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.


25. What is the radian measure of the smaller angle formed by the hands of a clock at 7 o’clock?

1) π/2
2) 2π/3
3) 5π/6
4) 7π/6

Answer: 3) 5π/6

The smaller angle formed would be 5/12ths of the clock. The number of radians in the entire clock is 2π. (Note that the question asks smaller, so do not use 7/12.)

Multiply 5/12 * 2π = 10π/12 = 5π/6

26. What is the coefficient of the fourth term in the expansion of (a − 4b)₉?

1) -5,376
2) -336
3) 336
4) 5,376

Answer: 1) -5,376

The fourth term would be the x⁶ term. (x⁹, x⁸, x⁷, x⁶.) Note that 9 - 6 = 3. Three is an offset -- it's 4 - 1 -- and will be important.

The ninth row of Pascal's triangle starts 1, 9, 36, 84. And ₉C₃ = 84.

Since the first term has (-4)⁰, then the fourth term will have (-4)³, which is -64.

So the coefficient will be (84)(-64) = -5,376, which is Choice (1).

27. Samantha constructs the scatter plot below from a set of data.
Based on her scatter plot, which regression model would be most appropriate?

1) exponential
2) linear
3) logarithmic
4) power

Answer: 3) logarithmic

The data looks mostly linear, except for the initial points dragging it down.

If you draw a curve through the data, it would look like a logarithmic graph, which is Choice (3).

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.

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