This exam was adminstered in June 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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June 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. Is the product of √(1024) and -3.4 rational or irrational? Explain your answer
Answer:
The product of √(1024) and -3.4 is -108.8, which is a rational number. All numbers with terminating decimals are rational.
If you know binary, you might have recognized that 1024 is 210. The square root of 210 is 25, which is a rational number. The product of two rational numbers is always rational.
Note that you didn't actually have to have the product written to get full credit, so long as you stated that the radical was a rational number and the product was rational.
26. Describe the tranformations performed on the graph of f(x) = x2 to obtain the graph of g(x) when g(x) = (x - 3)2 - 4.
Answer:
The transformation is 3 units to the right and 4 units down.
If you weren't sure, you could have put both equations in your graphing calculator and looked at the graphs and the tables of values.
The vertex of f(x) is (0,0), and the vertex of g(x) is (3,-4).
27. The total profit earned at a garage sale during the first five hours is nodeled by the graph shown below.
Determine the average rate of change, in dollars per hour, over the interval 1 < x < 4.
Answer:
Look at the dollar values for x = 1 and x = 4. The two points are (1, 40) and (4, 100).
The average rate of change is (100 - 40) / (4 - 1) = 60 / 3 = 20
$20 per hour.
28. Subtract 3x(x - 2y) from 6(x2 - xy) and express your answer as a monomial.
Answer:
A monomial is one term. This means that something in the problem is going to cancel because the terms are not alike.
When subtracting, remember that the "from" value goes FIRST.
6(x2 - xy) - 3x(x - 2y)
6x2 - 6xy - 3x2 + 6xy
3x2
If you made one algebraic or arithmetic mistake, you could still get one credit. The word "monomial" was a big hint though.
State the domain of the funtion. State the range of the function.
29. A function is graphed on the set of axes below.
Answer:
The domain of the function refers to all the possible x values. It is all real numbers, from negative infinity to positive infinity.
The range of the function refers to all the possible y values. It is y > 3. The range cannot be any value less than 3, which is the minimum of the function.
30. Solve 6x2 + 5x - 6 = 0 algebraically for the exact values of x.
Answer:
Usually when they do to the trouble to state "exact values", it generally means that they don't want you to round any decimal solutions. This might mean the answer is irrational or that there is a repeating decimal.
If you aren't sure how to factor, you can use the Quadratic Formula.
I like using the Reverse Area model, and then Factor by Grouping. Full disclosure: I would not have said that 10 years ago. We live and learn and grown.
Using the standard form, ax2 + bx + c = 0, multiply (a)(c) = (6)(-6) = -36.
What two factors of -36 have a sum of +5? A quick check of the factors of -36 will give you -9 and +4.
So 6x2 + 5x - 6 = 6x2 + 9x - 4x - 6
6x2 + 9x - 4x - 6 = 0
3x(2x + 3x) - 2(2x + 3) = 0
(3x - 2)(2x + 3) = 0
(3x - 2) = 0 or (2x + 3) = 0
3x = 2 or 2x = -3
x = 2/3 or x = -3/2
You must write 2/3 as a fraction or use notation to indicate that it is a repeating decimal. If you write x = .7 or x = .67, etc., you would lose a point.
Quadratic Formula solution will be added soon.
31. Factor the expression x4 - 36x2 completely.
Answer:
When you see "completely", that's a hint that there's going to be more than one step.
Factor the GCF, which is x2.
x4 - 36x2 = x2(x2 - 36)
Now there is a difference of perfect squares to deal with. (You could have done this first if you wanted to.)
x2(x2 - 36) = x2(x + 6)(x - 6)
32. Determine the exact values of x2 - 8x - 5 = 0 by completing the square.
Answer:
If you use a different method and get the correct answer, you will only receive 1 credit. Again, "exact values" means that you shouldn't round any decimals, and should leave irrational numbers in radical form.
x2 - 8x - 5 = 0
Half of -8 is -4, and (-4)2 is 16, so add a zero pair of (16 - 16) to the left side of the equation.
x2 - 8x + 16 - 16 - 5 = 0
Reduce the perfect square.
(x - 4)2 - 21 = 0
(x - 4)2 = 21
x - 4 = + √(21)
x = 4 + √(21)
End of Part II
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