Thursday, January 13, 2022

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

Part I: Each correct answer will receive 2 credits.


25. What is the radian measure of the smaller angle formed by the hands of a clock at 7 o’clock?

1) π/2
2) 2π/3
3) 5π/6
4) 7π/6

Answer: 3) 5π/6


The smaller angle formed would be 5/12ths of the clock. The number of radians in the entire clock is 2π. (Note that the question asks smaller, so do not use 7/12.)

Multiply 5/12 * 2π = 10π/12 = 5π/6





26. What is the coefficient of the fourth term in the expansion of (a − 4b)9?

1) -5,376
2) -336
3) 336
4) 5,376

Answer: 1) -5,376


The fourth term would be the x6 term. (x9, x8, x7, x6.) Note that 9 - 6 = 3. Three is an offset -- it's 4 - 1 -- and will be important.

The ninth row of Pascal's triangle starts 1, 9, 36, 84. And 9C3 = 84.

Since the first term has (-4)0, then the fourth term will have (-4)3, which is -64.

So the coefficient will be (84)(-64) = -5,376, which is Choice (1).





27. Samantha constructs the scatter plot below from a set of data.
Based on her scatter plot, which regression model would be most appropriate?

1) exponential
2) linear
3) logarithmic
4) power

Answer: 3) logarithmic


The data looks mostly linear, except for the initial points dragging it down.

If you draw a curve through the data, it would look like a logarithmic graph, which is Choice (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:

Post a Comment