Summer Review for Students Who Will Take Algebra II in 2016-2017 1 Algebra II Summer Review To earn credit: Be sure to show all work in the area provided. Evaluating and Simplifying Applying Order of Operations: http://www.purplemath.com/modules/orderops2.htm Simplifying Radical Expressions: http://www.virtualnerd.com/algebra-1/radicalexpressions-equations/simplify Simplifying Complex Fractions: http://www.brightstorm.com/math/algebra-2/rationalexpressions-and-functions/simplifying-complex-fractions/ Simplifying Complex Fractional Expressions: http://www.montereyinstitute.org/courses/developmentalmath/course_text2_resou RCE/U15_L1_T4_text_final.html Evaluate each expression. 1. ( 4 3)(1 (3 + 5)) 5 2. 2 3 1 4 6 3. Evaluate ab 3a 2 if a = 2 and b = -5 4. Evaluate x 2 + 4x 3 if x = 2 Simplify each of the following expressions. Leave all answers with positive exponents. 5. 9(x 2 + 1) + 6(x 2 + 1) 6.. 3t 4 v 3 21t 2 v 6
Summer Review for Students Who Will Take Algebra II in 2016-2017 2 7. ( 2 3) 2 8. 3 24 + 7 6 54 9. 3( 5 6) 2 10. 2 ( 3 2 + 8) Solving Equations and Inequalities Solving Equations with Variables on Both Sides: http://hotmath.com/help/gt/genericalg1/section_1_4.html Solving Quadratic Equations by Factoring: http://www.purplemath.com/modules/solvquad.htm Solving Quadratic Equations - Extracting the Root: http://www.purplemath.com/modules/solvquad2.htm Solving Quadratic Equations - Quadratic Formula: http://www.regentsprep.org/regents/math/algtrig/ate3/quadformula.htm Completing the Square: http://www.regentsprep.org/regents/math/algtrig/ate12/completesqlesson.htm Solve each equation. Absolute Value Equations: http://www.regentsprep.org/regents/math/algtrig/ate1/abslesson.htm Absolute Value Inequalities: http://www.regentsprep.org/regents/math/algtrig/ate2/absinequal.htm 11. 7z + 13 = 3z + 5 12. 7 9 b = b 10
13. x 3 =13 Summer Review for Students Who Will Take Algebra II in 2016-2017 3 Solve the inequality and graph the solution on the number line: 14. 2x 3 <17 15. 3x+ 14 > 4x+ 12
Summer Review for Students Who Will Take Algebra II in 2016-2017 4 16. 3 x + 7 >1 17. 3x 1> 5 or 2x + 4 <14 Solve for the indicated variable. 18. P = 2l + 2w (solve for l)
Summer Review for Students Who Will Take Algebra II in 2016-2017 5 Solve using the square root method (extracting the root). 19. 3x 2 11 = 1 Solve using the Zero Product Property. 20. x(2 x)(5x 3) = 0 21. 12x 2 5x = 2 Solve using the Quadratic Formula. 22. x 2 +8x =11
Summer Review for Students Who Will Take Algebra II in 2016-2017 6 Simplifying Polynomial Expressions Operations on Polynomials: https://www.youtube.com/watch?v=trpxmv29rx0 Dividing a Polynomial by a Monomial: http://www.mesacc.edu/~scotz47781/mat120/notes/divide_poly/monomial/divide_monomial.html 23. ( 3 6r 3 r 4 + 7r 2 ) (1 r 4 )+ ( 6r 4 9r 3 7) 24. (x 1)(2x 2 + 4x 1) 25. ( 4 3x) 2 26. 3x5 + 2x 4 8x 3 +12x 2 6x +1 2x 27. (2x +1)(5x)+ 6x6 7x 4 + 9x 3 3x 2 (x 2 5x)(x 3)
Summer Review for Students Who Will Take Algebra II in 2016-2017 7 FACTORING POLYNOMIALS Factoring Using Greatest Common Factor: http://www.regentsprep.org/regents/math/algebra/av6/lfaccom.htm Factoring Differences of Two Squares: http://www.regentsprep.org/regents/math/algebra/av6/lfactps.htm Factoring Perfect Square Trinomials: http://mathbitsnotebook.com/algebra1/factoring/fcperfsqtri.html Factoring Trinomials of the Form x 2 + bx + c : http://www.regentsprep.org/regents/math/algebra/av6/lgrouping.htm Factor by Grouping: http://www.purplemath.com/modules/simpfact3.htm Factoring Trinomials of the Form ax 2 + bx + c, a 1 : http://www.purplemath.com/modules/factquad2.htm Factor each polynomial completely. 28. 3x 3 y +12x 4 y 2 15x 2 y 5 z 3 29. 20x 2 +11x 3 30. 4x 2 25 31. 3x(5x +1) 2(5x +1) 32. 56x 2 24x 28x +12
Summer Review for Students Who Will Take Algebra II in 2016-2017 8 Linear Equations and Inequalities in Two Variables Understanding Slopes of Parallel and Perpendicular Lines: http://www.mathsisfun.com/algebra/line-parallel-perpendicular.html Graphing Equations of Vertical Lines: http://www.virtualnerd.com/algebra-2/linearequations-functions/writing/writing-horizontal-vertical-lines/vertical-line-example Graphing Equations of Horizontal Lines: http://www.virtualnerd.com/algebra-1/linearequation-analysis/horizontal-line-example.php Graphing Linear Equations in 2 Variables: http://www.mathwarehouse.com/algebra/linear_equation/ Writing Linear Equations: http://www.virtualnerd.com/algebra-2/linear-equationsfunctions/writing 33. Is the ordered pair (-1, 3) a solution to the equation 3x + y = 0? 34. Determine the slope of the line given by 2x 3y = 5. 35. Write y 3 = 5(x + 2) in standard form 36. Find the equation of the line that passes through the points (5, 3) and (9, 1). 37. Write the equation of the line in the graph shown.
