Date:______________ Name: _______________________

Algebra 2 Readiness Summer Review

The purpose of this packet is to help you review Algebra 1 concepts the summer before taking Algebra 2 (CP or Honors). Use this assignment as a practice and as a challenge. If there is something you do not remember, or even a concept you do not think you learned in Algebra 1, use online resources to review the material or at least become familiar with it. Khan Academy, or Purplemath are sites that may help. This assignment is due the first day of school and will be counted as your first grade of the year. Show your work directly on these pages. Your work is more important than your final answer. Your work will help your teacher determine where more review will be needed during the first quarter. The answers to this review appear on the back. Answers provided from you without supporting work, will not receive credit.

Order of Operations: Evaluate each expression. Leave your answers as fractions/improper fractions in simplest form where needed. No decimals - do not approximate your answers.

*Reminder: Order of operations (PEMDAS): Parenthesis/Grouping symbols, Exponents, Multiplication OR Division (from left to right), Addition OR Subtraction (from left to right).

1. (15 − 8) × 3 + 5 + 48 − 6 2. 18 ÷ 9 × (5 − 2) + 7 3. 4 + 2 + 8 − 60 ÷ 3 × 6 − 3

4. (𝑎 − 𝑏) ÷ 6, 𝑤ℎ𝑒𝑟𝑒 𝑎 = 6, 𝑏 = 12 5. 2𝑥 − 2𝑥 + 24, 𝑤ℎ𝑒𝑟𝑒 𝑥 = 2

6. , 𝑤ℎ𝑒𝑟𝑒 𝑥 = −1 7. 𝑎 + √16 − , 𝑤ℎ𝑒𝑟𝑒 𝑎 = 2

Linear Equations: Write your final answers in slope-intercept form where applicable.

*Reminder: it is generally easier to write an equation in point-slope form, to then rewrite it in slope-intercept form.

Calculating slope: 𝑚 =

Lines that are parallel have the same slopes.

Lines that are perpendicular have slopes that are opposite in sign and reciprocals of each other.

8. Find the slope of the line 9. Write the equation of a line that has slope containing the points (4, -3) 𝑚 = − and passes through the

and (-6, 4). point (18,-2). 10. Write the equation of the line 11. Write the equation of the line containing the containing points (1, 3) and (1, 11). point (-4, 6) and parallel to 3𝑥 − 2𝑦 = 8. 12. Write the equation of the line Containing the point (3, 56) and perpendicular to 3𝑥 − 2𝑦 = 8.

Forms of a Linear Equation: Slope-intercept form: 𝑦 = 𝑚𝑥 + 𝑏 Point-slope form: 𝑦 − 𝑦 = 𝑚(𝑥 − 𝑥 ) Standard form: 𝐴𝑥 + 𝐵𝑦 = 𝐶

Exponents: Simplify each expression. Your final answer should contain only positive exponents.

*Reminder:

13. (7𝑥) 14. (2𝑥 𝑦) (3𝑥𝑦) 15. −

16. (4𝑥 ) 17. 18. (3 + 2 )

19. + 1 20.

Properties of Exponents

𝑎 ∙ 𝑎 = 𝑎 (𝑎 ) = 𝑎 𝑎 = 1

(𝑎𝑏) = 𝑎 𝑏 𝑎 =

1

𝑎, 𝑎 ≠ 0

𝑎

𝑎= 𝑎 , 𝑎 ≠ 0

𝑎

𝑏=

𝑎

𝑏, 𝑏 ≠ 0

Radicals: Simplify each radical expression. Final answers should be rationalized. No decimal approximations.

*Reminder:

21. √24 22. 3√700 23.

24. 3√700 + 2√7 25. (2√6) ∙ (3√15) 26. √12 − √48

27. √75𝑥 ∙ √3𝑥 28. √

29. √

√

Properties of Radicals

√𝑎𝑏 = √𝑎 ∙ √𝑏 𝑎

𝑏=

√𝑎

√𝑏

𝑎 = √𝑎 𝑜𝑟 √𝑎 𝑥 = 𝑥 𝑜𝑟 √𝑥 = 𝑥

Simplifying Polynomials: Simplify each expression.

*Reminder: 𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐

(𝑎 + 𝑏)(𝑐 + 𝑑) = 𝑎(𝑐 + 𝑑) + 𝑏(𝑐 + 𝑑) = 𝑎𝑐 + 𝑎𝑑 + 𝑏𝑐 + 𝑏𝑑

30. (7𝑥 − 2𝑦) − (3𝑥 + 5𝑦) 31. −7𝑥(2𝑥 − 9) 32. (3𝑥 + 𝑦) + (2𝑥 − 𝑦)

33. (3𝑥 + 4)(2𝑥 − 9) 34. 7(3𝑥 + 10𝑥) − 4𝑥 35. 3𝑥 + 10𝑥 − 4(𝑥 − 7)

36. (3𝑥 + 5)(2𝑥 − 3) 37. (−3𝑥 + 𝑦)(2𝑥 − 𝑦)

Factoring: Factor each polynomial. If the polynomial is not factorable using integer coefficients, it is “prime”.

