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Name _____________________________ Aledo High School Pre-AP Geometry Summer Assignment 2016-2017 Pre-AP Geometry is a rigorous critical thinking course. Our expectation is that each student is fully prepared. Therefore, the following Algebra 1 concepts must be mastered prior to beginning Pre-AP Geometry. Solving linear equations Graphing linear equations Finding slope from ordered pairs and/or linear equations. Writing equations of lines in slope-intercept, point-slope and standard forms Solving systems of equations Multiplying binomials Factoring Solving quadratic equations by factoring and with Quadratic Formula Simplifying, multiplying, and adding radicals Solving right triangles using the Pythagorean Theorem Multiplying, dividing, adding and subtracting expressions with exponents, take a power to a power, simplifying expressions with negative exponents Adding, subtracting, multiplying, dividing, and simplifying fractions Solving literal equations Be prepared to turn in this assignment on the first day of school. You are expected to show all of your work in a clear and organized manner. I have included the correct answers on Page 8 of this packet so that you may check your answers as you work through the assignment. Aledo ISD staff will not be available for tutoring during the summer so you may need to look up some vocabulary through Google or other resources. You may also use the hints and examples that have been provided on Pages 9-10 of this packet. A test over these concepts will take place during the first week of school, and you will not be allowed to use a calculator to complete it. Please leave answers in simplified radical form or improper fractions (no decimals). I look forward to meeting you in August! Gena Berry Aledo High School Pre-AP Geometry 1 This assignment should be completed without the use of a calculator. All work must be shown to receive credit. Solve. Use improper fractions where appropriate. (No decimals or mixed numbers). 1. 4(3n + 5) – 2(2 – 4n) = 6 – 2n 2. 3x – 12 – 5x = 5 – 6x – 9 3. 2 1 x 7 3 6 5. 2(4x) – (x – 1) = 2 (1 – x) 4. 2 3 7 2 x x 15 5 15 3 6. 2 5 1 a a4 3 6 2 2 Graph each line: 2 7. y = x – 3 5 8. 3x – 2y = 12 10 y x -10 y 10 10 x -10 10 -10 -10 9. y = 3 10. x = -1 5 y 5 y x -5 5 x -5 -5 5 -5 Find the slope of each line: 11. y = -2x – 4 12. a horizontal line 13. a vertical line 14. y = -x 15. The line passing through A (-2, 3) and B (2,-4) 3 Write the equation of the line described. Show all equations in slope-intercept form. 16. Slope 2, y intercept –4 17. Passing through the points (-1,3) and (5, 7) 18. With undefined slope, passing through (2, 1) 3 19. Slope , passing through the point (5, -2) 5 Solve each system of equations using addition (elimination) or substitution. 20. 2x – 3y = 8 21. 3y – 2x = 4 x + y= 4 1 (3y – 4x) = 1 6 22. 5x – 2y = 3 2x + 7y = 9 23. 2x – 3y = 1 3x + 5y = 11 4 Multiply. 24. (x – 3) (x + 7) 25. ( 2x – 1)(5x + 3) 26. (x + 8) 2 27. (2x – 3) 2 28. (x – 2) (x + 2) 29. (7m – 1)(2m – 3) Factor. 30. a 2 + 9a + 18 31. 2a 2 + a – 15 32. 3y 2 – 14y – 24 33. b 2 – 8b + 16 34. x 2 – 81 35. 16p 2 – 25 Solve by factoring. 36. 3x 2 + 13x – 10 = 0 37. 2a 2 + 5a = -4(a + 1) 38. a2 – 4a = 21 5 Solve using the Quadratic Formula. Give exact answers in simplified radical form. 39. a 2 – 3a – 6 = 0 40. 