Cottonwood Classical Preparatory School CCPS Pre-Calculus with Statistics Summer Packet Greetings Pre-Calculus Student: Welcome to another successful year in math class at CCPS. The summer packet is one of the items the math department assigns in order to review students and determine what review needs to be done in order to start our year successfully. I appreciate you taking the time out of your busy summer schedule to work on this packet. I think if you do a bit over a week or so; you should be able to complete without much difficulty. That being said; if you have any problems with the packet or find you are taking longer than predicted; you may want to seek out some outside sources like videos on youtube or a math website or an Algebra 2 textbook. If possible, please try to refrain from asking your parents or guardians for assistance and seek to find the answers yourself. We are trying to make you the best independent problem-solvers we can and seeking out resources are part of that. All of this information will be needed sometime during the upcoming school year. These topics have been taught in previous math classes (not necessarily last year). You are responsible for all of this information and will be tested on it. YOU ARE EXPECTED TO BRING THIS COMPLETED PACKET WITH YOU ON THE FIRST DAY OF SCHOOL. It is expected that YOU will do the work. Your work must be neatly done on graph paper for problems (#1-5 all, a, b, c, and d columns), and loose-leaf notebook paper (1 side only). Be sure to number each problem and show all the steps taken to solve each problem. Please place a square around your answers. A requirement for your homework papers is to keep the problems in column form (2 columns per page). It is difficult to grade a paper if the problems are not in the appropriate format; so please aim for the expedient grading of your work. Keep your work legible and neat. Remember this is the first grade you will receive for Precalculus with Statistics. The packet will be graded for completion as a project grade. A test over review material will be taken within the first two weeks of school. Do your best. Good luck! I look forward to meeting and working with you this school year. Thanks again for your time and patience. Mrs. Spitz NAME
Precalculus Summer Review Material Name On graph paper, carefully draw the graphs of the following; make sure to label the axes and identify all characteristics of the graph (asympototes, y-intercepts, x-intercepts, directrix, focus and center) as applies. a b c d 1 y = x y = 1 3 x 4 y = 2(x + 1) + 3 x = 3 2 y = x 2 y = (x 3)(x + 1) y = x 2 2x 8 y = 1 2 (x 2)2 + 3 3 y = x 3 y = (x 1) 2 (x + 2) y = x y = 2 x 1 + 5 4 y = 2 y = 2 x y = log 2 x x 2 + y 2 = 9 5 (x 2) 2 + (y + 1) 2 = 16 Solve the systems of equations. 6. 8x 4y = 13 7. x 3y = 5 8. 2x y + 3z = 26 5x + 2y = 7 2x + 6y = 10 2y z = 12 7x 5y = 8 Factor the following expressions. 9. m 2 k 2 + 6k 9 10. 4x 3 + 7x 2 + 3x 11. (x + y) 2 1 4 12. (a + b) 2 (a + b) 20 13. x 2 + 2x xy 2y 14. 8a 2 + 24a 18 Simplify. 15. (2x 4 y 7 ( 3x 1 y 4 ) 16. (x+y) 2 (X+Y) 1 17. ( 7m 1 n 3 n 2 m 2 ) 2 18. (5 1 a 2 b 1 )(5 2 a 5 b 2 ) Find all solutions to the following problems. 19. x 4 + 49 = 50x 2 20. t 5 + 80t 21t 3 = 0 21. 9 (x 4) 2 = 0 22. (x + 2) 2 2(x + 2) 35 = 0 23. x 3 4x + 5x 2 20 = 0 24. d 3 64 = 0
25. y 4 13y 2 + 36 = 0 26. 5 x = x 1 3 27. x 2 x = 3 28. x 2 + 2 29. Complete the blank unit circle. Include measurements in degrees and radians. A copy has been provided for you at the end of the packet. Find the missing side. Round to the nearest tenth. 30. 31. = 3 Find the measure of the indicated angle to the nearest degree. 32. 33. Use the quadratic formula to solve for x. 34. 2x 2 4x 1 = 0 35. 2x 2 + 2x + 3 = 0 Solve the following rational equation for x. 36. 2 3x + 2 3 = 8 x+6 Function Notation Given f(x) = x 2 + x, answer the following questions. 37. Find f(0) 38. Find f(x) = 0 39. Find f ( 1 3 ) Find the distance between the two points, then find the midpoint. 40. Find the distance between (3,1) and (-5, 8).
Find the equation of the line that has the given characteristics. Leave your answer in the form indicated. 41. Slope = 3 ; y int: 2 4 3 42. Parallel to 2x + 3y = 4 43. Perpendicular to 4x 7y = 23 (Standard Form) through (-3, 6) through ( 2, 4 ) 3 5 (Slope-Intercept form) (Point-Slope Form) Pythagorean Theorem Use the diagram at the right to answer the following questions. Be sure to simplify (no decimal approximations, please). 44. Find b if a = 4 5, c = 2 45. Find c if a = 2 3, b = 6 46. If a = c, and b = 10, find a. Find the following using rules of special right triangles. 47. The hypotenuse of a 30-60 -90 triangle is 3 inches. Find the measure of the other two sides. 48. What is the length of the hypotenuse of a 45-45 -90 triangle if one leg measures 9 centimeters. Write in simplest form. Give exact answers only, no decimals. 49a. 25x 5 49b. 2x3 3 27 49c. 50 18 50. Find the probability in the experiment of selecting a single card from a standard deck of 52 cards. a) the card is a 2 b) the card is a face card c) the card is red or a face card GOOD LUCK!
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