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 2014
Part I: Each correct answer will receive 2 credits.
25. Which equation represents a graph that has a period of 4π?
1) y = 3 sin 1/2 x
2) y = 3 sin 2x
3) y = 3 sin 1/4 x
4) y = 3 sin 4x
Answer: 1) y = 3 sin 1/2 x
The graph of y = sin x has a period of 2π. When the argument of the sine function is halved, the period is doubled, which is a period of 4π.
22. The expression x2(x + 2) - (x + 2) is equivalent to
1) x2
2) x2 - 1
3) x3 + 2x2 - x + 2
4) (x + 1)(x - 1)(x + 2)
Answer: 4) (x + 1)(x - 1)(x + 2)
Before you try to multiply everything, notice that there are two terms, and each one has (x + 2) in it. This can be factored out.
x2(x + 2) - (x + 2) is the same as (x + 2)(x2 - 1)
Moreover, (x2 - 1) is the Difference of Squares, which can be factored into the conjugates (x - 1)(x + 1).
So x2(x + 2) - (x + 2) is the same as (x + 2)(x - 1)(x + 1), which is Choice (4).
27. Approximately how many degrees does five radians equal?
1) 286
2) 900
3) π/36
4) 5π
Answer: 1) 286
To convert, remember that 360 degrees is 2π radians, and 180 degrees is π radians.
Set up a proportion:
πx = (5)(180)
x = (5)(180)/π
x = 286.478...
Five radians is approximately 286 degrees.
More to come. Comments and questions welcome.
More Regents problems.
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