Tuesday, January 18, 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 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 exlny when x = 3 and y = 2.

Answer:


Substituting for x and y, we have e3 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.

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