Algebra 1 State Test Practice

Zeros and the minimum of the graph of a quadratic equation

2/28/2015

In the xy-coordinate plane, the graph of the equation y = 3x² - 12x - 36 has zeros at x = a and x = b,
where a < b. The graph has a minimum at (c , -48). What are the values of a, b, and c?
A.) a = 2, b = 4, and c = 2
B.) a = -2, b = 6, and c = 2
C.) a = -3, b = 3, and c = 0
D.) a = 3, b = 6, and c = 2

Zeros of a function

2/27/2015

Representing with equations

2/22/2015

Part A
Create a model that can be used to determine the total amount of prize money based on the amount of the first prize.

Part B
The talent contest has a total of $1,000 in prize money. What is the amount of money for each of the five prizes? Show your work.

Use the information provided to answer Part A and Part B.

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.

Creating linear models

2/19/2015

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Use the information provided to answer Part A and Part B.

The Water Watch program is encouraging customers to reduce the amount of water they use each day. The program is selling low-flow showerheads, which use 2 gallons of water per minute, for $54 each.

A family currently has a showerhead that uses 5 gallons of water per minute and is considering replacing it with one of the low-flow showerheads. The family uses the shower an average of 20 minutes per day and pays $0.002 per gallon of water.

Part A
Create a model that can be used to determine the cost savings, in dollars, for the family to purchase and use a low-flow showerhead in terms of the number of days.

Then determine the number of days at which the family will start saving money. Justify your answer in terms of the context.

Part B
One year after the low-flow showerhead is purchased, the cost of water increases by 5%. Create a new model to determine the cost savings, in dollars, with the increase in the cost of water.

Use your model to determine the number of days at which the family after the increase in the cost of water. Justify your answer.

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Finding solutions to a quadratic equation

2/18/2015

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What is one solution of the equation x² - 21.75x = -15.75?

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Examine solutions to an absolute value equation

2/17/2015

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Let |x| + |y| = c, where c is a real number.

Determine the number of points that would be on the graph of the equation for each given case:
Case 1: c < 0
Case 2: c = 0
Case 3: c > 0

Justify your answers.

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Percent application problem

2/16/2015

Phil and Matt made cookies for a fundraiser at their high school.
- Phil made 25% more cookies than Matt
- The cookies sold for $0.25 each
- After the sale, 25% of the combined total of their cookies remained.

Part A
Create an equation to represent the total amount of money that Matt and Phil earned at the fundraiser based on the number of cookies Matt made. Explain how you determined your equation.

Part C
Next year Phil and Matt may sell the cookies for $0.50 each. They plan to make the same total number of cookie, but they predict that they will only sell 70% of them given the price increase. Based on their prediction, should Phil and Matt raise the price of the cookies? Justify your answer.

Part B
Phil and Matt made a total of $72.00 selling the cookies. How many cookies did Phil make and how many cookies did Matt make? Show your work.

Using direct variation

2/14/2015

Consider the three points (-4,-3) , (20,15) , and (48,36).

Part A
Which points are on the same line that passes through (-4,-3) , (20,15) , and (48,36)?
Select all that apply.

A.) (-8,-6) B.) (-2,-1) C.) (0,0)
D.) (4,3) E.) (6,8)

Part C
Do the points on the line y = 3x - 2 have a constant ratio of the y-coordinate to the
x-coordinate for any point on the line except for the y-intercept? Explain your answer.

Part B
Use the information from Part A to explain why the ratio of the y-coordinate to the x-coordinate is the same for any point on the line except the y-intercept.

Explain why this is not true for the y-intercept.

Interpret the average rate of change of a function

2/3/2015

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At the beginning of an experiment, the number of bacteria in a colony was counted at time t = 0. The number of bacteria in the colony t minutes after the initial count is modeled by the function b(t) = 4(2)^t. Which value and unit represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment? Select all that apply.
A.) 24.0 E.) bacteria
B.) 24.8 F.) minutes
C.) 25.4 G.) bacteria per minute
D.) 25.6 H.) minutes per bacteria

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Algebra 1 State Test Practice Archives