ࡱ>  UTa 3bjbj͚ cI\I\}1  PPTTT$xxxPd,$xXP6 &&&&333WXXXXXX$ZL]~%XET3~1333%XPP&& jX9993P&:T&W93W996/T JV&4UWX0X+U`]6]8V]TV`33933333%X%X7$333X3333]333333333 > : TO: SHS Calculus Students 2016-2017 FROM: Col. Bradshaw SUBJECT: Calculus-DC Summer Assignment DATE: July 14, 2016 DUE DATE: Tuesday, September 6, 2016 Welcome to Calculus-Dual Enrollment! You are expected to complete the attached homework assignment before the beginning of the course. This is because of class time constraints and the amount of material that must be covered during the accelerated schedule this school year. I will grade your assignment packet, and after a short review, we will have a test on the material to determine if you will be successful in this course. SUMMER HELP: This assignment is challenging. Expect to work a minimum of about 12 hours. You are being asked to review all of the algebra, geometry, and trigonometry skills that you have ever learned and thats a lot! Please dont get discouraged if you have some trouble; it is to be expected. Refer to your precalculus notes when working these problems. I will be glad to help you with questions during the summer, anytime except the second week in August. You may either call or text me at 703-209-3030(C), or e-mail me at  HYPERLINK "mailto:jbradshaw@pdc.edu" jbradshaw@pdc.edu. TEXTBOOK: Our textbook for this class is Calculus, 10e, by Ron Larson and Bruce Edwards. We will use the book extensively in class. You are expected to study and learn from this textbook. If you want your own book at home, you can buy the 8th or 9th edition for less than $40 from Amazon or Ebay. These two editions are very similar to the 10th; however, the exercise problems are somewhat different. You may also check out an 8th edition book from the school to use at home. ONLINE RESOURCES: Your main online resource is  HYPERLINK "http://www.larsoncalculus.com/calc10" www.larsoncalculus.com/calc10. The videos are great. While working this packet, you can click on the Algebra Help tab. Another good online resource is MIT Open Courseware,  HYPERLINK "http://ocw.mit.edu/high-school/mathematics/" http://ocw.mit.edu/high-school/mathematics/. While doing your homework assignments, you may use CalcChat,  HYPERLINK "http://www.calcchat.com/book/Calculus-10e/" http://www.calcchat.com/book/Calculus-10e/, to help you solve problems. Do not copy the solutions, and do not use software such as  HYPERLINK "http://www.mathway.com" www.mathway.com for your homework problems that you turn in for grades. That is cheating! GRAPHING CALCULATORS: We will use the color TI-84 Plus CE in class. If you dont have one, you can order online from either schoolsavers.com, amazon.com, or ebay. You can also find them at local book stores, including Paul D. Camp, and retail stores such as Wal-Mart. NOTEBOOK and HOMEWORK: You are required to use a loose leaf three-ring binder for taking notes and completing assignments for this course as there are several handouts, and I collect your assignments for grading. All homework sections should be labeled separately, and the original problems should be written out, except for word problems. Do your work neatly in pencil. This assignment is worth 200 points. I will randomly pick ten problems from the worksheet to grade for correctness and effort; I will also grade your assignment on overall neatness and thoroughness. Complete all your work on separate paper. If you need more space for a problem, put it on separate paper stapled to the back, labelled clearly, and put a note for that problem that there is an attachment. All answers, except graphs and tables, should be boxed. I expect high quality work! Colonel Bradshaw  SHAPE \* MERGEFORMAT  Simplify using only positive exponents. 1.  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3.  EMBED Equation.DSMT4  4.  EMBED Equation.DSMT4  5.  EMBED Equation.DSMT4  6.  EMBED Equation.DSMT4  7.  EMBED Equation.DSMT4  8.  EMBED Equation.DSMT4  Find the domain and range of the following functions without a calculator if possible. Make sure to use interval notation (ex: [0, 3)). 9.  EMBED Equation.DSMT4  10.  EMBED Equation.DSMT4  11.  EMBED Equation.DSMT4  12.  EMBED Equation.DSMT4  13.  EMBED Equation.DSMT4  14.  EMBED Equation.DSMT4  15.  EMBED Equation.DSMT4  16.  EMBED Equation.DSMT4  17.  EMBED Equation.DSMT4  18.  EMBED Equation.DSMT4  19.  EMBED Equation.DSMT4  20.  EMBED Equation.DSMT4  Factor completely. 21.  