Wednesday, May 18, 2022

Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2011)



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 2011

Part I: Each correct answer will receive 2 credits.


21. For which equation does the sum of the roots equal −3 and the product of the roots equal 2?

1) x2 + 2x - 3 = 0
2) x2 - 3x - 2 = 0
3) 2x2 + 6x + 4 = 0
4) 2x2 - 6x + 4 = 0

Answer: 3) 2x2 + 6x + 4 = 0


The product of the roots is C/A, and the sum is -B/A.

Choice (1) has a sum of -3/1 = -3. Eliminate Choice (1).

Choice (2) has a sum of -2/1 = -2. Eliminate Choice (2).

Choice (3) has a sum of 4/2 = 2, and a product of -6/2 = -3. This is the correct choice.

Choice (4) has a sum of 4/2 = 2, and a product of -(-6)/2 = 3. Eliminate Choice (4).





22. The expression (2x + 4) / (√(x + 2)) is equivalent to


Answer: 4) [See Image]


See image.

Multiply by &radic(x+2)/&radic(x+2). Then factor (2x + 4)/(x + 2) = 2.





23. Which equation is sketched in the diagram below?



1) y = csc x
2) y = sec x
3) y = cot x
4) y = tan x

Answer: 1) y = csc x


The U shaped graphs are secant and cosecant, not tangent and cotangent. Eliminate Choices (3) and (4).

Sec x = 1 / cos x and csc x = 1 / sin x.

At x = 0, cos x = 1 and sin x = 0. That means that csc x is undefined at 0, as shown in the graph.

The correct choice is (1).





24. The expression log5(1/25) is equivalent to

1) 1/2
2) 2
3) -1/2
4) -2

Answer: 4) -2


If x = log5(1/25) then 5x = 1/25.

So x = -2, which is Choice (4).




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: