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 II: Each correct answer will receive 2 credits. Partial credit can be earned. One mistake (computational or conceptual) will lose 1 point. A second mistake will lose the other point. It is sometimes possible to get 1 point for a correct answer with no correct work shown.
25. Graph the function g(x) = √(x + 3) on the set of axes below.
Answer:
Put the equation in your graphing calculator. You will notice that the doman (the x values) start at x = -3, and that the function is undefined for x < -3. Only plot the points that have integer values, and only put an arrow on the right end.
The points you should plot are (-3,0), (-2,1), (1, 2), (6,3), and (13,4). There's a reason that they put the g(x) axis so far over to the left.
Your graph should look something like this:
In this example, a = 1, so the left side of the graph will have a slope of -1 and the right side will have a slope of 1. (h,k) is (-1,0) because there is a plus sign instead of a minus, and there is no k.
The graph will look like this:
26. The sixth-grade classes at West Road Elementary School were asked to vote on the location of
their class trip. The results are shown in the table below.
Determine, to the nearest percent, the percentage of girls who voted for Splashdown.
Answer:
To quote something I may have heard before, which applies to this problem specifically, boys don't matter.
You are only looking at the number of girls that voted for Splashdown and the total number of girls.
That would be 46 / (39 + 46 + 37) = 0.377..., which is 38%.
27. Solve the inequality -2/3 x + 6 > -12 algebraically for x.
Answer:
Isolate the variable. If you multiply or divide the inequality by a negative number, flip the sign around.
-2/3 x + 6 > -12
-2/3 x > -18
x < -18(-3/2)
x < 27
28. Determine the common difference of the arithmetic sequence in which a1 = 3 and a4 = 15.
Answer:
You can find the common difference the same way you'd find rate of change between the points (1,3) and (4,15).
(15 - 3) / (4 - 1) = 12 / 3 = 4.
You could also make buckets like 3, ___, ___, 15 and figure out what has to go in-between. They're 12 apart and it's three steps from 3 to 15.
There are many ways to imagine the problem with a similar method for solving.
Explain why A + B is irrational.
Explain why A * B is rational.
29. Given: A = √(363) and B = √(27)
Answer:
You don't have to get crazy wit the answers (even the irrational one! -- That's a joke.) Each question is worth 1 credit. You can keep it simple.
A + B is irrational because the sum of two irrational numbers will be irrational. You can write the sum, but make sure to add the "...". If you say anything else, don't say anything incorrect, like saying that it doesn't terminate without saying it doesn't repeat.
A * B is rational because they have a product of 99, which is a rational number.
This is true because 363 = (3)(11)(11) and 27 = (3)(3)(3), so the product will have 4 factors of (3) and two factors of (11). There is an even number of all the factors, so it is a perfect square. The square root of that product will have two factors of (3) and one factor of (11).
30. Use the quadratic formula to solve x2 - 4x + 1 = 0 for x.
Round the solutions to the nearest hundredth.
Answer:
The quadratic formula was specifically requested so any other method will lose half credit, which in this case is 1 credit.
Look at the image below:
x = 3.73 or x = 0.27
Don't forget to round up. That would be a silly way to lose 1 credit on a 2 credit problem after doing all that work.
31. Factor completely: 4x3 - 49x
Answer:
"Factor completely" almost always means multiple steps. The expression looks like a difference of perfect squares, but it isn't because the exponents are wrong. However, you can factor out one factor of x.
4x3 - 49x = x(4x2 - 49) = x(2x + 7)(2x - 7)
A difference of perfect squares will factor into two conjugates.
32. The function g is defined as
g(x) = x2 + 1, -2 < x < -2
Answer:
Plot the first expression for values of x that are less than -2, and plot the second expression only when x is between -2 and 2, inclusive.
It should look like this:
Some things to note: The absolute value graph must end with an OPEN CIRCLE because it is a boundary and it is not a part of the graph of the solution. The left side should have an arrow because the domain goes to negative infinity. There should be NO ARROWS on the second part because it is a specific range with a starting and an ending point. Both of those should be closed circles, without arrows.
End of Part II
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