EMBED Equation.DSMT4  22.  EMBED Equation.DSMT4  23.  EMBED Equation.DSMT4  Solve the following inequalities by factoring and making sign charts. 24.  EMBED Equation.DSMT4  25.  EMBED Equation.DSMT4  26.  EMBED Equation.DSMT4  27.  EMBED Equation.DSMT4  28.  EMBED Equation.DSMT4  29.  EMBED Equation.DSMT4   Describe, in words, the transformations that would take place to  EMBED Equation.DSMT4  in each of the following. 30.  EMBED Equation.DSMT4  31.  EMBED Equation.DSMT4  32.  EMBED Equation.DSMT4  33.  EMBED Equation.DSMT4  34.  EMBED Equation.DSMT4  35.  EMBED Equation.DSMT4  Determine if each function is even, odd, or neither. Show all work. 36.  EMBED Equation.DSMT4  37.  EMBED Equation.DSMT4  38.  EMBED Equation.DSMT4  39.  EMBED Equation.DSMT4  Solve each equation by factoring, graphing, or using the quadratic formula. 40.  EMBED Equation.DSMT4  41.  EMBED Equation.DSMT4  42.  EMBED Equation.DSMT4  43.  EMBED Equation.DSMT4  44.  EMBED Equation.DSMT4  45.  EMBED Equation.DSMT4  46.  EMBED Equation.DSMT4  47.  EMBED Equation.DSMT4  48.  EMBED Equation.DSMT4   Find the equations of all vertical (x = ?) and horizontal (y = ?) asymptotes (if they exist). 49.  EMBED Equation.DSMT4  50.  EMBED Equation.DSMT4  51.  EMBED Equation.DSMT4  52.  EMBED Equation.DSMT4  53.  EMBED Equation.DSMT4  54.  EMBED Equation.DSMT4  Simplify the following. 55.  EMBED Equation.DSMT4  56.  EMBED Equation.DSMT4  57.  EMBED Equation.DSMT4  58.  EMBED Equation.DSMT4  59.  EMBED Equation.DSMT4  60.  EMBED Equation.DSMT4  If  EMBED Equation.DSMT4 , find the following. 61.  EMBED Equation.DSMT4  62.  EMBED Equation.DSMT4  63.  EMBED Equation.DSMT4  64.  EMBED Equation.DSMT4  Solve each equation. 65.  EMBED Equation.DSMT4  66.  EMBED Equation.DSMT4  67.  EMBED Equation.DSMT4  68.  EMBED Equation.DSMT4  69.  EMBED Equation.DSMT4  70.  EMBED Equation.DSMT4  TRIGONOMETRY: Trig functions are used extensively in calculus. You must know the special triangles, 30-60-90 and 45-45-90, and you must memorize exact values of sin(), cos(), and tan() for  = 0, /6, /4, /3, /2,  and 3/2 radians, and be able to use these to find values in Quadrants II, III, and IV, as well as for evaluating secant, cosecant, and cotangent functions. We will work primarily with radians in calculus. You must know the trig definitions and the Pythagorean identity, cos2  + sin2  = 1. You should also be able to derive variations of the identity by dividing with cos2  or sin2  and rearranging terms. . Radian and Degree Measure Use  EMBED Equation.DSMT4  to convert back and forth between degrees and radians. 71. Convert to degrees: a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c. 2.63 radians 72. Convert to radians: a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c. 237 EMBED Equation.DSMT4  Angles in Standard Position 73. Sketch the angle in standard position. a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c.  EMBED Equation.DSMT4  d. 1.8 radians 74. Evaluate the following without using a calculator. a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4  e)  EMBED Equation.DSMT4  f)  EMBED Equation.DSMT4  Solve each equation on the interval  EMBED Equation.DSMT4 . Give exact values  EMBED Equation.DSMT4  if possible. 75.  EMBED Equation.DSMT4  76.  EMBED Equation.DSMT4  77.  EMBED Equation.DSMT4  78.  EMBED Equation.DSMT4  79.  EMBED Equation.DSMT4  80.  EMBED Equation.DSMT4  81.  EMBED Equation.DSMT4  82.  EMBED Equation.DSMT4  83.  EMBED Equation.DSMT4  Equation of a line Slope intercept form:  EMBED Equation.DSMT4  Vertical line: x = c (slope is undefined) Point-slope form:  EMBED Equation.DSMT4  Horizontal line: y = c (slope is 0) Use slope-intercept form to find the equation of the line having a slope of 3 and a y-intercept of 5. Determine the equation of a line passing through the point (5, -3) with an undefined slope. Determine the equation of a line passing through the point (-4, 2) with a slope of 0. Use point-slope form to find the equation of the line passing through the point (0, 5) with a slope of 2/3. Find the equation of a line passing through the point (2, 8) and parallel to the line  EMBED Equation.DSMT4 . Find the equation of a line perpendicular to the y- axis passing through the point (4, 7). Find the equation of a line passing through the points (-3, 6) and (1, 2). Find the equation of a line with an x-intercept (2, 0) and a y-intercept (0, 3). Answer the following questions over a variety of topics. 