4 3 4 3

2

√

4

Common Core Math II Summer Assignment 2017

Name _________________________

Use a separate sheet of paper to complete your responses. Be sure to show all work for each problem to

receive credit for this assignment. If you have any questions, email latoya.clay@hillsidehornets.net or

contact your grade level IB Coordinator.

Simplify each expression:

1. (2x2

+ 3x + 6) + (-5x2

+ 4x – 2)

4. 𝑥(𝑥 − 3)(𝑥 − 2)

7. (2𝑥 − 3)(2𝑥2 + 3𝑥 − 5)

10. √289𝑥5𝑦6

13. √9

16. √2(√6 − 10)

Factor each expression completely: 19. 2x

2 – 98x

22. a2x – b

2x +a

2y – b

2y

25. 65𝑥𝑦2 − 9𝑥3

28. 3𝑢2 + 𝑢𝑣 − 10𝑣2

31. 4𝑥4𝑛 − 4𝑥2𝑛 − 15

2. (8𝑥 − 3)(2𝑥 + 4)

5. (1

𝑥 − 2) (

3 𝑥 +

4)

8. (𝑟𝑛 − 5)(𝑟𝑛 + 5)

11. √𝑥2 − 4𝑥 + 4

14. 5√3 − 3√18 + 2√75

17. √50𝑥

20. 3x

2 + 5x + 2

23. x2

+ 64

26. 𝑡4 − 10𝑡2 + 9

29. 4𝑥2 − 16

32. 9 − 16𝑎8

3. 2𝑥2𝑦(5𝑥 − 𝑦)

6. (4x2

– 6x + 2) – (5x2

– 4x – 3)

9. (3𝑐 + 5𝑑)2

12. √3𝑥𝑦3 ∙ √12𝑥3𝑦2

15. (6 − √2)(5 + 2√2)

18. 4

21. 3x3

+ 6x2

– 3x – 6

24. 16x2

– 24x + 9

27. 6𝑡2 − 11𝑡 − 10

30. 1

𝑥2 − 1

33. 16 − 8𝑥 + 𝑥2

Solve: 34. Find the area and the perimeter of the figure:

2x+1

4x-1

35. If the area of a rectangle is 8𝑥2 + 10𝑥 + 3. Find the dimensions that would represent the length and width.

Solve by factoring:

1. 𝑥2 – 2𝑥 – 15 = 0

Solve by completing the square:

3. 𝑥2 + 3𝑥 – 8 = 0

2. 3𝑥2 – 13𝑥 = 10

4. 3𝑥2 – 12𝑥 + 4 = 0

Find the discriminant, give the nature of the roots, then solve using the quadratic formula:

5. 3𝑥2 + 11𝑥 + 4 = 0 6. 𝑥2 – 4𝑥 + 4 = 0 Use your calculator and solve the following equations by graphing:

7. 4𝑥2 + 2𝑥 – 5 = 0 8. 6𝑥2 + 108𝑥 + 480 = 0

Write in vertex form, give the vertex and axis of symmetry for the following:

4 9. 𝑦 =

3 𝑥2 + 12𝑥 + 6 10. 𝑦 = −𝑥2 + 10𝑥

Explain the transformation of the equation given from the parent function y = x2:

11. 𝑦 = (𝑥 – 5)2

+ 1 12. 𝑦 = ½ (𝑥 + 3)2 13. 𝑦 = −2𝑥2 – 6

For application problems, please write an equation and solve. Do not guess and check on these!

14. Charlie Brown has 48 feet of fencing to make a rectangular pen for Snoopy and his brother, Spike. He plans

to use the side of his house as one side of the pen and to divide the pen in half so that there are two separate

rectangular areas. What will be the dimensions that will maximize the area of the pens?

15. Peppermint Patty throws a baseball in the air; the equation y = 128t – 16t2

gives the ball’s height about the

ground after t seconds. What is the height after 2 seconds? What is the maximum height reached? For how

many seconds will the ball be in the air?

16. Donald Duck wants to build a swimming pool surrounded by a sidewalk of uniform width. He wants the

dimensions of the pool and sidewalk to be 16 meters by 20 meters. The pool has an area of 192 square meters. How wide should the sidewalk be?

y

Solve the following: Graph:

17. 𝑦 = 𝑥 + 2 𝑦 = 𝑥2

19. 𝑦 ≥ 𝑥2 – 2𝑥 𝑦 < −𝑥2 + 2𝑥

18. 𝑦 = 2𝑥 – 1 x 𝑦 = 𝑥2 − 4

20. The entrance to a tunnel is a parabolic arch modeled by the equation = −𝑥2 − 5𝑥 + 7 . A linear banner

stretched across the entrance is modeled by the equation y = 3x + 19 . What are the coordinates of where the

banner is attached to the entrance?

