Below is the algebra 2 optional summer assignments. All the topics below are prerequisite skills for algebra 2 and will NOT be re-taught. Students will be assessed on the following skills at the beginning of the school year.

Simplify each expression.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

1

22. 22. 23.

24. 25. 26.

27. 28. 29.

30. 31. 32.

33. 34. 35.

36. 37. 38.

39. 40. 41.

42. 43. 44.

2

45. 46. 47.

48.

Factor the expression completely. If it is not factorable, put prime.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16.

3

Solve for the variable.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

4

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32. 33.

34. 35. 36.

37. 38. 39.

40. 41. 42.

5

43. 44. 45.

46. 47. 48.

Rewrite each equation so that y is a function of x. (solve for y)

1. 2. 3.

Rewrite the equations in standard form . Then evaluate the discriminant, , and state the number and type of solutions.

1. Standard form: __________________________________

Discriminant = ___________________________________

# and Type of solutions: ____________________________

2. Standard form: __________________________________

Discriminant = ___________________________________

# and Type of solutions: ____________________________

3. Standard form: __________________________________

Discriminant = ___________________________________

# and Type of solutions: ____________________________

6

Decide whether the relation is a function. Then state the domain and the range.1. 2. 3.

yes / no yes / no yes / no

Domain:____________________ Domain:____________________ Domain:____________________

Range:_____________________ Range:_____________________ Range:_____________________

4. 5. 6.

yes / no yes / no yes / no

Domain:____________________ Domain:____________________ Domain:____________________

Range:_____________________ Range:_____________________ Range:_____________________

7. Use the graph to provide the following information:

x-intercept(s) _______________________

y-intercept(s) _______________________

zero(s) ________________________

domain ________________________

range ________________________

function? ________________________

( 4)f ______ ( ) 0f x , x _______

8. If . 9. If .

7

Input Output4 313 79 44 0

Match the equations with the correct form.

________ 1. Point Slope Form

________ 2. Standard Form

________ 3. Slope Intercept Form

Write the equation of the line given the information.1. m = 4 2. slope: –7 3. slope: –6 b = –5 y-intercept: 6 passes through (0, –5)

4. slope: 0 5. slope: undefined 6. passes through (–8, 3)passes through (–5, –3) passes through (–2, 8) and (–4, 1)

7. parallel to y = and 8. perpendicular to and

passes through (–1, 4) passes through (–6 , 8)

The variable y varies directly with the variable x. Write a direct variation equation that relates x and y.

1. 2.

8

The variable y varies inversely with the variable x. Write a direct variation equation that relates x and y.

1. 2.

Linear Word Problems:

1. Larry’s Limo charges a flat fee of $300 to rent a limo and $100 for each hour.

If y is the total charge for a rental, what does the x variable stand for? _________________________

Write an equation in slope-intercept form to represent the total cost of a given rental.

How much would Larry charge you to rent a limo for 3 hours?

2. You have $10 to spend in total and decide to use it all to buy candy. You decide to get a mixture of Kit Kat bars that cost 25 cents each and Milky Way bars that cost 35 cents each. How can you represent the various combinations of Kit Kat and Milky Way bars that you can buy with a linear equation in standard form?

The x would represent ___________________. The y would represent ______________________.

The equation in standard form would be _______________________________________

Sketch the graph and fill in the blanks.

1. y = 4 2. x = 1 3. y = x

slope: __________ slope: __________ slope: __________

y-intercept: __________ y-intercept: __________ y-intercept: __________9

y

x

y

x

y

x

4. y = –x 5. y = 6. y =

slope: __________ slope: __________ slope: __________

y-intercept: __________ y-intercept: __________ y-intercept: __________

7. 3x + 2y = –6 8. 9.

slope: __________ Open up or down? _________ Open up or down? _________

x-intercept: __________ Axis of Symmetry: ________ Axis of Symmetry: ________

y-intercept: __________ Max or Min?: ____________ Max or Min?: _____________

Domain:_____________ Vertex: __________________ Vertex: ___________________

Range: ______________ Domain: _________________ Domain: _________________

Range: __________________ Range: ____________________

y-intercept: ________________ y-intercept: _________________

x-intercepts: _______________ x-intercepts: _______________

Roots = Zeros = Solutions = ( )f x = y = 0 Roots = Zeros = Solutions = ( )f x = y = 0

10

y

x

y

x

y

x

y

x

y

x

y

x

10. 11. 12.

Open up or down? _________ Open up or down? _________ Open up or down? _________

Axis of Symmetry: ________ Axis of Symmetry: ________ Axis of Symmetry: ________

Max or Min?: ____________ Max or Min?: ____________ Max or Min?: _____________

Vertex: ________________ Vertex: __________________ Vertex: ___________________

Domain: ______________ Domain: _________________ Domain: _________________

Range: __________________ Range: ____________________ Range: __________________

y-intercept: ________________ y-intercept: _________________ y-intercept: _________________

x-intercepts: _______________ x-intercepts: _______________ x-intercepts: _______________

13. 14. 15.

11

y

x

y

x

y

x

y

x

y

x

y

x

16. 17. 18.

Solve the system by graphing. State the solution.

1. 2.

Solution: ______________________ Solution: ______________________

12

y

x

y

x

y

x

3. 4.

Solution: _________________ Solution: ________________________

Solve the system algebraically. State the solution.

1. 2. 3.

4. 5. 6.

13

System of Equations Word Problems:1. You buy 8 gallons of paint and 3 brushes for $152.50. The next day, you purchase 6 gallons of paint and 2 brushes for $113.00. How much does each gallon of paint and each brush cost?

2. The local pre-school ordered all new bicycles and tricycles for the new school year. Each bicycle and tricycle is shipped in its own box. Oddly, the manufacturer shipped all of the wheels in a separate box. If there are 16 boxes of bicycles/tricycles total and 45 wheels total, how many tricycles were ordered?

3. Jack has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have?

4. Two groups of people went to see Avatar in IMAX 3-D. The first group spent $73.50 on two adult and three children tickets. The other group spent $109.50 on five adult and two children tickets. What is the cost for each type of ticket?

Statistics:1. Find the mean, median, mode, range, and standard deviation of the data given the following sample. If necessary, round answers to nearest tenth.

11, 21, 14, 24, 15, 25, 22, 16, 11

Mean -________ Median-_________ Mode -________ Range -_________ Standard Deviation - _________14