June 6, 016 Dear Honors GSE Geometry Student: Congratulations for being placed in the Honors GSE Geometry class for the 016-017 school year! This is a fast-paced and rigorous college-preparatory math course that includes substantial work with the skills and concepts presented in each lesson. The course emphasizes more complex applications and challenging exercises than students might be exposed to in the traditional high school Geometry courses. You will be required to think, to apply what you know in new and different situations, and to use problem-solving skills. The course is one in which the concepts from the beginning lessons build upon one another and are essential to the mastery of the material that will be encountered later in the semester. In order to be successful, you must have strong foundational math skills and be consistent with your homework and study habits. It is our hope that you will not only learn the major concepts of this course but that you will also become more independent in your learning and study habits, skills that you will need to be successful in future honors-level and AP courses. It is your responsibility to be the best student you can be! Because of the pace of our curriculum, we will not be able to spend time in class reviewing skills that were presented in the pre-requisite courses. This packet represents a brief review of some of those topics that will be an important foundation for this course. Work all of the problems neatly on separate paper, numbering your work. You must show all work for each problem, not just an answer. Your final answer for each problem should be recorded on the answer sheet. The completed packet is due to your teacher on the first day of class, Monday, August 1, 016. These review problems represent your first graded assignment for this course and will help to verify that your course placement is correct. Your work will be graded for both completeness and accuracy. If you will also be taking GSE Honors Algebra II during the Spring 017 semester, you will complete a review packet over winter break for that class. You are not required to complete the packet for GSE Honors Algebra II because the topics covered in that packet represent concepts that you will be learning during the first semester in Honors GSE Geometry. Please feel free to e-mail me at raymond.furstein@cobbk1.org over the summer if you have any questions. Sincerely, Ray Furstein and Amanda Morton Teachers - GSE Honors Geometry
GSE Honors Geometry Pre-Requisite Skills Review * For all solutions involving inequalities, answers should be represented with a number line representing the set of all possible values, along with the interval notation representation of that set of values. Interval notation might not have been stressed in previous math courses, so please refer to the following Khan Academy video for help: https://www.khanacademy.org/math/algebra/algebra-functions/domain-and-range/v/introduction-to-interval-notation Part 1: Relationships Between Quantities mv 1. The tension caused by a wave moving along a string is found using the formula T. If m is the mass of the L string in grams, L is the length of the string in centimeters, and v is the velocity of the wave in centimeters per second, what is the unit of the tension of the string, T?. Isolate the variable v in the formula given in #1 above.. Write the possible range of values for the following expression: 4 14.1%? 4. Given that the width (w) of a rectangle is six units less than its length (l), write the expression for the area of a rectangle in terms of its length. 5. Maggie ran at a rate of 1 km/h. Convert her speed to meters per minute. 6. The ratio of students to faculty members in a high school is :5. If there are 80 faculty members, how many students are there? 7. The area of a rectangle was 15 cm. Every dimension was multiplied by a scale factor and the new area was.75 cm. What was the scale factor? 8. A tree casts a shadow 8.5 ft long at the same time that a nearby -foot-tall pole casts a shadow.75 feet long. Write and solve a proportion to find the height of the tree. 9. Solve the following proportion: 1 x 6 1x =============================================================================================== Part : Reasoning with Equations and Inequalities 10. Will owns a business that produces widgets. He must earn more in revenue than he pays in costs in order to turn a profit. It costs $10 in labor and materials to make each widgets, and his monthly rent for his factory is $4000. He sells each widget for $5. How many widgets does Will need to sell each month to make a minimum profit? 11. Solve for y in the following equation: 6 x 4 y 5 1. Solve: x 4 1 1 and sketch the solution on a number line. 1. Solve the following system using any method: 8y 6x 48 y x 1 14. A shop sells one-pound bags of peanuts for $ each and three-pound bags for $5 each. Nine bags are purchased for a total cost of $6. Use a system of equations to determine how many three-pound bags were purchased.
