UNION CITY HIGH SCHOOL Summer assignment for Pre-­‐Calculus This packet will help you review the Algebra skills that you will need in order to be successful in Pre-­‐Calculus. It is due on the first day of class. No excuses! 10% off each day that it is late. It will count as a test grade. Please complete the following problems showing all the work. In order to receive credit, you must show all your work. Your work must be neat and organized. You will be tested on these skills when you get back to school in the fall to make sure you know them. Do not have anyone else do this assignment for you. It is suppose to be your work. If you need help, please check out some websites such as www.khanacademy.org, www.algebra.com, www.math.com, www.purplemath.com, or feel free to email your teacher at their union city email address in the summer. The assignment will also be on the school’s website in case you lose it. Have a great summer and see you in the fall. 1. Solve 5x −12 = −3x + 36 2. Solve 3(x + 6) − 8 = 5x + 2(x − 3) 3. Solve 29 = 7 − (5x − 2) x x
4. Solve 7 − = 8 6
x+5 x−2
5. Solve =
4
3
x +1 x + 2
6. Solve
+
= 5 3
7
7. Solve 1− 4x = 5 8. Solve and graph −2x − 7 > 13 9. Solve and graph 2x − 5(x − 4) ≤ 4(x − 3) +11 10. Solve and graph 4 ≤ −3x +1 < 19 11. Simplify 2x(x-­‐3) 12. Simplify 4x 2 y(x + 6) 13. Simplify (5x+4)(x-­‐6) 14. Simplify (4x+1)(8x-­‐7) −2
" x 2 y −8 z 2 %
15. Simplify $ 2 −6 ' # xy z &
16. Simplify x 4 (−2x)3 (6x 0 )−2 17. Find the x and y intercepts of 3x-­‐6y=18 and then graph the line 18. Find the equation of a line with m=0 and goes through point (-­‐5,6) 19. Find the equation of a line with m=3/4 and goes through point (-­‐8,-­‐16) 20. Find the equation of a line that goes through points (4,-­‐4) and (-­‐6,21) 21. Find the equation of a line with x intercept 3 and y intercept -­‐8 22. Find the slope and y intercept of 5x+8y=-­‐32 and then graph the line 23. Find the equation of a line perpendicular to y=4x and through point (-­‐8,9) 24. Find the equation of a line parallel to y=-­‐2x+7 and through point (-­‐7,6) 25. Graph y>3x-­‐5 26. Determine whether the relation represents a function, then find the domain and range: (4,-­‐5), (-­‐2,7), (1,-­‐3), (5,3) and (-­‐2,-­‐8) x 3 − 337
27. Find f(7) for f (x) =
2x −11
x
28. Find the domain of x−2
2
29. Find the domain of 2
x −9
30. Find f(-­‐3) for f (x) = x 3 + 2x −15 31. Find the zero of the linear function f (x) = 5x +14 32. Find the zero of the linear function f (x) = 3x −11 33. Simplify 90 34. Simplify 175 35. Simplify 2 16 36. Simplify 6 500 20
37. Simplify 27
38. Simplify (2 + 3)(1− 4 ) 39. Factor x 2 + 9x + 20 40. Factor 4x 2 −15x +11 41. Factor x 2 −16 42. Factor 6x 2 + 21x +18 43. Factor 2x 3 −18x 44. Factor 30x 4 + 25x 2 − 5x 45. Solve x 2 = 289 46. Solve 2x 2 + 3 = 3 47. Solve by factoring x 2 + 7x = −10 48. Solve by factoring 3x 2 −11x − 20 = 0 49. Solve (4x + 2)2 = 196 50. Solve by quadratic formula x 2 − 4x − 5 = 0 51. Solve by quadratic formula 3x 2 − x − 2 = 0 52. Solve by completing the square x 2 − 6x − 391 = 0 x 2 + 6x + 8 x 2 − 5x + 4
53. Simplify 2
•
x − 4x + 3 5x +10
x 2 + 8x x 2 − 64
54. Simplify ÷
9x
3x 2
4
2x
55. Simplify 2
+
x + 5x + 6 x + 2
3
2
56. Simplify −
x −1 x − 2
3
3
−
57. Simplify x + 4 4 x
1 5
−
2
4 58. Simplify 3
8
59. Graph y = 2x 2 − 8x + 6 60. Graph y = 3(x −1)2 + 8