*Reminder:

38. 𝑥 + 6𝑥 + 5 39. 𝑥 + 𝑥 − 6 40. 𝑥 − 4𝑥 + 3

41. 4𝑛 − 24𝑛 42. 144𝑥 − 36 43. 2𝑥 + 7𝑥 − 4

44. 4𝑥 + 12𝑥 + 9 45. 2𝑥 + 10𝑥 + 12𝑥 46. 2𝑥 + 3𝑥 − 8𝑥 − 12

47. 3𝑥 + 18𝑥 + 24𝑥

Strategies 1. Factor out a GCF if possible 2. Difference of Squares: (𝑎 + 𝑏)(𝑎 − 𝑏) = 𝑎 − 𝑏 3. Trinomials: factors of 𝑎𝑐 that add up to 𝑏 4. Square of binomials:

𝑎 + 2𝑎𝑏 + 𝑏 = (𝑎 + 𝑏) 𝑎 − 2𝑎𝑏 + 𝑏 = (𝑎 − 𝑏)

5. Grouping

Solving Equations: Solve each equation.

*Reminder

48. 3(𝑥 + 7) + 5 = −2𝑥 − 8 49. = 5 50. (𝑥 + 4)(9𝑥 − 3) = 0

51. 𝑥 + 𝑥 − 12 = 0 52. 𝑥 + 2𝑥 − 35 = 0 53. 𝑥 + 3𝑥 = −1

54. |1 − 4𝑥| = 5 55. −4𝑥 + 7 ≤ 5 56. 2√𝑥 − 3 = 5

Strategies 1. Factor out a GCF if possible. 2. When solving quadratics, there are three approaches: a) factor and use the zero-product property (𝐼𝑓 𝑎𝑏 = 0, 𝑡ℎ𝑒𝑛 𝑎 = 0 𝑜𝑟 𝑏 = 0), b) use completing the square, or

use the quadratic formula: 𝑥 =±√

3. Cubic – try factoring by grouping. 4. For absolute value equations:

|𝑎 + 𝑏| = 𝑐

𝑎 + 𝑏 = 𝑐 𝑜𝑟 𝑎 + 𝑏 = −𝑐 5. Grouping

Graphing: Graph the following functions on the coordinate plane provided. Label at least three points on your graph.

57. 58.

59. 60.

61. 62.

63. 64.

Answers: page 1 of 3 1. 68 2. 13 3. -49 4. 4 5. 28

6. − 7. − 8. − 9. 𝑦 = − 𝑥 +6

10. 𝑦 = 2𝑥 + 1

11. 𝑦 = 𝑥 + 12 12. 𝑦 = − 𝑥 + 58

13.

14. 27𝑥 𝑦 15. −3𝑎

16. 64𝑥

17.

18.

19.

20.

21. 2√6 22. 30√7

23.

24. 32√7 25. 18√10

26. −2√3 27. 15𝑥 28. 5

29. √ √

30. 4𝑥 − 7𝑦

31. −14𝑥 + 63𝑥 32. −𝑥 33. 6𝑥 − 19𝑥 − 36 34. 21𝑥 + 66𝑥 35. 3𝑥 + 6𝑥 + 28

36. 6𝑥 − 9𝑥 + 10𝑥 − 15 37. −6𝑥 + 5𝑥𝑦 − 𝑦 38. (𝑥 + 5)(𝑥 + 1) 39. (𝑥 + 3)(𝑥 − 2) 40. (𝑥 − 3)(𝑥 − 1)

41. 4𝑛(𝑛 − 6) 42. 36(2𝑥 + 1)(2𝑥 − 1) 43. (2𝑥 − 1)(𝑥 + 4) 44. (2𝑥 + 3) 45. 2𝑥 (𝑥 + 3)(𝑥 + 2)

46. (2𝑥 + 3)(𝑥 + 2)(𝑥 − 2) 47. 3𝑥(𝑥 + 4)(𝑥 + 2)

48. 49. 14

50. , −4

51. -4, 3 52. -7, 5

53. ±√

54. −1,

55. 𝑥 ≥

56. 16 57-64. (See Graphs below)

Answers: page 2 of 3 57.

58.

59.

60.

61.

62.

Answers: page 3 of 3 63.

64. Vertex: (0,0) Axis of Sym.: x=0