Quadratic and Direct Variation

Answer the following questions, to recieve full credit you MUST show all work.

1. What are the roots of the equation x^2 - 5x = -4?

a. -4 and - 5
b. -1 and - 4
c. 4 and 5
d. 1 and 4


2. If y is tripled, what happens to x?

x = y / 2


a. x stays the same
b. x is decreased by 3
c. x is decreased by 1\3
d. x is tripled

Proportions - Defects

Apple manufactures iphones and checks some iphones for defects. Within the first five minutes of a work shift, an iphone is randomly selected from the completed iphones, and checked for defects. For the rest of the shift, every 10th iphone is checked for defects. On one shift, it is found that 300 out of 2,000 iphones have defects.

a. Based on these results, what is the probability of an iphone manufactured by the company being defective?

b. Estimate how many iphones out of 3,000 manufactured can be expected to be defective. What if 5,000 were manufactured?

Percents - Do want fries with that?

Yesterday, at Burger King where Dominique works, 60% of the customers ordered a burger. Show all work.



a. If 42% of the customers ordered a burger and fries, what is the probability that a customer who ordered a burger also ordered fries?



b. If 15% of the customers ordered a burger and onion rings, what is the probability that a customer ordered onion rings given that he/she ordered a burger?



c. If 36% of the customers ordered a burger and milkshake, what is the probability that a customer who ordered a burger also ordered a milkshake?

Sale Commission

Jennifer sells major appliances. She is paid a monthly salary of $1,600, plus a commission of 5% on the first $2,000 of monthly sales and 10% on the rest of her monthly sales over $2,000.

a. What is Jennifer's income for a month having sales of $5,938.50? Explain.

b. What if Jennifer worked at the same job but was paid a monthly salary of $1,000 plus a 15% commission on her monthly sales. Would she have paid more or less than the amount in part A for the same monthly sales? Explain.

The Average (mean) Test Score

On seven math tests, Sabrina Marie has the following scores: 82, 78, 88, 83, 91, 89, 94

a. Find Sabrina Marie's average score on these tests._____

b. If Sabrina Marie's were to receive a score of 77 on the eighth test, how would her average be affected? Explain how you got your answer.

c. What is the least score she would need on the eighth test to maintain the average she now has? Suppose her teacher does NOT round decimal averages up, for example, 81.5 = 81 (not 82). Explain your results.

Probability - Pick a Card

Kate wants to randomly pick a card from a standard deck of cards (52 total cards).

a. What is the probability of picking a red card or a king? Write an explanation stating the mathematical reason(s) why you chose each of your steps.


b. What are the odds in favor of picking a red card or a king? Write an explanation stating the mathematical reason(s) why you chose each of your steps.

Middle East Geography Quiz

TAKE THE MIDDLE EAST GEOGRAPHY QUIZ

Drag the country's name onto the map. There is no humbling score nor time limit, but rather this exercise is a learning tool. Don't be afraid to make an error, and once you finish the puzzle, you will be far more educated about this very intense part of our world.

http://www.rethinkingschools.org/just_fun/games/mapgame.html

Let us know how you did by commenting on how many you could do!

Monomials and Polynomials

A rectangular box has sides with lengths of (3x), (x-2), and (3x+1).

a. Write a polynomial to express the volume of the box. Explain why you did each step.

b. If x is 4 inches, what is the volume of the box? Show each step.

Probability - Picking Marbles

Tyree places 16 marbles in a bag - 8 green, 3 red, 1 yellow, and 4 blue.

a. What is the probability of picking 2 green marbles in a row if he replaces the first marble before picking the second marble? Write an explanation stating the mathematical reason(s) why you chose each of your steps.

b. What is the probability of picking 2 green marbles in a row if he does not replace the first marble before picking the second marble? Write an explanation stating the mathematical reason(s) why you chose each of your steps.

Systems of Equations

Corissa M. wants to join 1 of 2 gyms near her home. Each gym charges an enrollment fee for joining the gym and a monthly membership fee.

LA Fitness: Enrollment Fee: $55
Monthly Fee: $30


YMCA: Enrollment Fee: $95
Monthly Fee: $25

a. Calculate the cost of a 1-year membership at each gym. Explain all your work.

b. Write an equation for each gym's membership plan that describes the relationship between the number of months of membership (x) and the total cost (y).

c. Determine the number of months at which the total cost of membership at each gym will be the same amount of money. Explain why you did each each step.

Parallel and Perpendicular

David says that the equation y = 0.6x + 4 represents a line that is parallel to the graph of 5y - 3x = 10.

a. Is David correct? Explain how you know.

b. Carlos says that a line perpendicular to y = -6x + 3 would be the line represented by 6y = x + 30. Is Carlos correct? Explain how you know.

**If you need extra help putting the equation into slope intercept form "y=mx + b" check out this website.

http://www.howe-two.com/mathematicat/standardslope.html

Hope this helps!

Inequality

Graph the inequality y > -2x + 3 on the coordinate plane. Explain how you would graph the inequality without a calculator.

Cost of a Call

Here is your first open-ended item. Make sure you "explain how you know" how to solve the problem. Remember, to explain means to to give the meaning of something: give facts and details that make the idea easy to understand.

Question.
The cost of a long distance phone call to Africa is given by the function below where t is time in minutes. C(t) = 1.84 + 0.58t

a. How much will a phone call that last 15 minutes 30 seconds cost? Explain how you know.

b. If the cost of phone call is $5.32, what is the length of the phone call in minutes? Explain how you know.

Rubric

Scoring Rubric for Your Blog Entry

Score (%) In response to this item, the student---


90-100% demonstrates a thorough understanding of how to write and solve a problem from a given situation by correctly solving problems and clearly explaining procedure.


80-89% demonstrates a general understanding of how to write and solve the problem from a given situation by correctly solving problems and clearly explaining procedure with only minor errors or omissions.


65-79% demonstrates a partial understanding of how to write and solve the problem from a given situation by correctly performing a significant portion of the required task.



50-64% demonstrates minimal understanding of how to write and solve the problem from a given situation.


0% The response has given no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures as required by the task. Response may show only information copied from the question or another student.




* Taken from the Pennsylvania Department of Education Bureau of Assessment and Accountability 2009-2010