Pre-AP Algebra II Summer Packet 014 Name: Period: PLEASE READ THE FOLLOWING!!!!!!! Wait until a few weeks before school starts to work through this packet so that the material will be fresh when you begin Pre-AP Algebra II. The problems should be done without a calculator. All Work/Steps must be shown in an orderly manner and the work must be neat to receive credit. Box all answers. Place answers on the given answer sheets (attached at the end of packet). The packet will be due the second day of class, with a test the following week. You may need to look on the internet for examples to help if you are having difficulty. Please do the work yourself since you will be tested on your own. ******You will have access to a graphing calculator in class next year but it is important that you have access to one for use at home if at all possible. The best time to buy one is before school starts when stores are having back to school sales because that is when you will find the best price. TI-8 Plus graphing calculator or better (TI-84 Plus is faster) I look forward to seeing you when school starts. If you have questions e-mail Nancy McWhorter at nmcwhorter@pasadenaisd.org Order of Operations Simplify each expression showing all work. 1) 7 0 9 9 ) 7 ) 4 (6 ) 4) [( ) ( 6)] Fractions Simplify each expression and write in reduced fraction form, leaving improper fractions where applicable. No decimal answers. Show all work. 5 5 1 5 5) 4 6) 6 6 6 4 4 5 7) 8) 9 6 4 1 8
Simplifying Expressions Simplify each expression. Show all work. 9) 6b(8b ) b(4 + 4b) 10) 4(p + 8) (p 5) 11) (6r + 8) 7r( 8r) 1) 5x(x + 4) + (x x ) Solving Linear Equations Solve each equation. No decimal answers. If solution is a fraction, leave as improper fraction where applicable and remember to reduce. (check your solutions) Show all steps. Box answers. 7 1) 4 = 4(1+8n) 14) p 4 10 15) 75 9g = 5 ( 4 + g) 16) x 6 x 6 8 17) (a + 1) 5 = a 18) 6 (x + 5) = (x 1) 19) 4 (x + 4) +x = + 6(x + ) Solving Inequalities & Compound Inequalities Solve each of the inequalities and graph your solutions on a number line. (check your solutions) 0) 15 x > 6 1) + (n + 5) > 4(n + ) ) 6 < x + 4 < 10 Multiplying Polynomial Expressions - Find each product. Remember to combine like terms. Box answers. ) x (4x 6) 4) (x + 11) (x 11) 5) (5t 4)(t 6)
Multiplying Polynomial Expressions - Find each product & combine like terms. Show all work. Box answers. 6) (x + 7)(4x 6) 7) (x ) 8) (5x y)(5x + y) 9) (x )(x +)(x + 4) Factoring - Factor each expression completely. Remember: factor out GCF first. 0) 9n 1n 1) x 5 ) x + 7x + 1 ) x x 6 4) x + 6x 8 5) x 8 6) r +5r + 7) p 8p + 16 8) x 10x 1 9) x 5x 7 40) 6x 5 y 9xy 41) x 8x + 4 Solve each equation by factoring and using the Zero Product Property. (remember to the set the equation = to 0) Factor and set the factors = to 0 to solve. 4) x 1x = 0 4) n 16 = 0 44) x 4x = 45) x + 9x + 10 = 0 46) x = 9x 8 47) n 6n + 7n = 0
Exponents Simplify each expression. The simplified expression should have NO negative exponents. 48) ( y 0 4 5 4 7 0 5 xy) (x ) 49) y z ( xy z ) x 50) y(4 4 x y ) 7 4x y z 51) 5 10 0x y z x y 5) 8 16x y Radicals simplify each expression. Write your answer in simplified radical form. No decimals. 5) 18 54) 1 55) 7 56) 1 8 57) 1 9x 58) 8 5 4a c Radical Equations - Solve each equation by taking square roots. No decimals. 59) 4x + = 10 60) 5x 8 = 8 Solve each equation using the quadratic formula. Standard form: ax + bx + c = 0 Simplify and reduce final answer (no decimals) Quadratic Formula: x b b 4ac a 61) 4x 5x + 1 = 0 6) 6x x 1 = 0 6) 4x = 1x 9
Graph each linear equation using x- and y-intercepts. (Show how you get the intercepts) There are graphs provided on answer sheets. 64) x + y = 6 65) 6x y = 1 66) y + = (x + ) 67) x = 4y Slope - Find the value of x or y so that the line through the points has the given slope OR find the slope through the given y y1 points. m x x 1 68) (19, 7) and (0, y); slope(m): 6 69) ( 7, 1) and (x, 9); slope(m): 7 70) (8, - 6) and ( -4, ) slope (m) = Graph each linear equation using slope & y-intercept: y = mx + b. There are graphs provided on answer sheets. 71) 4x 5y = 10 7) x + 4y = 1 Linear Equations Write the point-slope and slope-intercept form of the equation of the line given the following information. Show all work. No decimals. All fractions reduced. On answer sheet, write point-slope form first and then write slope-intercept form. 7) through the point (1, ), slope (m) = 5 74) through the points (-, 5) and (6, 1)
Linear Equations Write the slope-intercept form of the equation of the line of the equation of the line given the following information. Show all work. No decimals. All fractions reduced. 75) through the point (1, 4), slope (m) = undefined 76) through the point (, 5), slope(m) = 0 77) through (0, -1) and parallel to a line with a slope of 4 78) through (, 5) and perpendicular to a line with a slope of System of Equations - Solve the following systems by graphing (the point of intersection is the solution) Graphs are provided on the answer sheets. Solution is shown as an ordered pair. 79) y = x 1 80) x + y = 81) x + y = 1 4 x + y = 6 y = x + 5 x y = 4 Solve the following systems using the substitution method. Solution is shown as an ordered pair. 8) x = 8y 11 8) y = x + 4 6x 6y = 4 y = 6x 8 Solve the following system using the elimination method. Solution is shown as an ordered pair. 84) x y = 1 x + 11y = 7
Name: Period: Pre-AP Algebra Summer Packet 014 Answer Sheet 1. 6. 51.. 7. 5.. 8. 5. 4. 9. 54. 5. 0. 55. 6. 1. 56. 7.. 57. 8.. 58. 9. 4. 59. 10. 5. 60. 11. 6. 61. 1. 7. 6. 1. 8. 6. 14. 9. 64 67. (attached graphs) 15. 40.. 68. 16. 41. 69. 17. 4. 70. 18. 4. 71 7. (attached graphs) 19. 44. 7. 0. 45. 74. 1. 46. 75.. 47. 76.. 48. 77. 4. 49. 78. 5. 50. 79 81. (attached graphs)
8. 8. 84. 64. 65. 66. x intercept (, ) x intercept (, ) x intercept (, ) y intercept (, ) y intercept (, ) y intercept (, ) Slope Slope Slope 67. 71. x intercept (, ) Slope-intercept form: y intercept (, )
7. 79. Slope-intercept form: Solution 80. 81. Solution Solution