Dear Future Algebra 2 Students and Parents: The Algebra 2 teachers in the Tigard-Tualatin School District look forward to working with you next year. It is our strong desire to help all students to achieve success in Algebra 2! Algebra 2 is a fast-paced course and now, with the new Common Core State Standards, Algebra 2 is becoming increasingly challenging as well. Algebra 2 students are now expected to have more advanced levels of conceptual understanding and to use advanced problem-solving skills to tackle more complex algebraic questions. In order for students to be successful in Algebra 2, they must have quality understanding of many math concepts, including number sense, graphing and solving linear and quadratic equations and inequalities, and functions and their domains and ranges. Without these skills, students are likely to struggle greatly with the pace and material covered in Algebra 2. In some cases, students may be withdrawn from Algebra 2 in order to learn the requisite skills in Algebra 1. The attached Algebra 2 Readiness summer packet is designed for students to review the skills necessary to be successful in Algebra 2. Completion of this Algebra 2 Readiness summer packet is highly recommended so that students are fully prepared for the challenges they will encounter next year in Algebra 2. Algebra 1 is the foundation for advanced math courses, including Algebra 2. Students who struggle to complete the Algebra 2 Readiness summer packet, which contains many basic Algebra 1 concepts, should strongly consider enrolling in Algebra 1 for the upcoming school year. With the implementation of the new, more rigorous Common Core State Standards for Algebra 1 and Algebra 2, next years’ students must have an even greater understanding of Algebra 1 than before in order to be successful in Algebra 2. The placement of students into the appropriate course, whether it be Algebra 1 or Algebra 2, is critical for student success. Parents can contact their student’s counselor to make schedule changes, if needed. The Algebra 2 Readiness summer packet is designed to include explanations of concepts and example problems so that students can relearn material they may have forgotten. Students can find additional help on the Holt textbook website by reviewing related examples and/or watching video tutorials. The Algebra 2 Readiness summer packet includes textbook section numbers at the top of each page, which correlate to the Holt Algebra 1 textbook. Use these section numbers to navigate to the appropriate areas of the Holt textbook website, which can be accessed using the following information:

Website: my.hrw.com (Be sure to omit the “www”.) Username: tuhsalgebra Password: ilovemath

Students can check their work with the answer key provided at the end of the packet. The answer key is meant to be a tool for students to check their progress and identify areas where further work is needed. Students should be sure to show their work throughout the packet and should not rely solely on the answer key during completion of the packet. The Algebra 2 Readiness summer packet is also available online on the Tigard-Tualatin School District website. We look forward to working with fully prepared Algebra 2 students and guiding them through a successful year in Algebra 2. Sincerely,

Algebra 2 Teachers of the Tigard-Tualatin School District

Algebra 2 Readiness Summer Packet

Name:

For additional help, view the example on factoring using the diamond and generic rectangle method:

http://www.youtube.com/watch?v=8swFkWviCjE

For additional help, view the example on factoring using the diamond and generic rectangle method:

http://www.youtube.com/watch?v=8swFkWviCjE

For additional help, view the example on factoring using the diamond and generic rectangle method:

http://www.youtube.com/watch?v=8swFkWviCjE

For additional help, view the example on factoring using the diamond and generic rectangle method:

http://www.youtube.com/watch?v=8swFkWviCjE

Algebra 2 Readiness Summer Packet Answers

Section 1-2 12. -4 13. -9.7

14. ! 49

15. 3 16. -10.3

17. ! 14

Section 1-3

19. 25• 94

20. 38• 32

21. 18• 61

22. ! 1564

23. 14

24. ! 718

25. 916

26. -4 27. -21

28. 85

29. ! 127

30. 114

Section 1-5 9. real number, rational number,

terminating decimal, integer, whole number, natural number

10. real number, rational number, repeating decimal

11. real number, irrational number

Section 1-6 1. 20; 23; 21 2. 16; 4; 7 3. 3; 9; 1 4. 9 5. -1 6. 14 7. 7 8. 97 9. 30 10. 13 11. 30 12. 16 13. 17.8 cm Section 1-7 7. yes 8. no 9. no 10. 4st 11. 6y3 + 5y 12. 12x3 + 6x4 13. 3x + 16 14. 10y – 10 Section 2-4 1. possible answer: add -3x to each side 2. possible answer: add 4x to each side 3. possible answer: add -15x to each side 4. -48 5. 2 6. 5 7. no solution 8. 1 9. all real numbers 10. no solution 11. all real numbers 12. -1

Section 3-5 1. add -6y to both sides 2. add -3p to both sides 3. add 3r to both sides 4. c > !4

5. x < 32

6. a >15 Section 4-2 1. D: {-2, -1, 0, 1}; R: {4, 1, 0} 2. D: {4, -2, -5}; R: {5, 6, 12} 3. D: {0, 1, 2, 3}; R: {5, 6, 7, 8} 4. D: {-3, -4, -5};

R: {10, 11, 12, 13} 5. D: -2 ! x ! 2; R: 1 ! y ! 4 6. D: -3 ! x ! 2; R: 1 ! y ! 3 7. no 8. yes 9. no Section 4-4 1.

