COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Summer Review of Algebra Designed for the Student Entering Accelerated/Honors Analysis Please print this packet in its entirety to be completed for evaluation on the second day of school All problems in this packet reflect concepts that you have learned in Algebra 1 and Algebra Complete each problem in the space provided on this packet Show all steps/work clearly. CIRCLE final answers. Refer to the Note Guideline on the Math website to help you with each concept Name Period Revised 014
Solving Equations in One Variable Refer to page 1 of the Note Guideline Solve. y y 1 1.. 1 6 1 Solving Inequalities in One Variable Refer to pages 1- of the Note Guideline Solve and Graph on a number line.. 11 + 4 4. -( + ) < 4-7 Solving Combined Inequalities Refer to page of the Note Guideline Solve and Graph on a number line. 5. + 7 1 or 5 4 < 6 6. 7 < 5 < + 11 1
Solving Absolute Value Equations and Inequalities Refer to page 4 of the Note Guideline Solve. 7. + = 4 Solve and Graph on a number line. 8. 1 9. 4 - + 1 < The Slope of a Line Refer to page 5 of the Note Guideline Given two points, find the slope. 1 10., 4 and, 11., and, 7
Graphs of Linear Equations in Two Variables Refer to page 5 of the Note Guideline Graph the following. 1. 5y 15 Graphs of Linear Inequalities in Two Variables Refer to page 8 of the Note Guideline Graph the following. 1. y 5 14. y
Finding the Equation of a Line Refer to page 6 of the Note Guideline Write the equation of the line in standard form that has the given conditions. 4, 15. Contains the point and has slope = 1 16. Contains the points (, -) and (, -) 17. Perpendicular to the line 4 y 18. Has -intercept - and y- intercept -1 8, and passes through the point Algebraic Solving of Systems of Linear Equations in Two Variables Solve the system of equations algebraically. Refer to page 7 of the Note Guideline 19. 8 y 0. y 5 0 6 4 y 5 6 y 9 5 4
Graphs of Systems of Linear Inequalities in Two Variables Graph the systems. Refer to page 9 of the Note Guideline 1. y 4 y 8. y 6 y 4 Relations and Functions Refer to page 7 of the Note Guideline. Given ( ) 1 1, 0, 1, find the range of f. Is the relation a function? How do you know? f with a domain D = Give the domain of each. 4. f ( ) 5. f ( ) 5
Addition and Scalar Multiplication of Matrices (HONORS ONLY) Refer to page 10 of the Note Guideline Use the following matrices to perform the given operations: 5 7 5 8 4 6 1 0 A B 6 1 E 1 8 F 1 5 1 4 0 6. A+B 7. F E 8. B + F 9. -E Laws of Eponents Refer to page 11 of the Note Guideline 4a 0. b b a 1.a a + 7 a. (y h k ) h (y h + k ) k. 0 y - r 4. p qr pq 5. a b a b 4 4 y 6. 5 6 y 6
Factoring Refer to pages 1-1 of the Note Guideline Factor. GCF 7. 14 5 y z + 10 y yz Difference of two Squares 8. c 4d 9. 6a 49b Sum/Difference of two Cubes 40. 16 Perfect Square Trinomials 41. 4k + 0k + 5 4. 5j 80j + 64 General Trinomials 4. 5 + 1 + 6 44. 10y + 4y Factor by Grouping: 45. + 5 9 45 7
Factor Completely 46. 100a 6b 47. 8u + 1 48. 16 + 40y + 5y 49. 8nm 10n +1m 15 50. 6 7 51. 4 + 1 5. 16 64 5. 16 4 y 1 Solve/Find the Roots by Factoring Refer to page 14 of the Note Guideline Solve by factoring. Indicate multiple solutions. Find the roots by factoring. 54. 4 + 4 = 0 55. t (t + 1) = 4 (t + 1) 8
Find the Zeros by Factoring Refer to page 15 of the Note Guideline Find the zeros by factoring. 56. f() = Simplifying Rational Algebraic Epressions/Determining Domain Refer to page 16 of the Note Guideline 57. 0 15 58. State the zeros and domain of f 5 Products and Quotients of Rational Epressions Refer to page 17 of the Note Guideline 59. y 6 1 y 9 60. y y y y 61. 5 6 18 9
Simplifying Comple Fractions Refer to page 18 of the Note Guideline 6. 1 4 1 4 Adding or Subtracting Rational Epressions Refer to page 17 of the Note Guideline 6. 4 1 4 4 1 64. 4 4 10
11 Solving Fractional Equations Refer to pages 18-19 of the Note Guideline Solve. 65. 1 6 66. 5 4 10 7 Solving Fractional Inequalities Refer to page 19 of the Note Guideline Solve. 67. 1 6 1 8
Roots of Real Numbers Refer to page 0 of the Note Guideline 68. 16 5 69. 9 70. 6 64 71. 81 4 16 7. 15 15a Find the real roots of each equation. 7. 5y + 16 = 17 74. 5 = 9 + 16 Properties of Radicals Refer to page 1 of the Note Guideline 175 75. 0 14 76. 50 Sums/Differences of Radicals Refer to page of the Note Guideline 77. 18 4 54 78. 5 15 79. 40 10 5 1
Binomials Containing Radicals Refer to pages of the Note Guideline 80. 6 6 4 81. 5 7 8. 5 1 5 The Imaginary Number I Refer to pages of the Note Guideline 8. 75 84. 6 85. i 5 86. 18 i 6 87. i 98 98 Solve. 88. + 144 = 0 89. u + 40 = 4 1
Comple Numbers Refer to page 4 of the Note Guideline 90. i 4 i 91. 6 7i 9. 8 i 6 i The Quadratic Formula Refer to pages 4-6 of the Note Guideline Solve using the Quadratic Formula. 9. 8 = 1 The Discriminant Refer to pages 7-8 of the Note Guideline Give the nature of the roots without solving. 94. m 8m 5 = 0 95. -0 = t + 8t 14
Graphing Quadratic Functions Refer to page 9 of the Note Guideline 96. Graph the quadratic function by calculating the verte and making a table of values. Then, answer the questions below. f() = + 8 Is the verte a ma or a min? Give the domain of the function. Give the range of the function. Dividing Polynomials (Long Division) Refer to pages 0- of the Note Guideline Find the quotient using Long Division. 97. 1 6 98. 9 1 4 15
Synthetic Division Refer to pages - of the Note Guideline Find the quotient using Synthetic Division. 99. 5 + 100. 4 +5 7 +5 Rational Eponents Refer to pages 4-5 of the Note Guideline 101. 15 10. 0 10. 4. 81 104. Write in Eponential Form. 4 16 a b 6 16
Solve. 105. 1 y 10 106. n 1 1 4 Composition of Functions Refer to pages 5-6 of the Note Guideline Given: f() = + 6 and g() =, find: 107. g(f(1)) 108. f(g( )) 109. g(f()) Inverses of Functions Refer to pages 6-7 of the Note Guideline 110. Find the inverse. 111. Verify that the functions are inverses by composition 6 f() = 5 + 1 f() = and f -1 () = 6 17