Saturday, October 30, 2021

Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2012)

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, January 2012

1. The yearbook staff has designed a survey to learn student opinions computations. on how the yearbook could be improved for this year. If they want to distribute this survey to 100 students and obtain the most reliable data, they should survey

1) every third student sent to the office
2) every third student to enter the library
3) every third student to enter the gym for the basketball game
4) every third student arriving at school in the morning

Answer: 4) every third student arriving at school in the morning

Surveying the students entering the building in the morning is the most random of the four choices. Not many students would be send to the office. And certain subgroups of people would be overrepresented or underrepresented by standing outside the library or the gym (or the offiice, too, for that matter), so there would be more bias in the results.

2. What is the sum of the first 19 terms of the sequence 3, 10, 17, 24, 31, …?

1) 1188
2) 1197
3) 1254
4) 1292

It's a short enough list that you might consider just adding the numbers in your calculator, but since the numbers are increasing by 7, if you make a mistake along the way, it'll through off your final answer.

The formula for adding a finite sequence is in the back of the booklet: S = n(a1 + an) / 2. However, we need to know a19.

Since the sequence has a common difference of 7, the explicit formula is an = 7(n - 1) + 3. So a19 = 7(19 - 1) + 3 = 129.

Put that into the formula: S = (19)(3 + 129) / 2 = 1254

3. Which expression, when rounded to three decimal places, is equal to -1.155?

1) sec (5π/6)
2) tan(49°20')
3) sin (-3π/5)
4) csc(-118°)

Choice (2) is the first one you can immediately eliminate. It would be in Quadrant 1, so it has a positvie value. Choice (3) can be eliminated because sin cannot be less than -1. The other all have negative values. Make sure you are measuring radians or degrees, as stated.

Choice (1) = -1.1547.

Choice (2) = 1.1639. Note: 20 minutes is .33333 degrees.

Choice (3) = -0.9510.

Choice (4) = -1.1325.

4. If f(x) = 4x - x2 and g(x) = 1/x, then (f ° g)(1/2) is equal to

1) 4/7
2) -2
3) 7/2
4) 4

Find f OF g OF 1/2.

g(1/2) = 1 / (1/2) = 2

f(2) = 4(2) - (2)2 = 8 - 4 = 4.

5. A population of rabbits doubles every 60 days according to the formula P = 10(2)(t/60), where P is the population of rabbits on day t. What is the value of t when the population is 320?

1) 240
2) 300
3) 660
4) 960

You can check each of the choices, or we can solve for t.

P = 10(2)240/60 = 10(2)4 = 160

P = 10(2)300/60 = 10(2)5 = 320. This is the answer.

Working backward:

320 = 10(2)t/60
32 = (2)t/60
25 = (2)t/60
5 = t/60
t = 300

More to come. Comments and questions welcome.

More Regents problems.

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