Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, June 2013)

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 2013

Part I: Each correct answer will receive 2 credits.


1. A market research firm needs to collect data on viewer preferences for local news programming in Buffalo. Which method of data collection is most appropriate?

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

Answer: 2) survey

A survey is the best method for collect data on viewer preferences.

2. What is the number of degrees in an angle whose radian measure is 8π/5 ?

1) 576
2) 288
3) 225
4) 113

Answer: 2) 288

The conversion is π radians = 180 degrees, so multiply 8π/5 by 180/π degrees.

8π/5 * 180/π = 288

3. Which diagram represents a relation that is both one-to-one and onto?

Answer: 4) [See Image]

One-to-one means that each x maps to one y and each y is mapped to by only one x. "Onto" means that there aren't any leftover elements in the range that are not mapped to.

Choice (1) is not one-to-one.

Choice (2) is one-to-one but not onto.

Choice (3) is not a function. (C has two outputs.)

Choice (4) is the answer.

4. The sum of the first eight terms of the series 3 - 12 + 48 - 192 … is
1) -13,107
2) -21,845
3) -39,321
4) -65,535

Answer: 3) -39,321

You are asked for the Sum of 8 terms in a series. There is no common difference, but there is a common ratio of -4. Use the formula in the back of the booklet for the Sum of a Finite Geometric Series.

S_n = a₁(1 - rⁿ) / (1 - r)
= 3(1 - (-4)⁸) / (1 - (-3))
= -39321

5. The simplest form of [IMAGE] is

1) 1 / 2
2) x / (x + 2)
3) x / 3
4) - x / (x - 2)

Answer: 2) x / (x + 2)

Multiply every term of the numerator and denominator by x² to eliminate the fractions within the fractions.

Next, factor each expression, and then cancel out common factors.

More to come. Comments and questions welcome.

More Regents problems.

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