Summer Assignment - PreAP PreCalculus Summer 2018 To All future students for the school year 2018-2019 : For the Precalculus course, students must have a tool belt of required skills and understanding to allow for them to be successful in the course. These skills reach as far back as their 6th/7th grade math class and is inclusive of every math class afterwards. It is important for students to not only have the abilities to complete math problems that deal with these skills, but also be able to accurately ascertain which skills are required to complete a myriad of mathematical challenges that Precalculus provides to them. The overall objective is to prepare students for future success in advanced mathematical courses such as Calculus. This assignment is broken into levels that illustrate the level of mastery and understanding a student is demonstrating when completing these problems. As a student moves to a higher level, s/he brings along with them the skills they have acquired in the previous level. These skills become prerequisites for the next level and are important to the student s success as they continually strive to level up their mastery and understanding. The level system for this assignment is broken down as follows: Level 1 - Algebra 1 understanding Level 2 - Advanced Algebra 1 / Geometric Understanding Level 3 - Algebra 2 Understanding & Comprehension (This is where you want to start this course) Level 4 - Advanced Algebra 2 understanding, comprehension, and mastery For a Precalculus student, ideally you want them operating at level 3 and above. Students who find themselves only being able to complete level 2 type questions should make the realization that additional assistance may be required (tutorials, additional resources to supplement learning, etc.) to help them reach level 3 and beyond. It is important for students to understand that we want them to finish the course being able to consistently complete level 3 / 4 type problems, but that from time to time within the course they may see a regression to level 2 / 1 problems based on complexity and content. They must keep in mind the overall goal of the course is to continuously work to reach that goal even when difficulties and challenges manifest themselves. A student being able to persevere and achieve higher and higher levels will find success overall in future mathematical endeavors. WIth that said, if students require some additional assistance, they can Google search each topic and/or problem, but can also look to these websites for help/support. They websites are: http://www.purplemath.com/ https://www.khanacademy.org/ http://sosmath.com/ http://www.shelovesmath.com/ Remember to work on this assignment throughout the summer and if you have any questions, please reach out to roger.thurman@huttoisd.net for questions or utilize the above resources for additional insight and support. Good luck and look forward to see you in the fall.
Complete the following. Show work in a clear manner. Clearly indicate your final answer. Have this assignment completed and ready to turn in on the first class of PreAP PreCalculus
Level 1 - Basic Algebra Skills 1) Find the domain and range of the following. Determine if the relation is a function. a) (-1, 5), (-3, 2), (2, 0), (1, 2) b) (-4, 3), (-4, -1), (-2, 4), (0, 2) 2) Graph the following on the graphs at the end of this assignment. Label all critical points (intercepts, minimums, maximums, etc.) a) f(x) = x 4 c) f(x) = x e) y = x 2 + 3 b) x = 7 d) y = x 4 + 3 f) f(x) = (x + 1) 2 4 3) Evaluate the function for the given value of x. a) f(x) = 3x 11; f(0) b) f(x) = x 2 5; f( 1) c) f(x) = x + 5 + 1; f(2) 4) Determine the slope of the line that intersects the given points. a) (3, -5), (4, 4) b) (-2, 7), (-2, -2) c) (3, 9), (11, 0) 5) Write the equation of the line that passes through the given points. Write your equation in point-slope and slope intercept forms. a) (2, -3), (-1, -6) b) (-4, 0), (6, 7) c) (-2, 3), (5, 3) d) ( 1 2, 3 4 ), ( 5 4, 6 8 ) 6) Use slope intercept form to write the following equation(s): a) A line perpendicular to y = 2 x + 4 and passing through (6, -2). 5 b) A line parallel to y = 1 x 5 and passing through (-4, -6). 3 7) Identify properties of functions (linear & quadratic). a) Domain & Range b) Symmetry c) Asymptotes d) Intercepts e) Maximum/Minimum f) Slope (linear) g) Sketch a graph of the parent function Level 2 - Algebraic Manipulation & Evaluation / Geometry 8) Simplify. a) 200x 4 y c) c) 27 + 75 12 e) 4a 3 b 2 3a 4 b 3
