Final project 30 questions

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Final project 30 questions

Final project 30 questions
Final Project, Chapters 1 -5, and 7 Due August 9 th, 2022 Name_____ ____________________ There are 30 questions, and you must do 28 of them for full credit on the project. There is extra credi t available if you ans wer all 30 questions. Each question is worth 5 points for a total of 140 points , with 10 points extra credit a vailable. You are to work on the projects independently. You can turn in the final project during our class meeting, or submit in the D2L shell as one complete pdf by the due date. You may hand write or type the project . Please show all work for full or p artial credit, using the methods discussed in class. Each question will be graded based on the following rubric. 5 Points A five -point response answers the question correctly.  demonstrates a thorough understanding of the mathematical topics  may contain m inor errors that do not detract from the demonstration of understanding  indicates that the student has completed the task correctly, using mathematically sound procedures, all required work is provided 3-4 Points A three -four -point response is partially c orrect.  demonstrates partial understanding of the mathematical topics and/or procedures embodied in the task  addresses most aspects of the task, using mathematically sound procedures  may contain errors and/or an incorrect solution but provides complete pro cedures, reasoning, and/or explanations, all required work is provided 1-2 Point A one -two -point response is incomplete and exhibits flaws but is not completely incorrect.  demonstrates only a limited understanding of the mathematical topics and/or procedu res embodied in the task  may address some elements of the task correctly but reaches an inadequate solution and/or provides reasoning that is faulty or incomplete  exhibits multiple flaws related to misunderstanding of important aspects of the task, misuse of mathematical procedures, or faulty mathematical reasoning  may contain correct numerical answer(s) but required work is not provided 0 Points A zero -point response is incorrect.  insufficient in demonstrating an understanding of the mathematical topics embodied in the task.  the required work is not provided  may contain answers that are incorrect, irrelevant, incoherent, or are correct but arrived at using an obviously incorrect procedure. FYI: The absolute due date for all homework assignments and p rojects, incl uding the final project, is August 9th, 2022 at 11:59 pm. Any submissions posted after that date and time will not be accepted, and will result in a score of zero. Please make sure you have everything turned in before this da te and time. The re are two parts to this final exam. Part A consists of questions from Chapter 7, sections 1 -3. Part B consists of questions from Chapters 1 -5 and Chapter 7. Final Project, Chapters 1 -5, and 7 , page 2 Part A 1. Find the equation of a parabola with a focu s (0,3), and directrix = 1. 2. Determine the vertex, focal length , focus, and directrix for the parabola = 1 2(+ 3)2 3. Determine the vertex, focal length , focus, and directrix for the parabola = (− 3)2+ 1 Fin al Proj ect, Chapters 1 -5, and 7, page 3 4-5. (10 points ) Find the vertex, axis of symmetry, x -intercepts, y -intercept, focal length , focus, and directrix for the parabola. Sketch the graph, showing the focus and directrix. = 1 4(− 3)2− 4 6. Write the eq uation of a circle with center (−2,3) and radius √10 . 7. Determine the center and radius of the circle and sketch its graph. (+ 3)2+ (+ 3)2= 9 8. Find the equation of the ellipse with foci (0,3) and (0,−3), and y -intercepts (0,4) and (0,−4). Fin al Project, C hapters 1 -5, and 7, page 4 9. Sketch the graph of the ellipse and identify the foci. 2 16 + 2 9 = 1 10 -11 . (10 points ) Determine the foci and the equations of the asymptotes, and sketch the graph of the hyperbola. See p rocedures for graphing hyperbolas on pages 554 and 556. 