ࡱ> 241] 8bjbj:: 4PX*\X*\8((((4(o-ppppK"m y,,,,,,,$g.1-KK-pp)-&&&^pp,&,&&:v+,+pLB%!+ ,?-0o-+R/25!/2+/2+0"&--#o-/2> : Calculus BC Summer Work 2015 This practice material is designed to review three major topics from precalculus class needed for Calculus BC: parametrics, sequences and series, and polar equations. You must be able to do these problems without the use of a calculator, unless otherwise noted. You should be prepared to take a quiz on this material by the second day of school. Please contact me with any questions at  HYPERLINK "mailto:boisvertc@franklin.k12.ma.us" boisvertc@franklin.k12.ma.us. Section I: Parametrics For basic online help:  HYPERLINK "http://ltcconline.net/greenl/courses/107/PolarParam/PARAMEQ.HTM" http://ltcconline.net/greenl/courses/107/PolarParam/PARAMEQ.HTM A. A parametrization is given for a curve. (a) Graph the curve. Identify the initial and terminal points, if any. Indicate the direction in which the curve is traced. (Calculators may be used.) (b) Find a Cartesian (rectangular) equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? 1.  EMBED Equation   EMBED Equation   EMBED Equation  2.  EMBED Equation   EMBED Equation   EMBED Equation  B. Give a parametrization for the curve. 1. the line segment with endpoints (-2, 5) and (4, 3) 2.  EMBED Equation  Section II: Sequences and Series For basic online help:  HYPERLINK "http://www.mathsisfun.com/algebra/sequences-series.html" http://www.mathsisfun.com/algebra/sequences-series.html Arithmetic Sequences and Series For the following sequences, find the a. common difference b. tenth term c. a recursive rule for the nth term d. an explicit rule for the nth term. i. -1, 2, 5, 8, ii. 1, EMBED Equation , 4,  EMBED Equation , The second and fifth terms of an arithmetic sequence are -3 and 8 respectively. Find the first term and a recursive rule for the nth term. Find the sum of the arithmetic series:  EMBED Equation  Geometric Sequences and Series For the following sequences, find the a. common ratio b. the tenth term c. a recursive rule for the nth term d. an explicit rule for the nth term i. -2, 2, -2, 2, ii. 32, 16, 8, 4, The second and seventh terms of a geometric sequence are  EMBED Equation  and 16 respectively. Find the first term, common ratio, and an explicit rule for the nth term. Find the sum of the infinite geometric series, if possible. a.  EMBED Equation  b.  EMBED Equation  c.  EMBED Equation  Use a sum to express the rational number as a fraction: 7.14141414 A ball can bounce to 80% of the height from which it drops. If the ball is dropped from a height of 3 meters, how far does it travel by the time it hits the ground for the tenth time? (The ball goes down to the first bounce, then up and down thereafter.) Section III: Polar Equations For basic online help:  HYPERLINK "http://www.mathsisfun.com/polar-cartesian-coordinates.html" http://www.mathsisfun.com/polar-cartesian-coordinates.html Plot each point given in polar coordinates. 1.  EMBED Equation  2.  EMBED Equation  3.  EMBED Equation  For each point in A, find the corresponding rectangular coordinate. Find two sets of corresponding polar coordinates for the given rectangular coordinate. 1.  EMBED Equation  2.  EMBED Equation  3.  EMBED Equation  Use a graphing calculator to graph each polar curve. Then, replace the polar equation by an equivalent Cartesian (rectangular) equation. 1.  EMBED Equation  2.  EMBED Equation  3.  EMBED Equation  Graph circles, rose curves, limacon curves, and lemniscate curves given its equation. The following website gives the general form of the polar curve with its graph:  HYPERLINK "http://www.mathdemos.org/mathdemos/family_of_functions/polar_gallery.html" http://www.mathdemos.org/mathdemos/family_of_functions/polar_gallery.html Calculus BC Selected Answers 2014 Section I: Parametrics A. 1. a. initial point (4, 15) terminal point (-2, 3) traced right to left b.  EMBED Equation  for  EMBED Equation  2. a. initial point (2, 0) terminal point (2, 0) traced counterclockwise b.  EMBED Equation  for  EMBED Equation  B. 1.  EMBED Equation ,  EMBED Equation  for  EMBED Equation  OR  EMBED Equation ,  EMBED Equation  for  EMBED Equation  2.  EMBED Equation ,  EMBED Equation  for  EMBED Equation  Section II: Sequences and Series A. 1. i. a.  EMBED Equation  b.  EMBED Equation  c.  EMBED Equation  d.  EMBED Equation  ii. a. d = 1.5 b.  EMBED Equation  c.  EMBED Equation  d.  EMBED Equation  2.  EMBED Equation   EMBED Equation  3.  EMBED Equation  B. 1. i. a.  EMBED Equation  b.  EMBED Equation  c.  EMBED Equation  d.  EMBED Equation  ii. a.  EMBED Equation  b.  EMBED Equation  c.  EMBED Equation  d.  EMBED Equation  2.  EMBED Equation   EMBED Equation   EMBED Equation  3. a.  EMBED Equation  b. no sum c.  EMBED Equation  4.  EMBED Equation  5.  EMBED Equation meters Section III: Polar Equations A. 1. negative x-axis 2. Quadrant III 3. Quadrant I B. 1.  EMBED Equation  2.  EMBED Equation  3.  EMBED Equation  C. Answers may vary. 1.  EMBED Equation ,  EMBED Equation  2.  EMBED Equation ,  EMBED Equation  3.  EMBED Equation ,  EMBED Equation  D. 1.  EMBED Equation  2.  EMBED Equation  3.  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