Name _____________________

What you will need:

This packet

Optional and Helpful:

Internet access

App for phone with graphing calculator:

Possible for Droid: Wabbitemu

iPhone App: Calulate84, Desmos

Graphing Calculator Searches: Desmos, Geogebra

Plan:

1) To spend at least 30 – 40 minutes a day doing math.2) Goal: 1 Topic a Day3) Should you have questions or need help, I will be available for assistance on school days,

from Noon to 2pm, on Remind, Google email/Classroom. This does not mean you cannot reach out at other times it just means that the response may be delayed.

4) Feel free to watch extra videos and take this time to enrich your own learning.

Mrs. Alvira, Ms. Frankiewicz and Mrs. Pasquale

1

Time Line

Day 1 Solving Equations p. 4

https://www.youtube.com/watch?v=LDIiYKYvvdA

Day 2 Solving for y p. 5

https://www.youtube.com/watch?v=8c1lS5J8W4c

Day 3 Linear Equations and Graphing p. 6 & 7

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:graphing-slope-intercept-equations/v/graphing-a-line-in-slope-intercept-form

Day 4 Linear Word Problems p. 8 & 9

https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-heart-of-algebra/v/sat-linear-equation-easier

Day 5 Linear Systems p. 10 & 11

https://www.youtube.com/watch?v=9MPUSWUyaYU

Day 6 Writing Linear Systems p. 12 & 13

https://www.youtube.com/watch?v=g9wgksPn7vY

Day 7 Quadratic p. 14, 15, 16

https://www.youtube.com/watch?v=ad4CVuHFWrU

Day 8 Factoring Quadratics p. 17, 18

https://www.youtube.com/watch?v=nG6jYmX7J6c

Day 9 Solving Quadratics Using the Quadratic Formula p. 19, 20

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/v/using-the-quadratic-formula

2

Day 10 Quadratic Applications p. 21, 22, 23

http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-290s.html

Day 11 Functions (Intro) p. 24, 25https://www.youtube.com/watch?v=VUTXsPFx-qQ

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/v/testing-if-a-relationship-is-a-function

.

Day 12 Evaluating Functions p. 26, 27

https://www.youtube.com/watch?v=wvFeAVWHo_Q

Day 13 Intro to Inequalities (Number line and simple inequalities) p. 28, 29

https://www.youtube.com/watch?v=jrWmqEJjhLY

3

Day 1

Solving Equations

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities

Solve the following, showing all your work.

1.) 26 = 8 + v 2) 3 + p = 8

3.) 5p − 14 = 8p + 4 4.) p − 4 = −9 + p

5.) −8 = −(x + 4) 6.) 12 = 4(6x + 3)

7.) 4x + 8 = ½(6x – 12) 8.) 7y – 5y + 3 - 1 = 4y - 14

4

Day 2

Solving for y

1.) 2y = 4x – 10

2.) -3y = -6x – 15

3.) 2y + x = 12

4.) 2x + y = 8

State the slope and the y-intercept

5.) y = -2x -9

6.) -2y = 2x - 14

Solve for y and then state the y-intercept and the slope

7.) 2(y + 4x) = 10

8.) ½y – 4x = -10

5

Day 3

Graphing Linear Equations

1.) Identify the y-intercept2.) Plot the y-intercept3.) Identify the slope, use the slope to find

your next point (rise over run)+ Up - DownAlways right

Identify the slope and y-intercept, then graph the line

1.) y = ½x - 2 2.) y = 2x + 2

3.) y =−12 x + 4 4.) y = -3x

6

Remember whole numbers,

place a 1 underneath 4= 41

5.) y =−32 x 6.) y = 2

7.) 2y =−5x + 2 8.) -½y = x

7

Day 4 Linear Word Problems y = mx + b

Directions: Circle the fixed or start amount (y-intercept)Underline the rate of change (slope)Write your equation, answer the question

1. Suppose that the water level of a river is 34 feet and that it is decreasing in height at a rate of 0.5 foot per day. a. Write an equation for the water level, L, after d days. b. In how many days will the water level be 26 feet?

1. Suppose that the water level of a river is 34 feet and that it is decreasing in height at a rate of 0.5 foot per

day. a. Write an equation for the water level, L, after d days.

L= - 0.5d+34b. In how many days will the water level be 26 feet?

L= - 0.5d+3426= -0.5d+34-34 -34-8 = -0.5 d-0.5 -0.516 = d

2. For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. a. Write an equation for the cost, C, after h hours of babysitting. b. What do you think the slope and the y-intercept represent? c. How much money will she make if she baby-sits 5 hours?

3. A plumber charges $25 for a service call plus $50 per hour of service.a. Write an equation in slope-intercept form for the cost, C, after h hours of service. b. What will be the total cost for 8 hours of work? 10 hours of work?

4. Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. a. Write and graph the equation for the total pounds, P, of aluminum cans after w weeks. b. What does the slope and y-intercept represent? How long will it take Rufus to collect 400

pounds of cans?

8

5. A canoe rental service charges a $20 transportation fee and $30 dollars an hour to rent a canoe.

a. Write an equation representing the cost, y, of renting a canoe for x hours. b. What is the cost of renting the canoe for 6 hours?

6. A caterer charges $120 to cater a party for 15 people and $200 for 25 people. Assume that the cost, y, is a linear function of the number of x people. a. Write an equation in slope-intercept form for this function. b. What does the slope represent?c. How much would a party for 40 people cost?

7. Attorney A charges a fixed fee on $250 for an initial meeting and $150 per hour for all hours worked after that. Attorney B charges $150 for the initial meeting and $175 per hour.

a. Write an equation in slope-intercept form for each attorney. b. Find the charge for 26 hours of work for each attorney. c. Which is the better deal? d. At how many hours does this attorney become a better deal?

8. A video rental store charges a $20 membership fee and $2.50 for each video rented. Write a linear equation to model this situation.

a. If 15 videos are rented, what is the revenue? b. If a new member paid the store $67.50 in the last 3 months, how many videos were rented?

9

Day 5 Systems of Linear Equations

Things to remember

1. Make sure both equation are solved for y2. Graph both equations 3. Identify the solution point ( if possible)

1.

2.

3.

10

4. 2x+2y=10y=3x-7

( , )

5. 4x-3y=6y=6x-2

( , )

Day 6 Writing Systems of Equations11

1. Alicia purchased H half-gallons of ice cream for $3.50 each and P packages of ice cream cones for $2.50 each. She purchased 14 items and spent $43. Which system of equations that could be used to determine how many of each item Alicia purchased ?

Base on the fact that $3.50 for a H half gallon of ice cream, which 2 answers can you eliminate and state WHY ?

2. The Celluloid Cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, write a system of equations to determine how many adult tickets, a, and how many child tickets, c, were sold?

Based on the fact that it is $10.25 for an adult ticket, which answer(s) can you eliminate ?

3. During the 2010 season, football player McGee’s earnings, m, were 0.005 million dollars more than those of his teammate Fitzpatrick’s earnings, f. The two players earned a total of 3.95 million dollars.

Which system of equations could be used to determine the amount each player earned, in millions of dollars?

12

4. Lizzy has 30 coins that total $4.80. All of her coins are dimes, D, and quarters, Q. Which system of equations models this situation?

Based on the fact that dimes are worth $0.10, what 2 answers could you have eliminated ?

5. For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w.

Write the system of equations (do NOT solve)

Let water = w

Let juice boxes = j

Equation 1 (Teacher 1 focus): _____________________

Equation 2 (Teacher 2 focus): ____________________

6. Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.

Write the system of equations (do NOT solve)

Let popcorn = p

Let drinks = d

Equation 1 (Jacob focus): _____________________

Equation 2 (Zachary focus): __________________

13

Day 7 Parts of Quadratics

Given the following graphed quadratics state the following:

1.

Vertex(turning point) _____________Roots (Zeros/solutions/x-intercepts) ___________Equation of the aXis of symmetry (in x = form) ________

2.

Vertex(turning point) _____________Roots (Zeros/solutions/x-intercepts) ___________Equation of the aXis of symmetry (in x = form) ________

3.

Vertex(turning point) _____________

Roots (Zeros/solutions/x-intercepts) ___________

Equation of the aXis of symmetry (in x = form)

________

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4.

Vertex(turning point) _____________

Roots (Zeros/solutions/x-intercepts) ___________

Equation of the aXis of symmetry (in x = form)

________

5. What are the vertex and axis of symmetry of the parabola shown in the diagram below?

5.

6. A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds. For which interval is the ball's height always decreasing?

15

1) vertex: ; axis of symmetry: 3) vertex: ; axis of symmetry:

2) vertex: ; axis of symmetry: 4) vertex: ; axis of symmetry:

1) 0 ≤ x ≤ 2.5 2) 0 < x < 5.5 3) 2.5 < x < 5.5 4) x ≥ 2

7. Based on the table from the calculator:

State the vertex: _________

Root(s) (Solutions/zeros): __________

aXis of symmetry : ___________

Does this quadratic have a max/min ? Explain.

Would the value for a for this quadratic be positive or negative ? Explain.

8. Based on the table from the calculator:

State the vertex: _________

Root(s) (Solutions/zeros): __________

aXis of symmetry : ___________

Does this quadratic have a max/min ? Explain.

Would the value for a for this quadratic be positive or negative ? Explain.