2 9 − 2 16 = 1 Final Project, Chapters 1 -5, and 7 , page 5 Part B 12 -13 . (10 points ) Match the equation on the left with it’s definition and/or description on the right. Write the co rresponding letter in the space provided. a) 2− 5+ 6= 0 Exponential Equation ________ b) (− 3)2+ (− 2)2= 1 Linear equation in one variable ________ c) 2 4+ 2 9 = 1 Equation of an ellipse with center (0,0) and horizontal major axis ________ d) = 2 Equation of a circle with center (3,2) ________ e) 3+ 5= 0 Nonlinear inequality in two variables ________ f) 7− 13 = 7 Equation of an ellipse with center (0,0) and vertical major axis ________ g) 2 4− 2 9= 1 Linear equation in two variables ( in standard form) ________ h) = (− 3)2+ 2 Linear inequality in two variables ________ i) ≤ (− 3)2+ 2 Quadratic Equation with solution set {2,3} ________ j) > 3+ 5 Equation of a parabola with ver tex (3,2) ________ k) 2 9+ 2 4 = 1 Equation of a hyperbola centered at (0,0) opening up and down ________ 14. Julia has 8 coins consisting of quarters and dimes totaling $1.25 . How many quarters and how many dimes does she have? Use algebraic techniques. 15 . Solve the equation by factoring. 2− 12 = 4 16 . Solve the equation using th e quadratic formula. 22− 2+ 3= 0 Final Project, Chapters 1 -5, and 7 , page 6 17. Solve the absolute value inequality. Write the solution using set notation and graph it. |+ 5|< 3 18 . Determine whether each relation is a function , If it is a func tion, determine if it is one -to-one. a) {(4,−4),(1,−1),(0,0),(1,1),(4,4)} b) {(1,2),(3,4),(5,6),(7,8)} For questions 19 -21 , let ()= − + , and ()= +. Find the following . 19. (− )(−3) 20 . ( )(−1) 21 . ((2)) Final Project, Chapters 1 -5, and 7 , page 7 22 . Find the inverse of the function using the procedure for the switch -and -solve method on pg 241. ()= √+ 2− 5 23 -24 . (10 points) Do steps 1 -6 below, given the polynomial function . Show all your work and organize your findings in the table provided. ()= 3− 52 Strategy for Graphing a Polynomial Function (page 306): (1) Check for symmetry (by finding (−)) (2) Find all real zeros of the pol ynomial function (3) Determine the behavior at the corresponding x -intercepts . (4) Deter mine the behavior as → ∞ and → −∞ (5) Calculate the y -intercept . (6) Draw a smooth curve through the points to make the graph . (1) Symmetry:__________________________ (2) zeros_______________ x -interc epts ______________ (3) For each x -intercept fill in the blanks of the following at_______the graph ____________ the x -axis at_______the graph ____________ the x -axis (4) as → ∞, ()→ ________ and as → −∞, ()→ _______ or as the graph goes to the right, it also goes ________ and as the graph goes to the left, it also goes_________. (5) y -intercept___________ ___ Fin al Project, Chapters 1 -5, and 7, page 8 25. Sketch the graph of the rational function. Note that the function is not in lowest terms. Find the domain first. Then reduce the rational expression. Fill in the table of points to gra ph and graph the rational expression. ()= 2− 2− 8 − 4 Domain _______________ 26 . Sketch the graph of ()= 2. State the domain, the range, and whether the function is increasing or decreasing. (1) construct a table of values (points) to graph = () −2 −1 0 1 2 (2) Graph the points and draw a smooth continuous curve through the points (3) Domain ______________________ (4) Range _______________________ (5) Increasing or Decreasing _______________ = () −2 −1 0 1 2 Fin al Project, Chapte rs 1 -5, and 7, page 9 27 . Solve the equation. See strategy for solving exponential and logarithmic equations on page 384. log 2(− 2)+ log 2(+ 1)= 2 28 . Solve the system of equations using the substitution method . Write answer in set notation 4− 2= 8 = 2− 4 29 . Solve the system of equations using the addition method . Write answer in set notation. − 3= 7 2+ = −7 30 . Sketch the graph of the nonlinear inequality. > 2− 2

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