Summer Review for Students Who Will Take Algebra II in 2016-2017 9 38. Find the equation of the line that passes through the point (-3, 1) and is perpendicular to the graph of 5x + 4y = 12. 39. Solve: 3x + 8y = 20 3x + 6y = 14 40. Use the graph below to determine the solution to the system graphed.
Summer Review for Students Who Will Take Algebra II in 2016-2017 10 Geometry Finding Areas of Polygons: http://www.math.com/school/subject3/lessons/s3u2l4dp.html http://www.math.com/school/subject3/lessons/s3u2l4ex.html Finding Surface Area of Composite Solids: http://www.onlinemathlearning.com/surfacearea-composite-figures.html Finding Volume of Composite Solids: https://www.youtube.com/watch?v=0m6ldrrunf8 Using the Pythagorean Theorem: https://www.youtube.com/watch?v=d_y_owf1wsi Solving Right Triangles Using Trigonometry: http://www.virtualnerd.com/algebra- 2/trigonometric-functions/right-triangle/right-triangle-examples 41. Find the perimeter and area of the figure below. 42. Find the area of the figure below.
Summer Review for Students Who Will Take Algebra II in 2016-2017 11 43. Find the area of the shaded region below. 44. Find the volume and surface area of the following solid. 45. Solve for x, round your answer to the nearest tenth of a unit.
Summer Review for Students Who Will Take Algebra II in 2016-2017 12 46. The figure shows a right-circular cylinder and a right-circular cone. The cylinder and the cone have the same base and the same height. Part A: What is the volume of the cone, in cubic feet? Part B: What is the ratio of the cone s volume to the cylinder s volume? 47. The diagram shows two cylinders with bases that have the same center and heights of 12 millimeters. Write an equation that describes the volume, V, that is inside the larger cylinder but outside the one with the smaller radius r?
Summer Review for Students Who Will Take Algebra II in 2016-2017 13 48. In the right triangle ABC, in which A is the right angle, m B m C. Let sin B = r and cosb = s, What is sinc cosc? 49. Nell s kite has a 350 foot string. When it is completely out, Ian measured the angle to be 47.5. How far would Ian need to walk to be directly under the kite? 50. What number should be added to complete the square? x 2 + 20x + 51. In a basketball game, Marlene made 16 field goals. Each of the field goals were worth either 2 points or 3 points, and Marlene scored a total of 39 points from field goals. Part A: Let x represent the number of two-point field goals and y represent the number of three-point field goals. Write a system of equations in terms of x and y to model the situation. Part B: How many three-point field goals did Marlene make in the game?
Summer Review for Students Who Will Take Algebra II in 2016-2017 14 52. Functions W and Z are both linear functions of x. Which statement comparing the functions is true? Find all true statements. A. The slope of Function W is less than the slope of Function Z B. The slope of Function W is greater than the slope of Function Z. C. The y-intercept of Function W is equal to the y-intercept of Function Z. D. The y-intercept of Function W is less than the y-intercept of Function Z. E. The y-value when x = -4 for Function W is greater than the y-value when x = -4 for Function Z. F. The y-value when x = -4 for Function W is equal to the y-value when x = -4 for Function Z.
Summer Review for Students Who Will Take Algebra II in 2016-2017 15 53. A pool cleaning service drained a full pool. The following table shows the number of hours it drained and the amount of water remaining in the pool at that time. Part A: Plot the points that show the relationship between the number of hours elapsed. and the number of gallons of water left in the pool. Part B: The data suggest a linear relationship between the number of hours the pool had been draining and the number of gallons of water remaining in the pool. Assuming the relationship is linear, what does the rate of change represent in the context of this relationship? Part C: What does the y-intercept represent in the context of this relationship?