FARMINGTON HIGH SCHOOL HONORS ALGEBRA 2 SUMMER REVIEW PACKET Welcome to Honors Algebra 2! In this Honors course, we will cover many new topics that are vital for success in Pre-Calculus, the next course in our Math sequence. To do this, we will need to spend very little class time for review of Pre-Algebra and Algebra 1 concepts. The problems in this packet are designed to help you review topics from previous mathematics courses that are important for your success in this Honors Algebra 2 course. I look forward to working with you this Fall! This course will be challenging, both in material covered and in its pacing. You need to be at your best, academically, in terms of your knowledge of mathematics to make this a great year of learning and academic success!!! DIRECTIONS: Complete all problems in this packet, showing appropriate work on the page, or on additional sheets of lined paper. The packet will be collected during the first week of school (actual date announced on the first day of school). There will also be a quiz on topics covered in this packet at the end of the first week of school (Thursday or Friday). Since the purpose is to refresh your memory of these mathematical concepts, it would be best to begin work on this packet at the earliest mid-July. It will give you about six weeks to do the 100 assigned problems. Use the code below to join the Google Classroom class where you will be able to ask questions and I will be able to provide class information over the Summer! Helpful website: http://www.khanacademy.org/ Have a wonderful summer! Mr. Evasic Email: Thomas.Evasic@fpsk12.net Google Classroom Code for future Honors Algebra 2 students: ciawtnb Honors Algebra 2: Summer Packet NAME:________________________________ Show any necessary work. Use separate pieces of lined paper, if necessary. PART 1 Solve the equation. Check your solution. 1. 2. Solve the equation. 3. 4. Describe the values of c for which the equation has no solution. 5. 6. Write the sentence as an inequality. 7. The quotient of n and 3 is less than 5. 8. 10 more than y is greater than or equal to 17. Solve the inequality. Graph the solution. 9. 10. Write and graph a compound inequality that represents the numbers that are not solutions of the inequality represented by the graph shown. 11. 12. Write an equation in slope-intercept form of the line with the given characteristics. 13. through: 14. through: 15. through: 16. through: Determine whether each relation is a function. If the relation is a function, determine whether the function is linear or nonlinear. 17. 18. Graph the equation and identify the intercept(s). If the equation is linear, find the slope of the line. 19. 20. Graph f and g. Describe the transformations from the graph of f to the graph of g. 21. 22. Graph the function. Describe the domain and range. 23. 24. Solve the system of linear equations using any method. 25. 26. Graph the system of linear inequalities. 27. 28. Evaluate the expression. Round to the nearest hundredth, if necessary. 29. 30. 31. Simplify the expression. Write your answer using only positive exponents. 32. 33. 34. Solve the equation. Check your solution. 35. 36. Find the sum or difference. Then identify the degree of the sum or difference and classify the polynomial by the number of terms. 37. 38. Find the product. 39. 40. 41. Factor the polynomial completely. 42. 43. 44. Solve the equation. 45. 46. Solve the equation using any method. 47. 48. 49. Graph the function. Compare the graph to the graph of 50. 51. Find the inverse of the function. 52. 53. Write an equation of the line that passes through the given point and is (a) parallel to and (b) perpendicular to the given line. 54. 55. Solve the equation. Check your solutions. 56. 57. 58. Find the mean, median, mode, and range of the data set. Round to the nearest tenth, if necessary. 59. 60. 20.1, 30.5, 22.3, 19.7, 17.5, 32.1 PART 2 In Exercises 1–5, solve the equation for x. 1. 2. 3. 4. 5. 6. The shape of a dome can be modeled by the equation where h is the height (in feet) of the dome from the floor d feet from its center. How far from the center of the dome is the height 50 feet? 7. Simplify using the order of operations: 8. A cab charges $0.10 per mile and a flat fee of $3.00. Write an equation to model the price y of an x-mile-long cab ride. 9. Use the discriminant to determine the number of solutions to the quadratic equation In Exercises 10–12, graph the equation, inequality, or system of inequalities. 10. 13. 11. If compute 12. 14. On a certain day there was a near constant snowfall rate of 0.50 inch per hour. After 4 hours there were 10 inches of snow on the ground (including some from the day before). Write an equation that models the amount of snowfall in inches y after x hours. You are traveling away from home at a constant speed. After 3 hours you are 60 miles from home and after 7 hours you are 160 miles from home. Write an equation that models y, your distance (in miles) from home after x hours. 15. Write an equation of the line that passes through the given point and is (a) parallel to and (b) perpendicular to the given line. 16. 17. In Exercises 18–20, solve the system using any method. 18. 21. 19. Simplify 20. 22. Simplify Solve the equation. 23. 24. Find the value of each variable. Round your answers to the nearest tenth. 25. 26. 27. Graph the equation Solve the equation. 28. 29. 30. Simplify 32. Solve 31. Simplify for x and y. The length of the base of a certain rectangle is modeled by the equation where b is the length of the base and A is the area of the rectangle. If the base of the rectangle is 8 inches, what is the area of the rectangle? 33. 34. Given a. 35. determine the following. (Simplify your answers, if possible.) b. Solve c. 36. Solve A rectangular yard has a length that is 7 feet longer than its width. If the perimeter of the yard is 46 feet, what is the area of the yard? 37. 38. Graph 40. Consider the inequality 39. . a. Solve for x. b. Graph the solution on the number line. Write an equation of the line.