June 2017

Dear Future Algebra 2 Trig Student,

Welcome to Algebra 2/Trig! Since we have so very many topics to cover during our 2018-19 school year, it is important that each one of you is able to complete these Algebra I problems. I will assume that you know how to use the algebraic and graphing skills necessary to complete these problems as we build on these topics throughout the year.

Remember these simple policies (that will also apply to each and every homework, quiz, test, and classwork assignment) in Algebra 2/Trig:

Show all work IN THE PACKET

When I say show your work, I mean every step of your algebraic work or sketch of a graph necessary.

Simplify all answers completely. Reduce all fractions, rationalize denominators, do not leave negative exponents (unless otherwise stated), etc.

Ask/search for help! Ask your friends, parents, teachers, tutors and use books and the internet to find help if you can’t remember a skill. Just make sure that in the end, you can complete the work independently, without the help, for next time.

Complete all work yourself, even if you are seeking the help of others.

Feel free to email Mrs. Handalagere (Mrs. H) during the summer at if you have any questions. I will be checking my email periodically, so be patient… I will get back to you! Do not wait until the last week (or night) of the summer to complete these. By then, it will be too late to get help.

Here are a few internet sites that may be of some help:

This assignment is optional. However, I strongly suggest that you complete this assignment. If completed and turned in by Friday, Sept. 7th, you can receive up to 2 extra credit points on your quarter grade. Your life this year in Algebra 2/Trig will be much better if you have mastered these skills prior to September.

We are look forward to working with you!

Algebra 2/Trig Team!!

SUMMER ASSIGNMENT FOR ALGEBRA II/TRIGONOMETRY

This summer assignment is designed to ensure that you are preparedfor Algebra II/Trigonometry. Nothing on the summer assignment is new. Everything is a review of topics students learned in Algebra I and Geometry. If you want to be successful during Algebra II/Trig, you must be able to understand and apply this information throughout next year. The assignment may be completed with another student but be certain that YOU understand how to complete every problem. Be sure to check every problem. Neatly show all work for each problem, using a pencil. Graphing calculators should not be used. There will be a quiz on the summer assignment during the second week of school.

If you need to review these topics or see examples of problems, werecommend the websites or which lists many Algebra review topics. If,after reviewing,you need further assistance, please e-mail Ms. Groves at with questions. She will try her best to answer your questions as soon as possible. The assignment should be completed and brought to school on the first day of class and will count for extra credit on your marking period grade if completed correctly and on time.

Simplify expressions, using order of operations:

1.[(8 4)  2 1]-32.3(x 8) 2(x + 5)3.643 12 + 8  6

Evaluate the expression.

4. when x = -25. when y = 46. when a = 3 ,b = -1

Simplify each expression.

7. 8. 9.

10. 11. 12.

13. 6  2[x 3  (x + 4) + 3(x 2)]14. x² + y² – [x(x + y) – y(y – x)]

15 7[2 – 3(x – 4) + 4(x – 6)]

Solving equations and inequalities. Be sure to show your work.

162(4x 7) = 3(x 10)177 = 7(2b + 5) 6(b + 8)

184x 4 = 3(2 x)192a 6 (3a + 4) = 10 4a

20. 21.

22. 3(2x + 25) – 2(x – 1) = 7823.

24. 5 [12  3(2  y)  2y] = 2 (1  y)25.

For #21 – 24 - Solve. Graph the solution to the inequality on a number line.

26.3  2x 1  527.3x + 1 2 or 3x + 1  7

28.3x 2  5x 329.7  2 5y3

Factor the following expressions.

  1. ax – ay + bx – by
  1. 2ax + 6ay + bx + 3by


Solve the following quadratic equations showing the requested method. Simplify when possible.

  1. Solve by factoring:
  1. Solve by factoring:
  1. Solve by factoring:
  1. Solve by factoring:
  1. Solve by quadratic formula:
  1. Solve by quadratic formula:
  1. Solve the system using substitution:

2x+ y= 5

x+ 3y = 5

  1. Solve the system using substitution:

3x = 2y– 6½

4x+ y = 6

  1. Solve the system using elimination:

2x+ 5y= 24

4x+ 3y= 20

  1. Solve the system using elimination:

x – 3y = -5

2y + 3x+ 4 = 0

  1. Write a system of equations and solve: The line with equation y + ax = c, passes through the points (1, 5) and (3, 1). Find a and c.
  1. Write a system of equations and solve: The curve y = ax2 + bx passes through (2, 0) and (4, 8). Find a and b.
  1. Find the slope and y-intercept and hence graph.
  1. Find the slope and y-intercept and hence graph.

  1. Find the equation of the line that passes through (2, 3) with a slope of 2.
  2. Find the equation of the line that passes through (3, -3) and (9, -1).

Solve the literal equation for the letter in square brackets.

  1. cb – ay +c = 5[c]
  1. abx + cd = ex[x]
  1. [a]

Simplify the following expressions using the properties above. Leave no negative exponents.


Simplify the following expressions using the property above. Express radicals as fractional exponents.



Simplify completely.


79. George’s apartment costs $2400 per month plus a $200 deposit. Write a function rule that relates the total cost to the number of months they rent. How much will it cost to rent the apartment for 2 year? Label your answer.

a. Write a function rule to calculate the total cost. ______

b. How much will it cost to rent the apartment for 1 year? ______

(HINT: x is the number of MONTHS)

80. The length of a rectangle is 2 more than three times the width. If the perimeter is 28in, find the width and the length.

Length: ______Width: ______

81. Jackie went shopping for a pair of shoes, socks and a belt. The shoes cost $7 more than ten times the cost of the belt. The socks cost $1 less than the cost of the belt. Jackie spent $132. How much did she spend on each item?

82. Suppose a camper took 2 hrs. to ride around a reservoir at 10mi./hr. at the beginning of the summer. By the end of the summer, she could ride around the reservoir in hrs. What was her rate at the end of the summer?(Hint: think direct or inverse variation).

83. A tree that is 5 feet tall casts a shadow 2 feet long. A nearby building casts a shadow that is 20 feet long. How tall is the building? (Hint: think direct or inverse variation).

84. Nora and Addison went shopping for new summer clothes. Nora bought 4 pairs of shorts and 7 tank tops for $102.50. Addison bought 2 pairs of shorts and 6 tank tops for $77.00. Find the cost of the shorts and tank top.

Equations: ______Shorts ______

______Tank Top ______

85. Kris is trying to decide which cell phone plan is best for her. She has two choices.

Choice A: $40.00 monthly charge plus $.25 per minute.

Choice B: $60.00 monthly charge plus $.05 per minute.

Write an equation that represents the cost per month for each plan. Solve the system of equations.

How many minutes is the break-even point? What advice would you give Kris? Be specific.

Equations:______Break-even point:______

______

Graph each system.

86. 87.

88. Circle the points that are solutions .

to the system graphed below?

A. (-3, 0)

B. (-5, 8)

C. (1, 3)

D. (3, 4)

E. (2, -4)

F. (0, 0)