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.
Simplifyeach expression.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10.11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 22. 23.
24. 25. 26.
27. 28.29.
30. 31. 32.
33. 34.35.
36.37. 38.
39.40. 41.
42. 43. 44.
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.
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.
22. 23. 24.
25. 26. 27.
28. 29. 30.
31. 32. 33.
34. 35. 36.
37. 38. 39.
40. 41. 42.
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: ______
Decide whether the relation is a function. Then state the domain and the range.
Input / Output4 / 3
13 / 7
9 / 4
4 / 0
1. 2.3.
yes / noyes / noyes / no
Domain:______Domain:______Domain:______
Range:______Range:______Range:______
4.5. 6.
yes / noyes / noyes / 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? ______
______ , ______
8. If . 9. If .
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 = 42.slope: –73.slope: –6
b = –5y-intercept: 6passes through (0, –5)
4.slope: 05. slope: undefined6.passes through(–8, 3)
passes through (–5, –3) passes through (–2, 8) and (–4, 1)
7.parallel to y = and8.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.
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 = 42.x = 1 3.y = x
slope: ______slope: ______slope: ______
y-intercept: ______y-intercept: ______y-intercept: ______
4.y = –x5.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 === 0Roots = Zeros = Solutions === 0
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.
16.17.18.
Solve the system by graphing. State the solution.
1. 2.
Solution: ______Solution: ______
3. 4.
Solution: ______Solution: ______
Solve the system algebraically. State the solution.
1. 2.3.
4. 5. 6.
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 - ______
1