2. 3. -3 4. 1 5. 0 6. 3 7. 1 8. 5

Section 5-1 1. no 2. yes 3. yes 4. no 5. no 6. yes 7. D: all real numbers;

R: all real numbers 8. D: x " 0; R: y " 0 9. D: {0, 1, 2, 3, 4};

R: {0, 0.5, 1, 1.5, 2} 10.

D: x " 0; R: y " 0 Section 6-2 1. (2, 3) 2. (7, 9) 3. (-4, 1) 4. (17, 7) 5. (3, 6) 6. (-1, 7) Section 7-1

1. 132

2. 11000

3. 625

4. 5y4

5. 8a3

6. 9x3

y2

7. x4

y

8. ab

9. 5y2

x4

Section 7-1 continued 10. 4 11. 512 12. 200 13. -8 14. 324

15. 116

Section 7-2 1. right; 1,000,000 2. left; 0.01 3. right; 10,000 4. positive; 103 5. negative; 10-4 6. positive; 107 7. positive; 6.12 • 107 8. negative; 4.5 • 10-4 9. positive; 4.67 • 106 10. 7451 11. 0.00004231 12. 293,000,000 Section 7-3 1. 27 2. 84 • 53 3. 212 • 33 4. m15n4 5. 68

6. 146

7. 159

8. 1x8y3

9. v12

u10

10. yes 11. no; 4h6 12. no; m3 13. 16x10 14. s12t9

15. !32y5

x20

Section 7-4 1. 25 2. x6y2

3. ba

4. 23

53= 8125

5. x18

y12

6. 9m6

n4

7. a3

b6

8. x4

y2

9. 94

10. 12527

11. z35

x5y15

12. c4

a8b12

13. y5

x5

14. 9m8

49

15. b15

32a10

16. 9n2

m2

17. 27x6

8

18. 16s12

r4

Section 7-5 1. 8 2. 3 3. 4 4. 6 5. 5 6. 2 7. -6x5 – 5x4 + x3; -6 8. –x3 + 5x2 + 2x; -1 9. 7x2 + 8x – 1; 7 10. quadratic binomial 11. cubic polynomial 12. 102 feet Section 7-6 1. no 2. yes 3. no 4. 3y2 + 10y 5. 4m4 + 3m 6. 12x5 + 18x4 7. 8x2 + 9x 8. m2 – 2m + 7 9. 10x3 + x2 + 3x + 9 10. 3y5 + 8y4 – 8y3 11. –x2 – 7x 12. 3x3 – 4x + 8 13. 5x4 – x3 + 7x2 + 3 14. 9x3 – 8x 15. 8t4 + 1 16. -2x3 + 4x + 4 17. t3 – t2 – 4t – 6 18. 4c5 – c3 + 8c2 – 7 Section 7-7 1. -10x3y4 2. -8x3y2z2 3. 3x3y3 4. 4x – 20 5. 3x2 + 24x 6. 2x3 – 12x2 + 6x 7. 5x + 45 8. -4x3 – 32x 9. 6x4 + 15x3 + 12x2 10. 3x2 – 21 11. 10a4b2 12. -5y3 + 35y2 – 10y 13. x2 – 9x + 18 14. x2 + 6x – 16 15. x2 – 9x + 18 16. x2 – 5x + 6

Section 7-7 continued 17. x2 – 49 18. x2 + 3x + 2 19. 2x3 + 10x2 + 20x + 24 20. 6x3 + 16x2 + 13x + 10 Section 8-2 1. 5x(4x – 3) 2. 11a(4a + 1) 3. 12(2y – 3x) 4. (x + 7)(5x + 2) 5. (a + 4)(3a – 2) 6. (4y + 1)2 7. (3x2 + 4)(6x + 5) 8. (5a2 + 6)(2a – 3) 9. (3x2 + 2)(7x + 4) 10. (10x2 + 3)(4x – 5) Section 8-3 1. (x + 2)(x + 8) 2. (x – 4)(x – 5) 3. (x + 12)(x + 1) 4. (x + 10)(x + 5) 5. (x – 9)(x – 4) 6. (x – 4)(x + 5) 7. (x + 1)(x – 4) 8. (x – 3)(x + 6) 9. (x – 7)(x + 2) 10. (x – 5)(x + 9) Section 8-4 1. (x + 2)(5x + 2) 2. (3x + 4)(x + 1) 3. (2x – 7)(x – 3) 4. (2x + 3)(2x + 1) 5. (3x + 5)(x – 4) 6. (5x – 1)(x + 7) 7. –1(2x – 5)(x + 1) Section 9-3 1. x = -2 2. (-2, -16) 3. (0, -12) 4. possible answers:

(-1, -15); (1, -7)

Section 9-3 continued 5. 6. 3 seconds 7. 144 feet 8. 6 seconds Section 9-6 1. x = 6, 3 2. x = -8, 5 3. x = 0, 7

4. x = 32

; -9

5. x = 15

; -2

6. x = -4, 2 7. x = -4, 3 8. x = -5 9. x = -8, 1 10. x = ± 7

11. x = 0, - 254

12. x = 5, -2 13. x = -3, -7 14. x ± 2 15. x = -1, 3