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 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 f(x) = |x + 1| on the set of axes below.
Answer:
You can put this in your calculator, but this is a fairly simple one. An absolute value funtion written in the form
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 table below shows the value of a particular car over time.
Determine whether a linear or exponential function is more appropriate for modeling this data.
Explain your choice.
Answer:
A linear function would be decreasing by approximately the same amount of money over time. An exponential function would be decreasing by approximately the same percentage or ratio over time.
10550 / 20000 = 0.5275, 5570 / 10550 = 0.52796..., 2940 / 5570 = 0.5278...
10550 - 20000 = -9450, 5570 - 10550 = -4980, 2940 - 5570 = -2630
An exponentional function is more appropriate because the value decreases to about 53% of the prior value every five years. That is, it is decreasing by 100% - 53% = 47%.
27. Is the product of √(8) and √(98) rational or irrational? Justify your answer.
Answer:
You can multiply and take the square root, or you can use factor trees.
√(8) * √(98) = √(784) = 28, which is a Rational number.
√(8 * 98) = √(2 * 2 * 2 * 2 * 7 * 7) = √( (2 * 2) * (2 * 2) * (7 * 7) ) = 2 * 2 * 7 = 28, which is a Rational number.
28. The ages of the last 16 United States presidents on their first inauguration day are shown in the table below.
Determine the interquartile range for this set of data.
Answer:
If you put this data into a list in your calculator, make sure you write down the Five Number Summary as your "work" for the problem.
To find the median and the quartiles, the data must be first put into order.
There are 16 pieces of data, so the median is between the 8th and 9th numbers, 54 and 55. The median is 54.5.
Q1 is between the 4th and 5th numbers, which are both 51, so Q1 = 51. Q3 is between the 12th and 13th numbers, which are 61 and 62, so Q3 = 61.5.
IQR = Q3 - Q1 = 61.5 - 51 = 10.5.
The cost of one pound of bananas, b, is twice as much as one pound of grapes.
Write an equation that represents the cost of one pound of bananas in terms of the cost of one
pound of apples.
29. The cost of one pound of grapes, g, is 15 cents more than one pound of apples, a.
Answer:
Rewrite the sentences as equations. The word "is" is your equal sign.
g = 15 + a
b = 2g
So b = 2(a + 15) = 2a + 30
Either of those two expressions should be acceptable after "b =".
Describe the transformation that maps f(x) onto g(x).
30. A student is given the functions f(x) = (x + 1)2 and g(x) = (x + 3)2.
Answer:
The +1 moves (translates) the function 1 unit to the left of the parent function (not listed), and the +3 moves the function 3 units to the left of the parent function.
So transformation that maps f(x) onto g(x) is a translation two units to the left.
31. Solve 3x2 - 5x - 7 = 0 algebraically for all values of x, rounding to the nearest tenth.
Answer:
"To the nearest tenth" tells you that it's not likely to be an integer and could be an irrational answer. If that is the case, do not answer in radical form. Convert it to a decimal and evaluate.
If you multiply 3*(-7), you get -21. There are no factors of -21 with a sum of -5, so you need to use the Quadratic Formula. See below:
x = 5/6 + &radic(109)/6 = 2.57... or x = 5/6 - &radic(109)/6 = -0.90...
x = 2.6 or x = -0.9
32. Factor completely: 3y2 - 12y - 288
Answer:
The words "factor completely" usually mean that there will be more than one step. When you are finished, look again to make sure you actually are finished.
3y2 - 12y - 288
3(y2 - 4y - 96)
3(y + 8)(y - 12)
End of Part II
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