OHS Algebra 2 Summer Packet Good Luck to: Date Started: (please print student name here) Geometry Teacher s Name: Complete each of the following exercises in this formative assessment. To receive full credit for this assignment, you must show all your work in this packet and complete ALL of the problems in the packet. You may use a calculator to assist you, but this cannot serve as a replacement for showing work. This assignment is due on the first day of school (at the start of your class). This packet consists of Common Core State Standards review material, from previous grades. Reference sheets are included in this packet to help you complete your work. Failure to complete this packet may put you at a disadvantage. For assistance in completing individual problems, you should refer to your notes from previous classes, online resources, or work with your peers and family members. If you find you are having trouble with an item, skip it, and come back to it later, but persevere in trying to solve the problem. There will be time, with your teacher in class, devoted to answering any questions regarding this summer packet. You will be assessed on this material in class, so make sure you understand how to do all of these items in this packet. You will need a TI-84 graphing calculator for Algebra class. If you have any questions regarding this assignment, please contact Mrs. Cathy Hall, Mathematics teacher at hallc@oxfordpublicschools.org or Ms. Alicia Salvatore, Mathematics teacher at salvatorea@oxfordpublicschools.org
Algebra 2 Summer Packet Show all work, including formulas used and all steps to the solution. Evaluate each expression if a = 8.2, b = 3, c = 4, and d = 1 2. 1. ab b 2. c 2 1 b d 3. (b c) 2 + 4a Properties of Real Numbers Simplify each expression. 4. 40s + 18t 5t + 11s 5. 3 p 1 r 3 r 1 p 4 5 5 2 6. 9(7e 4f) 0.6(e + 5f) Solving Linear Equations Solve each equation. Check your solution. 7. 17 = 9 a 8. 2 3 m = 1 2 9. 8 = 2(z + 7.5) 10. 2x+5 3 = 10 x 5 11. 5x + 32 = 7x 14 12. 4(2k 3) = 36 13. 2(x 1) + 4 = 20 14. 3x 7 = 15 14x
15. Tom has a collection of 30 hats and Anita has a collection of 18 hats. Tom is adding 1 hat per month to his collection while Anita is adding 5 hats per month to her collection. Find the number of months after which they will have the same number of hats. Solve each equation or formula for the specified variable. 16. 2xy = x + 7, solve for x 17. S = 2πrh + 2πr 2, solve for h 18. V = 4 3 πr3, solve for r Simplify expressions using properties of exponents. Simplify the expression. 19. 4 2 4 3 20. 3 2 3 2 21. (k 2 ) 4 22. ( 2 3 )4 23. (3ab) 4 24. ( 3x 4 ) 5 25. x2 y 8 x 4 y 5 26. 10m 2 n 5m 5 n 6 27. (w 2 j 4 ) 3 ( j 7 j 3 )
Linear Equations and Functions Graph the equation of the line. 28. y = 5x 29. y = 1 x 1 2 30. 2x + 5y = 10 31. y + 4 = 3(x + 2) 32. y = 2 33. x = 4 Write the equation of the line given the following conditions. 34. Write the equation of the line in slope intercept form if m = 3, b = 5 35. Write the equation of the line in point slope form if m = 9; P( 1,4) 36. Write the equation of the line that passes through (5,2) and ( 1,4). Use the point slope form.
Linear Regression Calculator Steps: Y = Clear any equations Highlight Plot1 (arrow up, click enter) Click STAT 1: Edit (To CLEAR any data from L 1, arrow up so L 1 is highlighted, press CLEAR and arrow down) Enter the x data into L 1 Enter the y data into L 2 TO VIEW SCATTER PLOT: Click ZOOM 9: ZoomStat TO FIND EQUATION IN SLOPE-INTERCEPT FORM (y = ax + b) STAT CALC 4: LinReg ENTER
Find the best-fitting line. 37. The table below shows the number of hours you studied before your eight math tests and your percent score on each test. Find the line of best fit for the relationship between number of hours you studied and your percent score. Number of Hours 8 5 12 10 2 9 11 14 Score (%) 75 62 80 85 35 70 82 95 a.) Approximate the line of best fit. b) Using linear regression, find the line of best fit. Round values to two decimal places. 38. Find the linear regression of the data. Let x = years since 1980 and y = population (in thousands). Polynomials Monomial: one term expression Binomial: two term expression Trinomial: three term expression Polynomial: is a monomial or the sum of monomials Examples: 3x 3 + 4x 2 2x + 5, 8x, x 2 + 4x + 2 Standard form of a Polynomial: the terms are written in descending order of exponents from left to right When you multiply two binomials, use the FOIL method or Box method.
Write the simplified expression in standard form (exponents decreasing from left to right). 39. Add (x 3 7x 2 + 3) + (x 3 x 2 1) 40. Subtract (x 2 5) (2x 2 + x 3 6) 41. Multiply (3x 2)(x + 5) 42. An area rug has a length of x + 3 and a width of x + 4. Find the area of the area rug. A = lw 43. Multiply (2x 1)(2x + 1) 44. Multiply (x 5) 2 45. A rectangular room has a length of x + 5 46. Multiply 3x(x 7)(x + 1) and a width of 3x + 4. Find the perimeter of the room.
Factoring quadratic expressions Factoring is an essential tool in Algebra 2. You should master all of the following techniques. Greatest Common Factor: Example: 5x 2 + 10x = 5x(x + 2) Difference of Two Squares: Example: 9x 2 16 = (3x + 4)(3x 4) General Trinomial ( easy and split the middle term ): Example : x 2 5x + 6 = (x 3)(x 2) and 2x 2 5x 3 2x 2 + 1x 6x 3 (2x 2 + 1x) + ( 6x 3) x(2x + 1) + 3(2x + 1) (2x + 1)(x 3) Perfect Square Trinomials: Example : x 2 + 16x + 64 = (x + 8) 2 Factor the expressions. 47. x 2 + 6x + 8 48. x 2 10x + 24 49. x 2 + 2x 48 50. x 2 7x 18 51. x 2 49 52. 25x 4 5x 2 53. x 8 x 5 + x 4 x 54. 3x 2 6x 9 55. x 2 + 14x + 49 56. x 2 25 57. 2x 2 + 15x + 7 58. 2x 2 17x 19