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.


1. A doctor wants to test the effectiveness of a new drug on her patients. She separates her sample of patients into two groups and administers the drug to only one of these groups. She then compares the results. Which type of study best describes this situation?

1) census
2) survey
3) observation
4) controlled experiment

Answer: 4) controlled experiment

This is a definition question. The question described how to conduct a controlled experiment.

2. If f(x) = x / (x² - 16), what is the value of f(-10)?

1) -5/2
2) -5/42
3) 5/58
4) 5/18

Answer: 2) -5/42

Substitute and evaluate. Simplify your fraction so that it matches one of the choices.

f(-10) = -10 / (100 - 16). The answer is negative, so eliminate Choices (3) and (4).

f(-10) = -10/84 = -5/42, which is Choice (2).

3. An auditorium has 21 rows of seats. The first row has 18 seats, and each succeeding row has two more seats than the previous row. How many seats are in the auditorium?

1) 540
2) 567
3) 760
4) 798

Answer: 4) 798

There is an even number of seats, so eliminate Choice (2).

There are 18 seats in the first row, 20 in the second, 22 in the third, and 18 + 2(20) = 58 seats in the last row.

You can add those numbers or take a shortcut. 18 + 58 = 76, 76 * 10 = 760, 760 + 1/2(76) = 798, which is Choice (4).

4. Expressed as a function of a positive acute angle, cos (−305°) is equal to

1) −cos 55°
2) cos 55°
3) −sin 55°
4) sin 55°

Answer: 2) cos 55°

There are 360 degrees in a complete circle. Moving -305 degrees is the same as moving positive 55 degrees. So the answer is cos 55. There's no need to switch signs or functions.

5. The value of x in the equation 4^{2x + 5} = 8^3x is

1) 1
2) 2
3) 5
4) -10

Answer: 2) 2

This is a siple enough problem that you could just substitute and evaluate. However, it is a good problem wo solve because this is a decent open-ended question if you had no choices:

4 is 2² and 8 is 2³, so rewrite the equation using a base of 2. Then set the exponent expressions equal to each other.

2^{2(2x + 5)} = 2^(3)(3x)

4x + 10 = 9x

10 = 5x

x = 2

Check: 4^{2(2) + 5} = 4⁹ = 262144; 8³⁽²⁾ = 8⁶ = 262144. Check!

More to come. Comments and questions welcome.

More Regents problems.

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