Student Answer Response Sheet

Student Name: ______Student ID #: ______School Name: ______

ALGEBRA 1 QUARTER 1 QLM

PART 1:

1) a) Write an algebraic expression to model the following phrase: the price of a meal plus a 15% tip for the meal.

b) What could the expression represent, including units?

c) What if the tip is 20% instead of 15% and 3 people are sharing the cost evenly. How can you represent the amount each person pays with a simplified algebraic expression? Identify the units for the expression.

2) Why is the expression not the correct factored form for

3) Given the expression: a) What is the largest coefficient?

b) How many terms are in the polynomial?

4) Simplify and justify steps: Given:

4(a + 2b) = 3(2a – b) + 6a – 7b

4a +8b – 6a + 3b + 6a – 7b

4a – 6a + 6a + 8b + 3b – 7b

a(4 – 6 + 6) + b(8 + 3 – 7)

a(4) + b(4) 4a + 4b

Baseball Math 5) A pitcher’s Winning Percentage is determined by dividing the number of games the pitcher won by the sum of the number of games won and lost. If Randy Johnson has won 18 games and lost 6 games, what is his Winning Percentage? (Write the answer to the nearest thousandth.)

6) A player’s Fielding Average is determined by adding the number of putouts and assists the player gets, divided by the total number of putouts, assists, and errors the player has. If Nomar Garciaparra has 185 putouts, 11 assists, and 4 errors, what is his Fielding Average? (Write the answer to the nearest thousandth.)

PART 2:

1. Acceleration is the measure of how fast a velocity is changing. The formula for

acceleration is a = Vf − Vi, where a represents the acceleration rate, Vf is the final t

velocity, Vi is the initial velocity, and t represents the time in seconds.

a. Solve the formula for Vf.

b. What is the final velocity of a runner who is accelerating at 2 feet per second squared for 3 seconds with an initial velocity of 4 feet per second?

2. Deandre's doctor must decide how much medicine he needs for each dosage. The dosage (d), in milligrams, depends on Deandre's body mass (m), in kilograms. The formula below is used to calculate the dosage of his medicine.

d = 0.1m2 + 5m a. Explain what the variables “d” and “m” represent within the context of the problem. Underline the textual evidence that supports your response.

b. Explain what 80 kilograms means within the context of the problem. Circle the textual evidence that supports your response.

c. Which variable are you required to solve for? Box the textual evidence that supports your response.

d. Determine the dosage needed, in milligrams, if Deandre's body mass is 80 kilograms.

3. Solve for “x”: - (x – 3) = 2 (x – 5) + 4x. 5 4

4. The following is a student solution to the inequality

There are two mathematical errors in the student’s work. Identify at what step each mathematical error occurred and explain why they are mathematically incorrect.

a) The first mathematical error occurred going from line ____ to line ____. The

student should have ______

b) The second mathematical error occurred going from line ____ to line ____. The student should have ______

5. A high school is having a talent contest and will give different prizes for the best five acts in the show. First place wins the most money, and each place after that wins $50 less than the previous place.

Part A: Create an equation that can be used to determine the total amount of prize money based on the value of the first place prize. Enter the model in the space provided below.

Part B: The talent contest has a total of $1000 in prize money. Solve the equation from Part A to determine the amount of money that exists for each of the five prizes. Enter your answer(s) and calculations in the space provided below.

Part C: Reason abstractly and quantitatively by explaining what your solution(s) means within the context of the problem.

Part D: Use validation methods to justify that your solutions are correct. Use may use words, symbols, or both in your response

PART 3: 1) The Customer A certain business keeps a database of information about its customers. a) Let C be the rule which assigns to each customer shown in the table his or her home phone number. Is C a function? Explain your reasoning.

Customer Name Home Phone Number Heather Baker 3105100091 Mike London 3105200256 Sue Green 3234132598 Bruce Swift 3234132598 Michelle Metz 2138061124

b) Let P be the rule which assigns to each phone number in the table above, the customer name(s) associated with it. Is P a function? Explain your reasoning.

c) Explain why a business would want to use a person's social security number as a way to identify a particular customer instead of their phone number.

2) Suppose f is a function.

a.) If 10=f(−4), give the coordinates of a point on the graph of f. b.) If 6 is a solution of the equation f(w)=1, give a point on the graph of f.

3) John makes DVDs of his friend’s shows. He has realized that, because of his fixed costs, his average cost per DVD depends on the number of DVDs he produces. The cost of producing x DVDs is given by C(x)=2500+1.25x. a) John wants to figure out how much to charge his friend for the DVDs. He’s not trying to make any money on the venture, but he wants to cover his costs. Suppose John made 100 DVDs. What is the cost of producing this many DVD’s? How much is the cost per DVD? b) John is hoping to make many more than 100 DVDs for his friends. Complete the table showing his costs at different levels of production.

Number of 0 10 100 1000 10000 100000 1000000 DVDs Total Cost Cost per DVD c) Explain why the average cost per DVD levels off.

d) Find an equation for the average cost per DVD of producing xDVDs.

4) 4a)

4b) Statements Answers The car is not moving. Graph ______The car is traveling at a steady speed. Graph ______and Graph ______

Graph Equation Table Rule

D b) Graph A c) Graph B

d) Graph C

e) Graph D

6) a) Best Print C =

b) c) Show how Susie may have calculated C and t.

Scoring Rubric / Success Criteria Conceptual Understanding 42 Total Points Part I: Seeing Structure in Expressions 9 Score: _____ (1a, 1b, 1c, 2, 3a, 3b, 4, 5, 6) One point for each part of each problem Part II: Reasoning With Equations and 13 Score: _____ Inequalities (1a, 1b, 2a, 2b, 2c, 2d, 3, 4a, 4b, 5a, 5b, 5c, 5d) One point for each part of each problem Part III: Interpreting Functions 20 Score: _____ (1a, 1b, 1c, 2a, 2b, 3a, 3b, 3c, 3d, 4a, 4b, 5a, 5b, 5c, 5d, One point for each part of each problem 5e, 6a, 6b, 6c, 6d) Execution of Mathematical 12 Total Points Practices MP1: Make sense of a problem and 2 Score: _____ persevere in solving them

Analyze and explain the meaning of the problem one point per bullet Actively engage in problem solving (Develop, carry out, and refine a plan) MP2: Reason abstractly and quantitatively 3 Score: _____ Represent a problem with symbols one point per bullet Explain their thinking

Examine the reasonableness of their answers/calculations MP3: Construct a viable argument and 1 Score: _____ critique the reasoning of others

Justify solutions and approaches MP4: Model with mathematics 2 Score: _____ Use representations to solve real life problems one point per bullet Apply formulas and equations where appropriate MP6: Attend to precision 3 Score: _____ Calculate accurately and efficiently

Explain their thinking using mathematics vocabulary one point per bullet

Use appropriate symbols and specify units of measure MP7: Look for and make use of structure 1 Score: _____ Use knowledge of properties to efficiently solve problems Final Score ____/54