This exam was adminstered in August 2022. 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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August 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.
Explain what might have happened in the interval between D and E State how many miles per hour the bus was traveling during this interval. What was the average rate of speed, in miles per hour, for Thomas's entire bus trip?
33. Thomas took a 140-mile bus trip to visit his grandparents. His trip is outlined on the graph below.
Answer:
Between D and E, the distance was unchanged. The bus might have stopped moving for 1/2 hour.
The interval where the bus traveled the fastest would have the steepest slope. The slope of AB is 20/.5 = 40. The slope of CD is 90/1.5 = 60. The slope of EF is 30/1 = 30. Between C and D the bus went the fastest.
The bus was moving at 60 mph during this time. (Note: if you just counted boxes to find the steepest slope, then you need to work it out here.)
The entire trip was 140 miles in 4 hours, and 140/4 = 35 miles per hour.
Based on your graph, state one value of x that satisfies f(x) = g(x). Explain your reasoning.
34. Graph f(x) and g(x) on the set of axes below.
g(x) = 1/2 x + 1
Answer:
Graph and label both equations.
One point of intersection is (4,3). The point is on both lines, so it is a solution to both equations. So for x = 4, f(4) = g(4) = 3.
Make sure you state the value of x. Don't just give the intersection point. This sounds silly, but it's important. It's what the question asked.
The other point looks like x = 1/2, but unless you solve it algebraically, or check it in the calculator, don't assume that it is just from eyeballing the graph. That said, x = 1/2 is, in fact, the other solution.
35. A store sells grapes for $1.99 per pound, strawberries for $2.50 per pound, and pineapples for $2.99 each. Jonathan has $25 to buy fruit.
He plans to buy 2 more pounds of strawberries than grapes. He also plans to buy 2 pineapples.
If x represents the number of pounds of grapes, write an inequality in one variable that models this scenario.
Determine algebraically the maximum number of whole pounds of grapes he can buy.
Answer:
Let x = # of pounds of graphs, and 1.99x = the cost of x pounds of grapes. Let x + 2 get the number of pounds of strawberries he buys, and 2.50(x + 2) = the cost of x + 2 pounds of strawberries. He cannot spend more than $25.
1.99x + 2.50(x + 2) + 2(2.99) < 25.00
1.99x + 2.50x + 5.00 + 5.98 < 25.00
4.49x + 10.98 < 25.00
4.49x < 14.02
x < 3.12...
The maximum number of whole pounds of grapes he can buy is 3.
Label the solution set S.
36. Solve the system of inequalities graphically on the set of axes below.
1 > 2x - y
Is the point (-5,0) in the solution set? Explain your answer.
Answer:
First, rewrite these inequalities so that they are more useful. That could be Standard Form, if you like, or Slope-Intercept. The latter can be put into a calculator.
y + 3x < 5 can be rewritten as y < -3x + 5.
1 > 2x - y is the same as y > 2x - 1. (Add y to each side, then subtract 1 from each side.)
Draw and label the lines.
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.
Your graph should look similar to this:
The point (-5, 0) is in the solution set because it's in the section with the "S".
Note 1: If your graph is incorrect, answer according to what is on your graph if, for example, (-5,0) is not in the section shaded twice, you would say "No".
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. If you substitute (-5,0) into each inequality, you will have two true statements, which means that it is a solution to the system.
End of Part III
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