1. SUMMER REVIEW for students entering GEOMETRY REMEMBER: Your high school mathematics courses require you to use concepts learned in previous math classes. Use this Summer Review to review skills that you will need to be successful in geometry. Surfs up! Make waves with math!

2. Give two ways to write each algebraic expression in words. NOTE: Answers will vary! 1. x + 32. 2m – 73. 5y 9/22/2015Mrs. McConaughy Geometry 2 Possible phrases for each of the previous expressions : 1. 3 more than a number; a number increased by 3 2. 7 less than twice a number; twice a number decreased by 7 3. 5 times a number

3. Evaluate each expression for x = 8, y = 5, and z = 4. 4.x + y 8 + 5 13 5. x/z 8/4 2 9/22/2015Mrs. McConaughy Geometry 3

4. Evaluate each expression. 6. (-2) 3 -8 4/9 9/22/2015Mrs. McConaughy Geometry 4

5. Find each square root. 8. 9. 9/22/2015Mrs. McConaughy Geometry 5 Time to recall your perfect squares! 8. 9. -6 7

6. Write all classifications that apply to each real number (natural, whole, integer, rational, irrational.) 10. 8/9 11. 12 9/22/2015Mrs. McConaughy Geometry 6 HINT: Use the Venn Diagram.

7. Simplify each expression. 12. -24 + 2 2 – 4 · 3 13. │ 10 - 5 2 │ + 5 - 24 + 4 – 4 · 3 │ 10 - 25 │ + 5 - 24 + 4 – 12 │ - 15 │ + 5 -20 – 12 │ 15 │ + 5 - 32 20 14. 12x + 30x 15. 8y 2 – y 2 42x 7y 2 16. 4n + 11n 2 17. 4 (2x – 5) DONE 8x - 5 18. 2(x + 5) – 3 (x – 2) Time flies when you’re having fun! 9/22/2015Mrs. McConaughy Geometry 7 Recall: Order of Operations, Combining Like Terms, Absolute Value - x + 16

8. Solve each equation. 19. 2x + 6 = 10 20. 2x = 4 x + 3 = 40 x = 2 x = 37 21. 2 (x + 1) = 14 22. 2 (3x + 1) – 8x = 12 x = 6 x = -5 23. 4x + 5 = 7x + 11 24. -7x – (x – 3)= 2 (5x – 3) x = -2 x = ½ 25. Take a break! 9/22/2015Mrs. McConaughy Geometry 8 x = 10

9. Write and solve each proportion. 26.The ratio of band members to non- band members in Seneca Valley Intermediate High School is 2:5. There are 875 students in grades 9 and 10. How many band members are there? 27. Seneca Valley track star I. M. Fleetfeet ran at a rate of 6 mi/h. What is this speed in miles/minute? 9/22/2015Mrs. McConaughy Geometry 9 250 band members; 625 non- band members 1/10 mile/minute or.1 mile/minute

10. Solve each inequality and graph on a number line. 28. 18 + 2x ≤ 50 x ≤ 16 16 29. 7 – 2t ≤ 21 t ≥ - 7 -7 9/22/2015Mrs. McConaughy Geometry 10 Recall: RULE: When multiplying or dividing an inequality by a negative number, always reverse the symbol of inequality.

11. Find the slope of each line. 30.31. 9/22/2015Mrs. McConaughy Geometry 11 m = 0 Slope, m, is undefined

12. Find the slope of the line containing the given points. 32. (1,2) & (7, -2) 33. (- 4,10) & (0,3) Time to cool off with ski bird! 9/22/2015Mrs. McConaughy Geometry 12 m = -2 – 2 7 - 1 = -4/6 = -2/3 m = 10 – 3 -4 - 0 = 7/-4

13. Graph each equation. 34. y = -2 35. x = 4 36. y = - ½ x + 4 37. y = 5x - 3 NOTE: Remember to label your lines! 9/22/2015Mrs. McConaughy Geometry 13

14. Write the equation of the line in slope-intercept form. 38.slope = ½; y-intercept = -5 39. slope = -3; y-intercept = 0 40. through the points (1,-4) and (3,2) 9/22/2015Mrs. McConaughy Geometry 14 y = mx + b; y = 1/2x - 5 y = mx + b; y = -3x Step 1: Find slope, m. Step 2: Use point- slope form of a line. y = 3x - 7

15. 41. Find the x and y intercepts of -2x + 4y = 7. x-intercept: (-7/2, 0) y-intercept: (0, 7/4) 42.Is the point (4, 14) on the line y = -3x + 2? Explain. No, because when substituting x and y values into the equation, y = -3x + 2, your final equation is 14 = -10, which is false, since 14 ≠ -10. 43. Solve the system of equations by graphing. y = x – 3 y = -x + 1 9/22/2015Mrs. McConaughy Geometry 15 HINT: Step 1. Graph each line on the coordinate plane using slope-intercept method. Step 2. Find the coordinates of the point of intersection.

16. Simplify. Recall: Basic Rules for Exponents 44. 2 5 · 2 6 45. (2 5 ) 6 2 11 or 2,048 2 30 46. a 4 · b 2 · a 5 47. (4x 2 y 6 )(-2x 3 y 4 ) 2 a 9 b 2 16x 8 y 14 48. 3 3 or 27 49. 3ab 5 9/22/2015Mrs. McConaughy Geometry 16

17. Evaluate each function for the given input value. 50. For y = 2x + 10, find y when x = 6. 51. For y = ½ t – 3, find y when t = 12. 9/22/2015Mrs. McConaughy Geometry 17 Y = 2(6) + 10 Y = 12+ 10 Y = 22 Y = ½ (12) -3 Y = 6-3 Y = 3

18. Evaluate the exponential function. 52. The function y = 2(3) x models an insect population after x days. What will the population be on the 5 th day? 9/22/2015Mrs. McConaughy Geometry 18 Substitute 5 for x to determine 486 insects.

19. Add or subtract the polynomials. 53. (2x 2 – x) + x 2 + 3x – 1) 3x 2 +2x -1 54. (a 4 – 2a) – (3a 4 – 3a – 1) (a 4 – 2a) – 3a 4 +3a + 1 -2a 4 + a + 1 9/22/2015Mrs. McConaughy Geometry 19 Recall: Combine like terms. Like terms have the same variable and the same exponent. Distribute the negative.

20. Multiply. 55. (5x 2 ) (4x 3 ) 56. 5 (2x 2 + x + 4) 57. (x + 2) (x – 5) 58. (x -5) 2 59. (2x + 7) (2x – 7) 60. (x – 3) (x 2 + 2x + 3) 9/22/2015Mrs. McConaughy Geometry 20 20x 5 x 2 -3x-10 4x 2 - 49 10x 2 + 5x + 20 x 2 - 10x + 25 x 3 + 2x 2 + 3x - 3x 2 - 6x - 9 + x 3 - x 2 - 3x - 9

21. Factor completely. 61. 4x 2 – 3x 62. x 2 + 6x + 8 63. x 2 – 10 x + 16 64. x 2 + 7x -18 65. x 2 + 12x + 36 66. 25x 2 - 81 67. 5x 2 – 14x + 8 68. 4x 2 + 19x - 5 9/22/2015Mrs. McConaughy Geometry 21 x (4x – 3) (x – 8) (x-2) (x + 6) 2 (5x - 4) (x – 2) (x + 4) (x + 2) (x + 9) (x - 2) (5x - 9) (5x + 9) (4x - 1) (x + 5)

22. You’re finished! 9/22/2015Mrs. McConaughy Geometry 22