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 II: Each correct answer will receive 2 credits. Partial credit is available.


28. Express the product of (1/2 y² - 1/3 y) and (12y + 3/5) as a trinomial.

Answer:

Use FOIL or the Area model or the Distributive Property. Whichever method you like best and are most comfortable with.

(1/2 y² - 1/3 y) (12y + 3/5)

= 6y³ + 3/10 y² - 4y² - 1/5 y

= 6y³ - 3 7/10 y² - 1/5 y

29. In a study of 82 video game players, the researchers found that the ages of these players were normally distributed, with a mean age of 17 years and a standard deviation of 3 years. Determine if there were 15 video game players in this study over the age of 20. Justify your answer.

Answer:

If the mean is 17 and the standard deviation is 3 years, then 20 is 1 standard deviation above the mean.

That means that if there's a normal distribution then 9.2 + 4.4 + 1.7 + .5 + .1 = 15.9% of the players.

82 * 15.9 = 13.

There were not 15 video game players over the age of 20.

30. Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is −27.

Answer:

The sum of the roots is -b/a. The product of the roots is c/a. If you use a = 1, then you only have to worry about -b and c. If -b is 6, then b = -6. And c = -27.

So one equation would be x² - 6x - 27 = 0.

31. Evaluate e^xlny when x = 3 and y = 2.

Answer:

Substituting for x and y, we have e^{3 ln 2}, which can be written as e^{(ln 2) ^3}.

That becomes simply 2³, which is 8.

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.