92. Let f be a linear function where  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 . Find  EMBED Equation.DSMT4 . 93. Find an equation for the line, in point-slope form, that contains  EMBED Equation.DSMT4  and is perpendicular to  EMBED Equation.DSMT4 . Find the distance between the points  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 . Use the table to calculate the average rate of change from t = 1 to t = 4. t01234 EMBED Equation.DSMT4 87512 Order the points A, B, and C, from least to greatest, by their rates of change.  If  EMBED Equation.DSMT4 , find  EMBED Equation.DSMT4  (the inverse of g). Find the points of intersection in the graphs of  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 . Rewrite  EMBED Equation.DSMT4  as a single logarithmic expression. 100. Sketch a graph of the piecewise function  EMBED Equation.DSMT4 . 101. Describe the left and right end-behavior of the function  EMBED Equation.DSMT4 . 102. Find the domain and range of each function (without a calculator if possible). a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4   d)  EMBED Equation.DSMT4  e)  EMBED Equation.DSMT4  f)  EMBED Equation.DSMT4  103. The circle below has a radius of 6 ft. Find the area and circumference of the circle, then find s.  104. Find the area of the trapezoid.  105. Find the missing sides and angles of the triangle. Then find its area.  106. Find the volume of a washer with outer radius of 18 ft., inner radius of 15 ft., and height of 3 ft. 107. Rewrite  EMBED Equation.DSMT4  into an equivalent expression using only natural logarithms. Three sides of a fence and an existing wall form a rectangular enclosure. The total length of fence used for the three sides is 240 ft. Find x if the area enclosed is 5500 ft2. The number of elk after t years in a state park is modeled by the function  EMBED Equation.DSMT4 . What was the initial population? When will the number of elk be 750? What is the maximum number of elk possible in the park? Simplify  EMBED Equation.DSMT4 . Use long division, or synthetic division, to rewrite the expression  EMBED Equation.DSMT4 . Rewrite  EMBED Equation.DSMT4  in vertex form  EMBED Equation.DSMT4  by completing the square. Sketch a graph of the piecewise function  EMBED Equation.DSMT4 . Use a graphing calculator to solve  EMBED Equation.DSMT4 . Do the lines  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  intersect?  The function  EMBED Equation.DSMT4  is graphed below. Find the following. a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  d)  EMBED Equation.DSMT4  e)  EMBED Equation.DSMT4  f)  EMBED Equation.DSMT4      Calculus-DC Review Packet Name: ___________________________________  PAGE \* MERGEFORMAT 9 Exponent Rules: RuleExample1x1 = x51 = 52x0 = 150 = 13x-1 = 1/x15-1 = 1/54(xm)(xn) = xm+n(x2)(x3) = x2+3 = x55xm/xn = xm-nx3x2 = x3-2 = x16(xm)n = x(m)(n)(x3)2 = x(3)(2) = x67(xy)n = xnyn(xy)3 = x3y38(xy)-n = x-ny-n(xy)-3 =x-3y-39x-n = 1/xnx-2 = 1/x2 Transformations of Function Graphs-f (x) reflect f (x) over the x-axisf (-x)reflect f (x) over the y-axisf (x) + kshift f (x) up k unitsf (x) - kshift f (x) down k unitsf (x + h) shift f (x) left h unitsf (x - h) shift f (x) right h unitsAf (x) multiply y-values by Af (Bx)divide x-values by B Vertical Asymptotes Determine the vertical asymptotes for the function. Set the denominator equal to zero to find the x-value for which the function is undefined. If the numerator is not equal to zero at that x-value, that is the vertical asymptote. Horizontal Asymptotes Determine the horizontal asymptotes using the three cases below. Case I. Degree of the numerator is less than the degree of the denominator. The asymptote is y = 0. Case II. Degree of the numerator is the same as the degree of the denominator. The asymptote is the ratio of the leading coefficients. Case III. Degree of the numerator is greater than the degree of the denominator. There is no horizontal asymptote. The function increases without bound. (If the degree of the numerator is exactly 1 more than the degree of the denominator, then there exists a slant asymptote, which is determined by long division.) Complex Fractions When simplifying complex fractions, multiply by a fraction equal to 1 which has a numerator and denominator composed of the common denominator of all the denominators in the complex fraction. 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