Friday, November 12, 2021

Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Algebra 2/Trigonometry Regents, January 2012

Part I: Each correct answer will receive 2 credits.

25. Which function is one-to-one?

1) f(x) = |x|
2) f(x) = 2x
3) f(x) = x^2
4) f(x) = sin x

Answer: 2) f(x) = 2x

In a function, every x has exactly one y. In a one-to-one function, every y also has only one x.

The inverses to an absolute-value, quadratic or sine function will not be functions. The outputs have multiple inputs.

26. If p varies inversely as q, and p = 10 when q = 3/2, what is the value of p when q = 3/5?

1) 25
2) 15
3) 9
4) 4

Answer: 1) 25

If p varies inversely as q then p1q1 = p2q2

(10)(3/2) = p2(3/5)

p2 = (10)(3/2)(5/3) = 25

27.Which equation is graphed in the diagram below?

1) y = 3 cos(π/30 x) + 8
2) y = 3 cos(π/15 x) + 5
3) y = -3 cos(π/30 x) + 8
4) y = -3 cos(π/15 x) + 5

Answer: 4) y = -3 cos(π/15 x) + 5

The minimum for the graph is 2 and the maximum is 8, so the midline is 5. So the equation will end with "+ 5". Eliminate Choices (1) and (3).

The value for Cos(0) is 1, which is the maximum for y = cos x. The graph starts at a minimum, which means that the function starts with -3 not 3. Choice (4) is the solution.

Additionally, the period of a cosine graph is 2π. This graph has a period of 30 (not 30π), and 2π/30 = π/15, which would have eliminated Choices (1) and (3).

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.

I also write Fiction!

You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below.
Preorder the softcover or ebook at Amazon.

Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides.
Available in softcover or ebook at Amazon.

If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

No comments: