June 2022 Algebra 1 Regents, Part III

This exam was adminstered in June 2022. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.

More Regents problems.

June 2022

Part III: Each correct answer will receive 4 credits. Partial credit can be earned. One mistake computational will lose 1 point. A conceptual error will lost half credit, or 2 points. It is sometimes possible to get 1 point for a correct answer with no correct work shown.


33. The graph below models the height of Sma's kite over a period of time.

Explain what the zeroes of the graph represent in the context of the situation.

State the time interval over which the height of the kite is increasing.

State the maximum height, in feet, that the kite reaches.

Answer:

The zeroes of the graph represent when the kite is on the ground. Its height is zero.

There are two intervals where the kite's height is only increasing and doesn't decrease.. They are 0 < t < 1/2 and 1 < t < 2.

The kites's maximum height is 60 feet, which happens at t = 2 minutes.

This problem doesn't require any work to be shown because it assumes that you are gathering information from the graph provided.

34. On the set of axes below, graph f(x) = x² - 1 and g(x) = 3^x.

Based on your graph, for how many values of x does f(x) = g(x)? Explain your reasoning.

Answer:

Graph and label both equations. Label the points of intersection.

According to the graph, there is only on value of x where f(x) = g(x), which is the point where the graphs intersect.

Note: if you make a graphing error, you should answer this question based on your graph. If your graph shows, e.g., 0 or 2 points of intersection, then you should answer that number and explain that your graph says so. You will lose credit for the graphing error but you will NOT lose credit for the final question if it is consistent with your graph.

35. An insurance agent is looking at records to be determine if there is a relationshop between a driver's age and percentage of accidents cause by speeding. The table below shows his data.

State the linear regression that models the relationshop between the driver's age, x, and the percentage of accidents caused by speeding, y. Round all values to the nearest hundredth.

State the value of the correlation coefficient to the nearest hundredth. Explain what this means in the context of the problem.

Answer:

Put the information into lists L₁ and L₂. Use the Linear regression fuction to find y = ax + b and the value of r.

To the nearest hundredth, a = -0.96, b = 64.74, and r = -0.98. (Ignore r². We don't need that.)

So y = -0.96x + 64.74 and r = -0.98.

In the context of this problem, there is a strong correlation between the age of the driver and the number of accidents caused by speeding.

36. Solve the system of inequalities graphically on the set of axes below. Label the solution set S. 2x + 3y < 9
2y > 4x + 6

Determine if the point (0,3) is a solution to this system of inequalities. Justify your answer.

Answer:

To use your graphing calculator, you need to rewrite the inequalities in slope-intercept form. Note that you must use the Original equations when labeling the graph.

2x + 3y < 9

3y < -2x + 9

y < -2/3 x + 3

2y > 4x + 6

y > 2x + 3

Remember that "<" means a dotted, dashed or broken line and you must shaded under the line. The line itself is NOT part of the solution.

The > means use a solid line and shade above the line. A solid line IS part of the solution set.

Make a large "S" in the section of the graph that is shaded twice.

The point (0,3) is not a solution because it is on the broken line and the broken line is not a part of the solution.

Note 1: If your graph is incorrect, answer according to what is on your graph if, for example, (0,3) is not on the dotted line.

Note 2: If you didn't draw the graph, you could still answer this last part algebraically for a point. Solving counts as justification. You must have justification -- "Yes" or "No" by itself will NOT get any credit.

End of Part III

How did you do?

More to come. Comments and questions welcome.

More Regents problems.

I also write Fiction! You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Preorder the softcover or ebook at Amazon. Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.