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Honors Algebra 2 Summer Assignment – Practice Problems for Prerequisite Skills

All work must be neatly shown for each problem.

Welcome to Honors Algebra 2! I look forward to getting to know you and working with you during the 2014-2015 school year. While you are enjoying your summer, please take time to complete the attached assignment. This packet is designed to help you make the transition into this challenging course as smooth as possible. One thing for sure – the more you do over the summer, the easier it will be when school starts and the more comfortable you will feel with the pace of the class.

You should recognize the concepts in this packet from Algebra 1 and Geometry. It is very important that you complete the summer work. Packets WILL BE COLLECTED on the FIRST day of school. A completion grade will be assigned to all students. Answers are attached at the end of this packet so you can check your solutions.

We will spend some time in class reviewing the prerequisite skills covered in this packet, but we will not complete problems from this packet, as they are your responsibility to complete over the summer.

You will be tested on this material within the first two weeks of school.

Test on sections A through C will be on Tuesday, August 19th, 2014.

Test on sections D through F will be on Friday, August 23rd, 2014.

It is mandatory to have a graphing calculator for all courses beginning with Algebra 2. (Recommended: TI-Nspire Touchpad, TI-84 Plus Silver Edition or equivalent)

Contact:

You can reach me by email grahaman@, but please understand that I do not check my email as frequently in the summer as I do during the school year.

Give me your best work while giving yourself the opportunity to get off to a great start! I look forward to meeting you in August!

- Mr. Graham

Sections a – c: Quiz 1 concepts

a. Solve single-step and multi-step equations (Ch 1.3) and inequalities (Ch 1.5) in one variable

Solve each equation. Check your answer.

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

Solve each inequality. Graph each solution on a number line.

7. [pic] 8. [pic]

9. [pic] 10. [pic]

Solve each equation for y.

11. [pic] 12. [pic]

13. [pic] 14. [pic]

b. Write linear equations in standard form and slope-intercept form when given two points, a point and the slope, or the graph of the equation (Ch 2.2, 2.3, and 2.4)

Write each equation in slope-intercept form. Then, graph each equation on the graph provided.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

Write an equation of each line in slope-intercept form.

5. slope = –2; (2, 1) 6. slope = 0; (–2, 3) 7. slope = [pic]; (–3, 5)

Using the point-slope form, write the equation of the line through each pair of points. Equations should be written in slope-intercept form.

8. (–2, –3) and (2, –1) 9. (–5, –2) and (–3, 8) 10. (11, 8) and (–2, –3)

Write the equation of the line through each point. Write the final equation in slope-intercept form.

11. through (7, 1) and perpendicular to [pic]

12. through (2, 9) and parallel to [pic]

13. through (3, 1) and perpendicular to [pic]

14. through (–6, 2) and perpendicular to [pic]

c. Graph a linear equation using a table of values, x- and y-intercepts, or slope-intercept form (Ch 2.2, 2.3, and 2.4)

Find the x and y-intercepts and then graph each line.

1. [pic] 2. [pic]

Sections d – f: Quiz 2 concepts

d. Graph linear inequalities (Ch 2.7) and solve systems of linear inequalities (Ch 3.3)

Graph each inequality. Put inequalities in slope-intercept form first.

1. [pic] 2. [pic] 3. [pic]

Solve each system of inequalities by graphing.

4. [pic] 5. [pic] 6. [pic]

e. Solve systems of two linear equations using various methods, including elimination, substitution, and graphing (Ch 3.1 and 3.2)

Solve each system of equations by graphing. State the solution. Describe the system as consistent and dependent, consistent and independent, or inconsistent.

1. [pic] 2. [pic] 3. [pic]

Use substitution to solve the system of equations.

4. [pic] 5. [pic] 6. [pic]

Use elimination to solve the system of equations.

7. [pic] 8. [pic] 9. [pic]

f. Add, subtract, and multiply polynomials (Ch 5.1 and 5.2)

Simplify. Write each answer in standard form.

1. (6d – 10d3 + 3d2) – (5d3 + 3d – 4) 2. (–4s3 + 2s – 3) + (–2s2 + s + 7)

Simplify each product.

3. 4v3(2v2 – 3v + 5) 4. –t2(2t4 + 4t – 8)

5. (2h + 6)(5h – 3) 6. (b – 5)(b – 11)

Simplify each product (continued).

7. (x + 3)(x2 – 2x + 4) 8. (2x2 + 2x – 6)(3x – 4)

g. Factor a common monomial from a polynomial (gcf), factor trinomials in the form [pic] and [pic], and factor the difference between squares (Ch 5.4)

Factor each polynomial using the greatest common factor (gcf).

1. 12x – 9 2. –20w2 + 16w 3. 12n3 – 36n2 + 18

4. 18h4 – 27h2 + 18h 5. 34g3 + 51g2 + 17g 6. 15c4 + 24c3 – 6c2 + 12c

Factor each trinomial in the form [pic].

7. [pic] 8. [pic] 9. [pic]

10. [pic] 11. [pic] 12. [pic]

13. [pic] 14. [pic] 15. [pic]

Factor each polynomial using the grouping method.

16. [pic] 17. [pic] 18. [pic]

Factor each trinomial in the form [pic].

19. [pic] 20. [pic] 21. [pic]

22. [pic] 23. [pic] 24. [pic]

Factor each difference of squares. If the binomial cannot be factored write “prime.”

25. [pic] 26. [pic] 27. [pic]

28. [pic] 29. [pic] 30. [pic]

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