2a 2 + 5a + 1 = 0 Simplify. 41. 45 42. 3 72 43. 5 32 44. 7 3 3 3 45. 3 6 24 46. 7 8 5 2 Use the Pythagorean Theorem to find the value of the variable. Give exact answers in simplified radical form. 47. 48. y 2 x 2 4 49. In little league baseball, the distance of the paths between each pair of consecutive bases is 60 feet and the paths form right angles. How far does the ball need to travel if it is thrown from home plate directly to second base? 6 Simplify. Use only positive exponents in your answers. 50. a5 a a-2 16x 2 y 51. 2xy 52. (2n)4 (3n)2 54. 40 𝑐 −3 53. (3x2y)2 (-4xy3) 55. ( 2𝑥𝑦 4 𝑥2 3 ) 56. Find the area and perimeter of the rectangle. A = __________________ (2a)2 P = __________________ (3b2)3 Solve each literal equation for the stated variable. 57. Solve P = 2l + 2w for w 59. Solve V r 2h for h 58. Solve A = 1 bh for h 2 9 60. Solve F = C + 32 for C 5 7 ANSWERS: Page 2 5 1. 11 2. 2 43 3. 4 4. –5 1 5. 9 6. – 19 Page 3 7. 11. –2 12. 0 13. Undefined 14. –1 7 15. 4 Page 4 16. y = 2x – 4 2 17. 𝑦 = 3 𝑥 + 1 1 -10 y 1 43. 20 2 20. (4, 0) 2 21. (-1, ) 3 22. (1, 1) 23. (2, 1) 5 5 x y 5 - 48. 14 49. 60 2 ft. 25. 10x 2 + x – 3 26. x 2 + 16x + 64 52. 144n 6 27. 4x 2 – 12x + 9 53. -36x 5 y 5 28. x 2 – 4 54. 29. 14m – 23m + 3 30. (a + 6)(a + 3) 31. (2a – 5)(a + 3) 32. (3y + 4)(y – 6) y - 10. 47. 2 5 2 - 9. 45. 5 6 46. 140 50. a 4 51. 8x 24. x + 4x – 21 1 44. 4 3 Page 7 2 - 5 17 4 3 Page 5 x 40. 42. 18 2 3 x 3 33 2 11 19. 𝑦 = − 5 𝑥 + 1 y 39. 41. 3 5 18. x = 2 -10 8. Page 6 5 x 33. (b – 4) 2 34. (x – 9)(x +9) 35. (4p – 5)(4p + 5) 2 36. x = or x = -5 3 1 37. a = -4 or a = 2 38. a = 7 or a = -3 55. 𝟏 𝒄𝟑 𝟖𝒚𝟏𝟐 𝒙𝟑 56. A = 108a 2 b 6 P = 8a 2 + 54b 6 P 2l 57. w 2 2A 58. h b V 59. h 2 r 5 60. C F 32 9 - 8 NEED HELP? Here are some examples and hints that might point you in the right direction. Solving Linear Equations Multiplying everything by the common denominator & cancelling will get rid of any pesky fractions! Then, you can solve the equation the way you normally would. Slope & Equations of Lines Slope-Intercept Form y = mx +b (m = slope, b = y-intercept) y 2 y1 x 2 x1 Slope Formula m= Horizontal Lines Vertical Lines Slope = 0 (y = #) Slope is Undefined. (x = #) Solving Systems of Linear Equations Elimination (Addition) x+y=7 2x + y = 5 Add the equations: -2x – 2y = -14 2x + y = 5 -y = -9 y=9 Plug the value of x into one of the equations: -2(x + y = 7) 2x + y = 5 Substitution x+y=7 2x + y = 5 Solve one equation for a single variable: x + y = 7 y = -x +7 Plug the expression for y into the other equation and solve for x. x + (9) = 7 x = -2 2x + (-x +7) = 5 2x – x + 7 = 5 x+7=5 x = -2 Solution: (-2, 9) Solution: (-2, 9) (-2) + y = 7 y=9 Factoring Review Multiplying Polynomials Perfect Square (a+b)2 = (a+b)(a+b) = a2 + 2ab + b2 Trinomials (a-b)2 = (a-b)(a-b) = a2 – 2ab + b2 F.O.I.L. 9 Factoring (Special Case) Factoring a Difference a2 – b2 = (a + b)(a – b) of Squares Quadratic Formula For the quadratic equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 𝒙= −𝒃±√𝒃𝟐 −𝟒𝒂𝒄 𝟐𝒂 Simplifying Radical Expressions Examples: Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Properties of Exponents Examples: a. 𝑥 2 ∙ 𝑥 5 = 𝑥 (2+5) = 𝑥 7 b. (2𝑥𝑦)3 = 23 ∙ 𝑥 3 ∙ 𝑦 3 = 𝑥 2+5 = 8𝑥 3 𝑦 3 c. (𝑦 4 )5 = 𝑦 4∙5 = 𝑦 20 d. e. (4) = 43 = 64 𝑧 3 𝑧3 𝑧3 f. 𝑚9 20𝑥 2 𝑦 −4 𝑧 5 4𝑥 4 𝑦𝑧 3 = 𝑚9−6 = 𝑚3 𝑚6 20 = 4 5𝑧 2 𝑥 (2−4) 𝑦 (−4−1) 𝑧 (5−3) = 5𝑥 −2 𝑦 −5 𝑧 2 = 𝑥 2 𝑦 5 10