goldfis, wile in 1993, tere were 400 goldfis. In wat year were tere 500 more rabbits tan goldfis?

2 THEME 3 Intersecting Circles and Diagonal Lines: 5) Sally is walking in a straigt line troug te Circular Forest, wic as te sape of a perfect circle. Se enters te forest at a point 10 km east and 4 km nort of te center of te forest. Se exits te forest at Point P and continues walking in te same direction. Point P is due sout of a point 3 km due east of te center of te forest. Wen se is due sout of te center of te forest, ow far from te center is se? 6) You are sailing your boat near a radar antenna. Te radar will detect anyting witin 10 km in any direction. You start sailing from a point 12 km east and 8 km nort of te radar. You will sail directly to a point 8 km west and 14 km sout of te radar. You sail at a constant speed of 6 km/r. For wat lengt of time will your sailboat be detectable by te radar? THEME 4 Closest Point on a Line to Anoter Point: 7) Adam starts 400ft west and 300ft nort of Ms. Longo s office. He wanders in a straigt line, and ends up 100ft east and 400ft sout of Ms. Longo s office. If Adam gets witin 175ft of Ms. Longo s office, e ll get caugt. Does Adam get in trouble? 8) Aidan is walking in a straigt line from is ouse to Caal s ouse. Aidan s ouse is 8km due nort of Barra s ouse. Caal s ouse is 5km east and 7km sout of Barra s ouse. Impose a coordinate system wit Barra s ouse at te origin. On Aidan s walk, ow close does e come to Barra s ouse? Sow all work. THEME 5 - Functions Inside Functions (including function compositions) 9) If f x 10) If f x ( ) = 5x, find and simplify f ( x + ) f ( x) ( ) = x 2, find and simplify f ( x + ) f ( x) 11) If f ( x) = 3x 2 + 2x 5, find and simplify f ( x + ) f ( x )

3 THEME 6 Multipart Functions wit Lines and Circles 12) Find te multipart functions f(x) for te graps below a) b) A (0,4) B (16,9) C (21,14) D (29,6)

4 THEME 7 Multipart Functions wit Area 13) You ave pizzas saped as sown below. You are going to cut te pizza wit a vertical cut x inces from te left edge. Express te area to te left of te cut as a multipart function of x. a) b)

5 ANSWERS: 1) a) x(t) = t y(t) = t 2) a) x t b) d = ( t) 2 + ( t) 2 ( ) = 35 7t, y(t) = 3.6t b) x( t) = t, y(t) = t c) d = 115.9t t ) 74 years 4) ) km 6) ours 7) His closest distance to Mr. Hegarty s office is feet, so YES e gets caugt. 8) 2.53 km 9) 5 10) 2x+ 11) 12x+4 12) a) 5 x if 0 x 16 f(x) = ( x 21) 2 if 16 x 21 x + 35 if 21 x 29 b) x if -2 x 3 f(x) = 3 4 (x 5) 2 if 3 x 7 3 ( 5 x 7 ) + 7 if 7 x 12 13) a) b) Area = 5x if 0 x ( 2 x 8 # ) 5+ 1 ( 2 x 18 & % )( $ ' if 8 x 18 Oter optional resources: Mr. G s old precalc review for 4,5,6,8. Tis is more skill based practice tat I used in prior years. Find it on te tab Documents for UW Pre-Calc. Also use te Mat 120 website and witin Arcives searc out previously given midterms, but if you see problems for Quadratric Modeling (C 7 modeleing), Inverses (C 9) or Exponentials (C 10), skip tese!