This exam was adminstered in June 2023. These answers were not posted until after the Independence Holiday weekend, well after the school year ednded.
More Regents problems.
June 2023
Part III: Each correct answer will receive 4 credits. Partial credit can be earned.
33. Graph f(x) = |x| + 1 and g(x) = -x2 + 6x + 1 on the set of axes below.
Based on your graph, determine all values of x for which f(x) = g(x).
Answer:
Put both of these equations into your graphing calculator and check the table of values. Make sure you either draw off the edge of the chart, or include arrows at your endpoints. And draw enough to show all the points of intersection. And remember to label at least one of the lines.
Your graph should look like this:
The values of x where f(x) = g(x) are 0 and 5.
Do NOT write coordinates. They asked for x values.
34. Jean recorded temperatures over a 24-hour period one day in August in Syracuse, NY. Her results
are shown in the table below.
Her data are modeled on the graph below.
State the entire interval over which the temperature is increasing.
State the three-hour interval that has the greatest rate of change in temperature.
State the average rate of change from hour 12 to hour 24. Explain what this means in the
context of the problem.
Answer:
Increasing means where there's a positive slope on the graph. The graph is increasing between hour 6 and hour 12. You could write it as [6,12] or 6 < x < 12, or just write it in words from 6 to 12. Whether it is an open or closed interval is debatable at this level, so either answer would've been accepted. College professors are free to argue otherwise in the comments, or to write to NY State and tell them that they are big doody heads.
The interval with the greatest rate of change would be the same as the one with the steepest slope. It is obvious from the graph, but you could measure the rise over run, that the hours from 9 to 12 have the greatest change. Note that it doesn't say positive change. However 9 to 12 is steeper in a positive direction than any of the negative slopes in the chart.
The average rate of change from hours 12 to 24 is the slope between (12,92) and (24,74).
(74 - 92) / (24 - 12) = -18/12 = -3/2.
In the context of this problem, the temperature was dropping 3 degrees every 2 hours.
35.Solve the following system of inequalities graphically on the set of axes below.
x < 3y + 6
Label the solution set S.
Is the point (4,-2) in the solution set?
Explain your answer.
Answer:
If you can graph the first inequality, which is in Standard Form, great! If not, rewrite it along with the second one in slope-intercept form so you can graph it.
3y > -2x - 6
y > -2/3 x - 2
-3y < -x + 6
y > 1/3 x - 2
Notes: Both lines will have y-intercept at (0,-2). The first inequality has a solid line with a negative slope. The second inequality will have a broken (or dashed) line and a positive slope. Both inequalities will be shaded above their lines.
Your graph will look like this. The S will go in the top section, which is shaded twice with the crisscross pattern. Remember to label at least one of the lines, and use the original inequalities, not the ones you put in your calculator.
No, (4,-2) in not in the solution set. It is not in the section label S. It is in a section that is only a solution to one of the inequalities. (Phrase it however you like.)
NOTE: If you make a graphing error, such as shading below the dashed line, then (4,-2) may be in the solution set of your graph. If so, then your answer will be Yes. You will not be penalized twice. (You will lose a point for the graphing error.)
36. Suzanna collected information about a group of ponies and horses. She made a table showing the height, measured in hands (hh), and the weight, measured in pounds (lbs), of each pony and horse.
Write the linear regression equation for this set of data. Round all values to the nearest hundredth.
State the correlation coefficient for the linear regression. Round your answer to the nearest hundredth.
Explain what the correlation coefficient indicates about the linear fit of the data in the context of the problem.
Answer:
Enter the data into Lists L1 and L2 on your calculator. Run the linear regression. If you didn't get values for r and r2, then you need to run the command DiagonsticsOn from the Catalog. You will need the r value.
When you run the linear regression, you will get a = 184.89 and b = 1706.07, to the nearest hundredth.
So the equation will be y = 184.89x - 1706.07.
The correlation coefficient is 0.99, which is the value of r to two decimal places.
The context is this: As the height of the horse increases, the weight of the horse increases.
If you said that there's a strong positive correlation, that would be true, but it wouldn't state the context of the problem.
End of Part III
How did you do?
More to come. Comments and questions welcome.
More Regents problems.
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