**DON’T FORGET TO STUDY HOW TO DERIVE THE QUADRATIC FORMULA BY COMPLETING THE SQUARE!!!!!***

Conditional Probability

1. Donald, the quarterback, has 2 wide receivers. He throws to Goofy three out of five plays and Goofy

drops the ball 90% of the time. Donald throws to Pluto two out of five plays and Pluto is able to catch

the ball 70% of the time.

a. What is the probability that ball was caught, by either Goofy or Pluto?

b. What is the probability that the ball was dropped, by either Goofy or Pluto?

c. Given that the ball is dropped, what is the probability that it was passed to Pluto?

d. Given that the pass is caught, what is the probability that it was Goofy who caught it?

2. The Venn diagram displays the results of a survey of 100 families regarding

technology in their homes. Computer (C), VCR (V) and fax machine (F).

a. What is the probability that families have a computer given that they have a fax machine?

b. Given that a family has a computer, what is the probability that they also have a fax machine?

c. What is the probability that families have a VCR given that they do NOT have a fax machine?

3. Given the following two-way table, answer the following questions:

a. 𝑃(𝑏𝑙𝑎𝑐𝑘 ℎ𝑎𝑖𝑟|𝑏𝑟𝑜𝑤𝑛 𝑒𝑦𝑒𝑠) b. 𝑃(𝑔𝑟𝑒𝑒𝑛 𝑒𝑦𝑒𝑠|𝑏𝑙𝑜𝑛𝑑 ℎ𝑎𝑖𝑟) c. 𝑃(𝑏𝑟𝑜𝑤𝑛 ℎ𝑎𝑖𝑟|𝑏𝑙𝑢𝑒 𝑒𝑦𝑒𝑠) d. 𝑃(ℎ𝑎𝑧𝑒𝑙 𝑒𝑦𝑒𝑠|𝑛𝑜𝑡 𝑏𝑟𝑜𝑤𝑛 ℎ𝑎𝑖𝑟) e. 𝑃(𝑛𝑜𝑡 𝑔𝑟𝑒𝑒𝑛 𝑒𝑦𝑒𝑠|𝑏𝑙𝑜𝑛𝑑 ℎ𝑎𝑖𝑟)

Exercises 4-7, use the data in the table below, which shows the employment status of individuals in a

particular town by age group.

Age Group Full-time Part-time Unemployed

0-17 24 164 371

18-25 185 203 148

26-34 348 67 27

35-49 581 179 104

50+ 443 162 173

4. If a person in this town is selected at random, find the probability that the individual is employed

part-time, given that he or she is between the ages of 35 and 49.

5. If a person in the town is randomly selected, what is the probability that the individual is

unemployed, given that he or she is over 50 years old?

6. A person from the town is randomly selected; what is the probability that the individual is employed

full-time, given that he or she is between 18 and 49 years of age?

7. A person from the town is randomly selected; what is the probability that the individual is employed

part-time, given that he or she is at least 35 years old?

Exercises 8-11, compute the conditional probabilities 𝑷(𝑨|𝑩)𝒂𝒏𝒅 𝑷(𝑩|𝑨) 8. P(A) = 0.7, P(B) = 0.4, P(AB) = 0.25

9. P(A) = 0.45, P(B) = 0.8, P(AB) = 0.3

10. P(A) = 0.6, P(B) = 0.18, P(AB) = 0.07

11. P(A) = 0.2, P(B) = 0.5, P(AB) = 0.01

12. Determine which of the sets shown in exercises 5 – 8 are independent.

Exercises 13-16, use the data in the following table, which shows the results of a survey of 2000

gamers about their favorite home video game systems, organized by age group. If a survey participant

is selected at random, determine the probability of each of the following.

Age Group Sony PlayStation 2

Microsoft Xbox Nintendo GameCube

Sega Dreamcast

0-12 63 84 55 51

13-18 105 139 14928 113

19-24 248 217 2783 169

25+ 191 166 10488 136

13. The participant prefers the Sony PlayStation 2 system.

14. The participant prefers the Microsoft Xbox, given that the person is between the age of 13 and 18.

15. The participant prefers Nintendo GameCube, given that the person is between the ages of 13 and 24.

16. The participant is under 12 years of age, given that the person prefers the Sega Dreamcast machine.

A pair of dice are tossed. Find the following probabilities: 17. the sum on the two dice is 8, given that the sum is even

18. the sum on the two dice is 12, given that doubles are rolled

19. doubles are rolled, given that the sum on the two dice is less than 7

20. the sum on the two dice is 8, given that the sum is more than 6