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Name:Skills Review for Students Entering Algebra IIThe following is a review of math skills that you will be expected to apply in your AlgebraII course next year. Complete this review over the summer. It is due on the first day of classand will be worth three homework credits.The purpose of the packet is to provide an opportunity for you to refresh yourself on somemath skills that you will be using throughout the Algebra II course. Solutions to theproblems are attached and students are expected to check their answers. If you havedifficulty with any topic, it is recommended that you invest some time over the summerreviewing those particular skills, so that you will come to Algebra II prepared for success.One way to review would be look on-line for tutorials and practice problems on that topic.Some suitable sites are listed h.com/http://www.purplemath.com/Calculators should NOT be used on this packet.Show all work where calculations are necessary.
Operations with IntegersEvaluate the expression.1. 12 84. 6 4 9 2. 5 183. 56 7 30 62 42 205.Operations with Rational NumbersEvaluate the expression. Write your answer in simplest form.7.3 4 5 58.2 7 3 1210.4 27 9 1611.18 6 7 149. 12.65 9.599 2 5 1 9 6 312.
Square Root ConceptsEvaluate the expression.13.4915. 2 8114. 36Simplifying Square RootsSimplify the expression. Rationalize the denominator when necessary.16.2819. 3 11 5 1117.8 1220.128 5018.95Evaluating ExpressionsWrite a variable expression for the verbal phrase.21. 76 divided by x22. -8 minus x, times 5
Evaluate the expression for the given value of the variable.23. 6 x when x 724.ywhen y 12111Simplifying ExpressionsSimplify the expression.26. 10 x 5 3x 25. 28 13x 16 27. 6 x 2 5x 12 3x 2 8 x 10 228. 4 y 2 y 3 yProperties of PowersEvaluate the expression.29. 3 323 2 30. 3 131.5654
Simplify the expression. The simplified expression should have no negative exponents.32.4 x136 x 2 33. 3x x 4 234. 4xy Simplifying Expressions with PowersSimplify the product.35.x 2 y 18 x 4 y 2 3 y 3 x3 xy 636.2 x 2 y 3x 4 3 y 3 x 2 8 y 2Evaluate the expression. Write the result in scientific notation. 37. 3 105 2 108 38.3.6 10 51.2 10 110 x y 253
Solving EquationsState the inverse.39. Subtract 1740. Divide by -741. Multiply by 0.5Solve the equation.42. x 15 843.3x 18444. 5x 3 17Solving InequalitiesSolve the inequality.45. x 7 1248.x1 12346. 9 5 x47. 8x 4849. 6 5x 1150. 9 2x 33
Solving Multi-Step Equations and InequalitiesSolve the equation, if possible.51. 16 x 24 7 x 6 52. 4 2 x 1 3 8 x53. 5 2 x 3 15 10 x54. 5x2 125Solve the inequality.55. 3 4 5 x 3x56. 8 2 x 4 x 5 Writing and Solving Proportions57.x 3 4 658.x 6 4 x 41659.2 x 7 33x
Pairs of similar triangles are shown. Find the missing lengths of sides.60.b12543aPlotting PointsPlot the ordered pair in a coordinate plane and tell whether it is in Quadrant I, 2, 3, or 4.62. 1, 6 61. 3,5 yyxxSlope-Intercept Form of a Linear EquationFind the slope and y-intercept of the graph of the equation.63. y 2 x 964. 3x 4 y 2465. y 2x 714
Graph the equation.66. y 2 x 367. y 3x 4yyxxQuick Graphs Using InterceptsFind the x-intercept and the y-intercept of the line. Graph the equation. Label the points where theline crosses the axes.68. y x 569. 6 x 2 y 12yyxx
Common Monomial FactorsFind the greatest common factor and factor it out of the expression.70. 2 x3 20 x2 14 x71. 3x5 y 2 21x 2 y 772. 15x5 10 x4 5x273. 2 x 2 y 3 7 xy 7Factoring x 2 bx cFactor the trinomial.74. x 2 3x 275. x 2 12 x 3676. x 2 2 x 4877. x 2 3x 40
Factoring ax2 bx cFactor the trinomial.78. 2 x 2 x 679. 9 x 2 24 x 1680. 3x2 17 x 5681. 12 x 2 46 x 36Factoring Special CasesFactor the expression.82. 16 x 2 8183. x 2 20 x 10084. 144 x 286. x3 11x 2 28x87. 3x3 15x2 12 xFactor the expression completely.85. x5 9 x3
Skills Review for Students Entering Algebra II—Answer Key1. 42. 233. 84. 305. 26. -------77.518.129. 3.059310.411. 61312.1813. 714. 615. 1816. 2 717. 4 63 5519. 8 1120. 13 27621.x22. 8 x 523. 4224. 1125. 13x 1226. 13x 527. 9 x 2 3x 2228. 8y y 229. 35 243330.231. 52 2518.2 15x3133.9x1034. x 6 .50.51.52.53.54.55.56.57.58.59.60.6x 2y6y646 10133 106Add 17Multiply by 7Divide by 0.5x 7x 24x 4x 5x 14x 6x 4x 1x 18x 2No real solutionx is any real numberx 5x 1x 1x 2x 3x 7a 9b 1561. Quadrant 25(-3,5)62. Quadrant 4-5(1, -6)63.slope: -2y-int: 0,9 364.4y-int: 0, 6 slope: 1765. 1 y-int: 0, 2 slope:66.5y 2x 3
67.573.y -3x 4GCF: xy 3 xy 3 2 x 7 y 4 74. x 2 x 1 75. x 6 x 6 76. x 8 x 6 -568.x int : 5, 0 y int : 0, 5 77. x 8 x 5 78. 2 x 3 x 2 79. 3x 4 3x 4 80. 3x 7 x 8 81. 2 2 x 9 3x 2 82. 4 x 9 4 x 9 83. x 10 -5y x-569.y int : 0, 6 87. 3x x 4 x 1 GCF: 2 x72.385. x x 3 x 3 86. x x 4 x 7 -571.84. 12 x 12 x x int : 2, 0 6x 2y -1270.2 2 x x 2 10 x 7 GCF: 3x 2 y 23x 2 y 2 x3 7 y 5 GCF: 5 x 25 x 2 3x3 2 x 2 1
Skills Review for Students Entering Algebra II The following is a review of math skills that you will be expected to apply in your Algebra . math skills that you will be using throughout the Algebra II course. . Skills Review for Students Entering Algebra II—Answer Key 1. 4 2. 23 3. 8 4. 30 5. 2 6. ----- 7. 7 5 8. 1 12 9. 3.059 10. 3 4 11 .
