This exam was adminstered in June 2023. These answers were not posted until after the Independence Holiday weekend, well after the school year ednded.
More Regents problems.
June 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. Solve the equation algebraically for x:
-2.4(x + 1.4) = 6.8x - 22.68
Answer:
You have the choice of using the Distributive Property first, or dividing both sides of the equation by -2.4. In this case, dividing by -2.4 will lead to infinite decimals, and you don't want to round in the middle of the problem, so let's use the Distributive Property.
-2.4(x + 1.4) = 6.8x - 22.68
-2.4x - 3.36 = 6.8x - 22.68
19.32 = 9.2x
x = 2.1
26. The function f(x) is graphed on the set of axes below.
State the zeroes of f(x).
Explain your reasoning.
Answer:
The zeroes of the function are the values of x that make f(x) = 0. In other words, it's the values on the x-axis where the graph crossing the x-axis (which is the line y = 0 or f(x) = 0).
The zeroes are -2, 2, and 3.
I gave a reason above, but you could write something like those are the values of the x-intercepts.
Do NOT write points/coordinates, such as (-2,0). That isn't what they asked for.
The number 12 is the y-intercept. It is not a correct answer.
A more interesting question -- and the one that I expected -- was to give a possible equation for this function.
The definition of the function is f(x) = a(x + 2)(x - 2)(x - 3), but what is the value of a?
When x = 0, according to the graph f(0) = 12. And (0 + 2)(0 - 2)(0 - 3) = 12. So a = 1.
So the function is f(x) = (x + 2)(x - 2)(x - 3).
27. Breanna creates the pattern of blocks below in her art class.
A friend tells her that the number of blocks in the pattern is increasing exponentially.
Is her friend correct?
Explain your reasoning
Answer:
The friend is not correct. It is increasing by 2, a constant rate of change, or a common difference, which means it's a linear pattern not and exponential one.
28. The data set 20, 36, 52, 56, 24, 16, 40, 4, 28 represents the number of books purchased by
nine book club members in a year.
Construct a box plot for these data on the number line below.
Answer:
You can use the calculator to sort the data, and even have it give you the Five Number Summary that you need to construct the box-and-whisker plot.
If you don't know how to do that, you can do it by hand since there are only 9 data items.
The numbers is order are:
4, 16, 20, 24, 28, 36, 40, 52, 56
The mminimum number is 4 and the maximum number is 56. There are nine numbers, so the fifth number is the one in the center, the median, which is 28.
There are four numbers less than the median. Q1 is halfway between the 2nd and 3rd numbers. Halfway between 16 and 20 is 18. Likewise, Q3 is halfway between the 7th and 8th numbers. Halfway between 40 and 52 is 46.
So the Five-Number Summary, which you should write down, is: Min = 4, Q1 = 18, Med = 28, Q3 = 46 and Max = 56.
Plot points above these positions on the number line. Note that the scale has already been set. Then draw a box that goes through Q1 and Q3 and add a vertical line through the median. Finally, draw the two whiskers from Q1 to the Min and Q3 to the Max.
Your answer should look like this:
29. Given: A = x + 5 and B = x2 - 18
Express A2 + B in standard form.
Answer:
Substitute each expression. Square the binomial (x + 5). Combine like terms. Rewrite in Standard form with the term with the highest exponent going first.
(x + 5)2 + x2 - 18
x2 + 10x + 25 + x2 - 18
2x2 + 10x + 7
That's it.
30. The two relations shown below are not functions.
Explain how you could change each relation so that they each become a function.
Answer:
Important: they don't want you to just tell them why it is not a function. You MUST state something that would fix the relation, making it a function.
In Relation 1: you could make (4,20) an open circle, or you could make (4,30) an open circle, or you could even remove the entire middle segment from 2 < x < 4.
In Relation 2: you CANNOT say "change one of the -4's to another number". That is not specific enough. Plus, it isn't entirely true. There are other numbers that you are not allowed to change it to if you want the result to be a function.
In Relation 2, you could say, remove (-4, 0), or change (-4,4) to (-3,4), or something specific like that. If you change the x value for x = -4, do NOT change it to a number that is already there.
31. Factor completely: 2x2 + 16x - 18
Answer:
"Factor completely" almost always means multiple steps. Remove the Common Factor (2) from each term and then factor the trinomial into two binomials.
2x2 + 16x - 18 = 2(x2 + 8x - 9) = 2(x + 9)(x - 1)
Your final answer will have three terms.
32. Solve 3d2 - 8d + 3 = 0 algebraically for all values of d, rounding to the nearest tenth.
Answer:
The fact that it has to be rounded to the nearest tenth usually means that you want to use the Quadratic Formula because you might not be able to factor it otherwise.
These numbers look like they would work out with the "borrow and payback" method, or the reverse box method, or whatever you may have heard it called. However, they will not. You need to factors of +9 with a sum of -8. You can't do that with integers. So let's use the Quadratic Formula.
Follow along on the image below:
Rounded, the solutions are d = 2.2 and d = 0.5.
End of Part II
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