16

Day 8 Factoring to Solve Quadratics

1. x2 + 5x + 6 = 0

2. x2 + 7x + 6 = 0

3. x2 + 6x + 8 = 0

4. x2 + 7x + 12 = 0

17

5. x2 - 36 = 0

6. x2 + 10x + 25 = 0

7. x2 + 8x + 16 = 0

8. x2 + 6x + 5 = 0

18

Day 9 Solving Quadratics Using the Quadratic Formula

Steps1 – Make sure equation is set = to 02 – Label a, b, and c3 – Plug values into the formula 4 – Solve for BOTH the + and - √❑

Solve the following:1.) x2 + 8x + 15 = 0

2.) x2 + 10x + 21 = 0

19

3.) 2x2 + 6x + 4 = 0

4.) 3x2 + 12x = -12

5. -2x2 = x + 2

6. -x2 + 2x = -3

20

Day 10 Quadratic Applications

Directions:READ the following.Sketch a picture of the quadratic(title the axes).Then based on the information answer the following questions.

1. The height of a rocket, at selected times, is shown in the table belowa. Sketch the situation, don’t forget to title the axes.

b. Would this situation have a maximum or minimum value? Explain.

c. What do the root(s) represent in this situation ? Explain.

d. What does the vertex represent in this situation ?

2. A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The equation would have the height, y, of the ball from the ground after x seconds.a. Sketch the situation, don’t forget to title the axes.

b. Would this situation have a maximum or minimum value? Explain.

c. What do the root(s) represent in this situation ? Explain.

21

d. What does the vertex represent in this situation ?3. Morgan throws a ball up into the air. The height of the ball above the ground, in feet, is

modeled by the function h(t) = −16t2 + 24t, where t represents the time, in seconds, since the ball was thrown. a. Sketch the situation, don’t forget to title the axes.

b. Would this situation have a maximum or minimum value? Explain.

c. What do the root(s) represent in this situation ? Explain.

d. What does the vertex represent in this situation ?

4. A ball is thrown into the air from the top of a building. The height, h(t), of the ball above the ground t seconds after it is thrown can be modeled by h(t) = −16t 2 + 64t + 80. How many seconds after being thrown will the ball hit the ground?a. Sketch the situation, don’t forget to title the axes.

b. Would this situation have a maximum or minimum value? Explain.

c. What do the root(s) represent in this situation ? Explain.

d. What does the vertex represent in this situation ?

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5. When an apple is dropped from a tower 256 feet high, the function h(t) = −16t2 + 256 models the height of the apple, in feet, after t seconds.a. Sketch the situation, don’t forget to title the axes.

b. Would this situation have a maximum or minimum value? Explain.

c. What do the root(s) represent in this situation ? Explain.

d. What does the vertex represent in this situation ?

6. Alex launched a ball into the air. The height of the ball can be represented by the equation h = −8t2 + 40t + 5, where h is the height, in units, and t is the time, in seconds, after the ball was launched.a. Sketch the situation, don’t forget to title the axes.

b. Would this situation have a maximum or minimum value? Explain.

c. What do the root(s) represent in this situation ? Explain.

d. What does the vertex represent in this situation ?

23

Day 11 Functions

1.State whether or not the following are functions. Explain your answer.

24

2. Four relations are shown below:I. {(1,2),(2,5),(3,8),(2,−5),

(1,−2)} II.

III.

IV. y = x2

State which relation(s) are functions. Explain why the other relation(s) are not functions.

3. A function is shown in the table below. If included in the table, which ordered pair, (−4,1) or (1,−4), would result in a relation that is no longer a function? Explain your answer.

4. Would the following graph pass the vertical line test ? Explain. Is it a function ?

25

Day 12 Evaluating Functions

Given the function: g(x) = 2x; find g(3) This just means find the value of the function when x = 3

Example: g(x) = 2x

g(3) = 2(3)

g(3) = 6

1) Given f (x) = ½x ; find f (-4.8) 2) Given f (x) = ½x ; find f (-4.8)

3) Given f (x) = -0.5x + 3 ; find f (-4) 4) Given f (x) = 3x -5 ; find f(2) + f(4)

5.) The graph of y = f(x) is shown below.

Which point could be used to find f(2)? 1) A 2) B

3) C 4) D26

6.) If f(x) = √2 x+36 x−5 , then f(3) =

7.) If f(x) = √2 x+33 x−5 , then f(23) =

8.) State which of the following are linear (constant rate of change) functions.

a. Y = -2x + 6 b. y = 5

c. y = x2 d. y = |x|

27

Day 13 Intro to Inequalities

28

Solve the following, then graph the solution on the number line.

9. 2x + 7 < -13

10. 3(x + 2) > -15

29