This exam was adminstered in June 2021. 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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June 2021 (v202)
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. Solve algebraically for y:
4(y - 3) < 4(2y + 1)
Answer:
The Distributive property is unnecessary but not incorrect if you use it. Since both sides have a multiplier of 4, the inequality can be divided by 4.
4(y - 3) < 4(2y + 1)
y - 3 < 2y + 1
-3 < y + 1
-4 < y
or y > -4
(rewriting to put the y on the left is not necessary, however, if you do, you must flip the inequality symbol)
26. Graph the function f(x) = | (1/2)x + 3 | over the invertal -8 < x < 0.
Answer:
If you are given an interval, DO NOT go beyond it, DO NOT use arrows. You should include solid (closed) circles at the two endpoints.
An absolute value graph is V-shaped. This one will have a slope on -1/2 on the left side of the vertex and +1/2 on the right side.
The vertex is (-6, 0) because the function can be written as f(x) = -1/2 |x + 6| + 0, with vertex (h, k) being (-6, 0).
You can use your graphing calculator, or you can just make a Table of Values by plugging in -8, -7, -6, -5, etc. Make sure you keep going until you hit the vertex.
27. The table below shows the height in feet, h(t), of a hot-air balloon and the number of minutes, t, the balloon is in the air.
The function h(t) = 30.5t + 8.7 can be used to model this table.
Explain the measning of the slope in the context of the problem.
Explain the meaning of the y-intercept in the context of the problem.
Answer:
The table is actually unnecessary for answering the questions because you already have the function that models it.
The slope, 30.5, represents how many feet the balloon is rising each minute.
The y-intercept, 8.7. represents the ballon's height from the ground before it started rising.
28. Factor x4 - 1 completely.
Answer:
Any time you see "factor completely", you can be pretty sure that there will be more than one step. Likewise, if you see an exponent of 4 (or generally anything above 2), you should suspect that there will be an extra step.
= (x2 + 1)(x2 - 1)
= (x2 + 1)(x + 1)(x - 1)
As you can see, the original expression was the Difference of Two Sqaures, which could be factored into two conjugates (such as (x+a)(x-a)). The square root of x4 is x2 because 2 is half of 4, and (x2)2 = x2 * x2 = x4.
However, x2 - 1 is also the Difference of Two Squares and can also be factored the same way. On the other hand, x2 + 1 has no real roots.
Fist, he subtracts 6.5 from 17.55 to get 11.05.
Next, he adds 11.05 and 17.55 to get 28.6.
He states that (5, 28.6) is a point on g(x).
Is he correct? Explain your reasoning.
29. Mike knows that (3, 6.5) and (4, 17.55) are points on the graph of an exponential function, g(x), andhe wants to find another point on the graph of this function.
Answer:
This is one of those times where if you say "Yes" or "No" without any explanation, you will not get any credit. You can't get a point for a 50-50 guess.
If you have the correct answer but answer but your reasoning isn't completely correct, you may only get one credit. And if you make a conceptual error (see below), you could get one credit as long as you are consistent.
No, Mike is not correct because he was trying to find slope of a straight line between the two points he had, but it is a linear function. This gives you 2 credits.
If you said, "Yes because Mike correctly calculated the slope between the two points and used that to find another point on the line", then you may have been awarded one point for the conceptual error of confusing a linear and an exponential function.
State the coordinates of the vertex.
30. Use the method of completing the square to determine the vertex of f(x) = x2 - 14x - 15.
Answer:
You can graph this to find the vertex in advance, or use the formula for the Axis of Symmetry. It may be easier to do if you already find the answer another way. You can get a point for stating the coordinates of the vertex if you find it using a different method than Completing the Square.
To Complete the square, keep in mind that the Axis of Symmetry is x = -b/(2a). You want to cut that middle coefficient in half. If you recall, (x + 1)2 = x2 + 2x + 1, and (x + 4)2 is x2 + 8x + 16. The middle term is always double and the last term must be a perfect square.
half of -14 is -7, so (x - 7) will be in our answer; (-7)2 = 49
f(x) + 49 = x2 - 14x + 49 - 15
f(x) + 49 = (x - 7)2 - 15
f(x) = (x - 7)2 - 64
The vertex is (7, -64)
Solve the formula C = 5/9 (F - 32) for F so that Josh can convert Celsius to Fahrenheit.
31. The temperature inside a cooling unit is measured in defrees Celsius, C. Josh wants to find out how cold it is in degrees Fahrenheit, F.
Answer:
Seriously, everyone should be able to do this, even outside of a math class. This is one of the most common examples given in math text books, and it's useful to know if you ever travel outside the U.S., or if you are from outside the U.S. and travel here.
9C = 5(F - 32)
9/5 C = F - 32
9/5 C + 32 = F
F = 9/5 C + 32
32. Solve 4w2 + 12w - 44 = 0 algebraically for w, to the nearest hundredth.
Answer:
Since they are asking for the nearest hundredth, you know that the equation isn't going to factor "nicely" and that you will have to use the quadratic formula. At least in this case, they didn't ask you to simplify the radical, which would have made it a more complicated problem.
There are two approaches you can take, and I will show them both because I am so Awesome, and modest, too.
w2 + 3w - 11 = 0
w = ( -3 + ( (-3)2 - 4(1)(-11) )(1/2) ) / (2(1))
w = ( -3 + ( 9 + 44 )(1/2) ) / 2
w = ( -3 + ( 53 )(1/2) ) / 2
w = 2.1400... or w = -5.1400...
w = 2.14 or w = -5.14
End of Part II
More to come. Comments and questions welcome.
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