2x 8 y b) ( x 2 (y 2 z 4 ) ) 1 d) a 56 21 9) Solve for the variable indicated. a) Find the value of w. b) Find the value of y. c) Find the value of x. d) Find the value of z. Use the figure to solve problems 10 e - j. e) Supplement of AEB f) Complement of AEB g) x = h) y = i) m DEC = j) m AED = Level 2 - Algebraic Manipulation & Evaluation / Geometry cont. 10) Determine the exact value based on the following figure (express answer in radical terms): a) AB = b) BC =
c) Explain in your own words how you determined the distance between AB & BC. Use complete sentences. 11) Determine the given lengths based on the figure below. The distance from the dog walker to the top of the power pole is 50ft. a) Height of the power pole = b) Distance from the tree to the top of the power pole = c) Distance from the dog walker to the bottom of power pole = d) Distance from the tree to the bottom of the power pole = e) Distance between the dog walker to the tree = Level 2 - Algebraic Manipulation & Evaluation / Geometry cont. 12) Determine the following measurement indicated based on the situation provided. a) Volume of the rectangular prism Volume =
In the sciences, quantities of liquids are measured in liters and milliliters. One milliliter of water has the same volume as a cube with edge length 1 centimeter. b) Tell what size cube has the same volume as a liter of water. c) In a science lab, liquids are often measured in tall, thin cylinders called graduated cylinders. One graduated cylinder has a diameter of 2 centimeters, and 8 milliliters of water are poured into it. Tell how high the water will reach. Round to the nearest tenth. Level 3 - Simplifying, factoring, & solving complex equations, and solving systems of equations/ inequalities. 13) Factor the following completely. a) x 2 + 2x 24 c) 2m 2 + 6m 108 e) 25a 2 9 b) 2y 3 8 d) z 3 + 27 f) 3b 2 8b + 4 14) Solve the following equations - (one step, two step, multi-step, rational, absolute value). a) 3x 2 = 9x c) x + 7 = x + 1 e) 3x 2 16x 7 = 5 b) 2h 3(h + 1) = 14 d) 1 x + 5 x = 2 f) 4 x 2 x = 1 x 15 2 3 3 5 3 15) Solve the following systems of equations. Utilize the method listed to solve each system. Determine if the system is consistent and independent, consistent and dependent, or inconsistent. a) b) c) 16) Solve the system of inequalities. If the system has no solution, state no solution. a) b) Level 3 - Simplifying, factoring, & solving complex equations, and solving systems of equations/ inequalities cont. 17) Simplify the following rational expressions. a) y 2 81 2y 18 b) x 2 +2x 3 x +2 x 2 + 2x x 2 1 b) 2x 3 4x 6 d) x x 2 2 1 3x x + 1 x +3 c) x 2 + 6x +9 18) Simplifying logarithmic expressions
a) log 8 0.5 b) log 2 16 c) log 5 1 19) Simplify 2 a) 1 5 b) 2 4i 1 i c) 3 81a 3 3a 8 b 2 b 5 20) Identify properties of functions (exponential and logarithmic functions). a) Domain & Range b) Symmetry c) Asymptotes d) Intercepts e) Maximum/Minimum f) Sketch a graph of the parent function 21) Identify the parent function, sketch the graph and identify the transformation. a) g(x) = 3x 4 + 2 c) h(x) = (x + 3) 3 2 e) s(x) = 1 2 (3x + 1) 2 + 1 b) v(x) = ( 1 3 ) 2 (x 2) 4 d) f(x) = 3(x 2) 1 Level 4 - Application of Skills - Real World Examples, higher level algebraic problems solving (polynomials of degree 3 or higher) and exponential/logarithmic equations. 22) Identify the linear factors of the polynomials provided. Provide all work utilized to determine factors. a) h(x) = 3x 2 11x 4 b) g(x) = 4x 3 + 10x 2 24x c) f(x) = 6x 4 + 7x 3 12x 2 3x + 2 23) Word Problem Application a) Rupert s Rent-a-Car will rent you a car for $55 per day with no mileage charge. Mark s Mobiles for-rent will rent you a car for $34 per day plus 15 cents per mile beyond the first 100 miles. For what number of miles is the total cost of a one-day rental the same for both rental companies?
b) Chad is standing on the roof of his apartment building when he throws a ball straight upward over the edge. The ball is 55 feet above the ground when he lets it go. The quadratic equation that models the path of the ball is p(t) = 16t 2 + 24t + 55. How long does it take for the ball to hit the ground? c) The chart below show the first, second, and third place finishes, and the total points earned by each of three schools competing in a track meet. How many points is a first place finish in an event worth? 24) Based on the graphs provided, determine the possible equation that represents the graphs. a) b) 25) Identify real and imaginary roots of polynomial functions. a) g(x) = x 3 x 2 + 2 b) f(x) = 2x 4 + 5x 3 + 3x 2 + 15x 9 26) Solve: a) log x + 1 2 log 16 = log 64 c) 3 x + 2 = 27 2 e) x 3 + 2x 2 9x 18 = 0 b) ( 1 7 ) x = 7 2x 9 d) x 4 + 25 = 26x 2