15. Which graph below would represent a system of linear equations that has multiple solutions? In your work, justify your answer by not only explaining why your choice works, but also why each of the others do not. A. B. C. D. 16. Write the pair of inequalities shown in the graph: 17. Will and his sister are saving to buy MP players. Will has $50 and plans to save $10 per week. His sister has $80 and plans to save $7 per week. How many weeks will it take for Will to have more money saved than his sister? 18. The average of Maggie s three test scores must be at least a 70 in order for her to pass the class. She got a 76 on the last test. She received the same score on her first and second tests. If Maggie did end up passing the class, then what was the lowest possible score that she could have gotten on the first two tests? =============================================================================================== Part : Linear and Exponential Functions 19. State the explicit formula for the general term of the following sequence: 0. Determine the function that represents the data given in the following table: n 1 4 5 a n 6 18 54 16 486 For the sequences represented in #s 1-4: a) Determine if it is arithmetic, geometric, or neither b) Find the common difference or common ratio (whichever is appropriate) c) Write an explicit formula d) Write a recursive formula e) Find a n 1. 6, 1, 4, 48,... n 7. 9, 0, 1, 4,... n 18. 7, 48,,... n 18 4., 5, 18, 11,... n 19 1 9,, 1,,...
5. A certain population of bacteria has a growth rate of 0.0 bacteria/hour. The formula for the growth of the A P o.7188 where P o is the original population and t is the time in hours. If you begin with 00 bacteria, approximately how many of the bacteria can you expect after 100 hours? bacteria s population is 0.0 t 6. The graph of a function passes through the points (4, ) and (6, 8). What are the coordinates of these points after the function has been stretched horizontally by a factor of? 7. Write the function modeled by this table: 8. Describe the transformation from the parent graph f x x x represented by f x 1. 9. What is the average rate of change over the interval [1, ] for each equation? What type of model is represented by each set of data? Equation A: 1,5,,5,,15, 4,65 Equation B: f x 5x 1 Find the average rate of change of each function on the given interval: 0. f x x 6, for x 16 8 1. f x x 6x 14, for 4 x 6, for 4 x 57. f x x 8 11 x. f x 4 7, for x 8 =============================================================================================== Part 4: Linear Equations For #s 4-47, solve each linear equation/inequality 4. 4x 7 1 5. x 7x 0 6. 6 x 7. x 6 4 8. 6x x 5 9. x 5 4 40. 1 x 9 4 4 x 5 41. 15 6 9x 9 x 4. 4. 0.45 0.8 1.0 0.48 8 x 44. 8x 5 x 5 5x 1
45. 5 x 1 x 6 9 x 1 x x 1 4 46. 47. x x x x 5 5 6 48. If 7x 4x 1x x 4, then what is the value of 18x? =============================================================================================== Part 5: Quadratic Equations Solve by factoring: 49. x 8x 195 0 50. x 6x 5 51. x 19 0 5. 14x 7x 1 0 5. x x 14 Solve algebraically (by finding the square roots): 54. x 98 0 55. 64x 11 0 56. x 1 1 5 6 6 Find the discriminant, then tell the type and number of solutions 57. x 14x 1 0 58. x x 10 0 59. 4x 0x 5 0 Solve using the quadratic formula: 60. x x 0 61. 4x 10x 1 x x Solve by completing the square: 6. x 4x 6. 5x 6x 8 64. x 5x 7 Write each quadratic equation in standard form: y x x 4 65. 66. y x 5 11 67. y x 8 7 0 Write the quadratic equation in vertex form. Identify the vertex and the axis of symmetry. 68. y x 6x 14 69. 70. y x x 7 y x x 5 10
NAME GSE Honors Geometry Summer Packet Answer Sheet 1... 4. 5. 6. 7. 8. 9. 10. 11. 1. 1. 14. 15. A) 16. B) C) D) 17. 18. 19. 0. 1. a) b) c) d) e). a) b) c) d) e)
. a) b) c) d) e) 4. a) b) c) d) e) 5. 6. 7. 8. 9. Equation A: 0. Equation B: 1... 4. 5. 6. 7. 8. 9. 40. 41. 4. 4. 44. 45. 46. 47. 48.
49. 50. 51. 5. 5. 54. 55. 56. 57. Discriminant: Number of Solutions: Type of Solutions: 59. Discriminant: 58. Discriminant: Number of Solutions: Type of Solutions: 60. Number of Solutions: Type of Solutions: 61. 6. 6. 64. 65. 66. 67. 68. Vertex Form: Vertex: Axis of Symmetry: 69. Vertex Form: Vertex: Axis of Symmetry: 70. Vertex Form: Vertex: Axis of Symmetry: