January 2023 Algebra 1 Regents, Part III

This exam was adminstered in January 2023. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.

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January 2023

Part III: Each correct answer will receive 4 credits. Partial credit can be earned. One computional or graphing mistake will lose 1 point. A conceptual error will lose 2 credits.


33. Anessa is studying the changes in population in a town. The graph below shows the population over 50 years.

State the entire interval during which the population remained constant.

State the maximum population of the town over the 50-year period.

Determine the average rate of change from year 30 to year 40.

Explain what your average rate of change means from year 30 to year 40 in the context of the problem.

Answer:

Each question is worth one credit, basically.

The population remained constant from year 20 to year 30.

The maximum population was 10,000 (during years 20 to 30).

The average rate of change from year 30 to 40 was -6000/10 or -600 people per year.

The town lost 600 people per year from year 30 to year 40.

34. The table below shows the number of math classes missed during a school year for nine students, and their final exam scores.

Write the linear regression equation for this data set. Round all values to the nearest hundredth.

State the correlation coefficient for your linear regression. Round your answer to the nearest hundredth.

State what the correlation coefficient indicates about the linear fit of the data.

Answer:

Put all the data in your graphing calculator and run a linear regression. Make sure you have DiagnosticsOn.

The equation, when rounded, is y = -2.81x + 97.55

The correlation coefficient is r = -.97.

The correlation coefficient indicates that there is a strong, negative relationship.

35. A fence was installed around the edge of a rectangular garden. The length, l, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.

Write a system of equations or write an equation using one variable that models this situation.

Determine algebraically the dimensions, in feet, of the garden.

Answer:

If the length if 5 less than 3 times the width, then l = 3w - 5. That's just translating the sentence.

The perimeter of a rectangular fence is P = 2L + 2W.

2(3w - 5) + 2w = 90

2(3w - 5) + 2w = 90
6w - 10 + 2w = 90
8w = 100
w = 12.5

The width is 12.5 and the length is 3(12.5) - 5 = 32.5.

Again, don't let fractions and decimals throw you off.

36. Given: 3y - 9 < 12
y < -2x - 4

Graph the system of inequalities on the set of axes below.

State the coordinates of a point that satisfies both inequalities. Justify your answer.

Answer:

Notice that the first inequality DOES NOT have an x term. You will graph a horizontal line after you rewrite it to isolate y.

3y - 9 < 12
3y < 21
y < 7

When graphing inequalities, remember that "less than or equal to" gets a solid line, and "less than" gets a broken or dashed line. Any point on the dashed line is NOT part of the solution. Don't pick any of those points for the final part of the question, especially not the point where the two lines meet.

Your final graph should look like the one beow. Make sure you label at least one of the lines. And add an "S" to the area that is the solution.

One point that satisfies both conditions is (-10,0) because it's in the double-shaded section of the graph.

You can also "justify" your answer by plugging it into both inequalites and showing that they are true statements.

End of Part III

How did you do?

More to come. Comments and questions welcome.

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