Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 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, January 2011

Part I: Each correct answer will receive 2 credits.


21. For which equation does the sum of the roots equal −3 and the product of the roots equal 2?

1) x² + 2x - 3 = 0
2) x² - 3x - 2 = 0
3) 2x² + 6x + 4 = 0
4) 2x² - 6x + 4 = 0

Answer: 3) 2x² + 6x + 4 = 0

The product of the roots is C/A, and the sum is -B/A.

Choice (1) has a sum of -3/1 = -3. Eliminate Choice (1).

Choice (2) has a sum of -2/1 = -2. Eliminate Choice (2).

Choice (3) has a sum of 4/2 = 2, and a product of -6/2 = -3. This is the correct choice.

Choice (4) has a sum of 4/2 = 2, and a product of -(-6)/2 = 3. Eliminate Choice (4).

22. The expression (2x + 4) / (√(x + 2)) is equivalent to

Answer: 4) [See Image]

See image.

Multiply by &radic(x+2)/&radic(x+2). Then factor (2x + 4)/(x + 2) = 2.

23. Which equation is sketched in the diagram below?

1) y = csc x
2) y = sec x
3) y = cot x
4) y = tan x

Answer: 1) y = csc x

The U shaped graphs are secant and cosecant, not tangent and cotangent. Eliminate Choices (3) and (4).

Sec x = 1 / cos x and csc x = 1 / sin x.

At x = 0, cos x = 1 and sin x = 0. That means that csc x is undefined at 0, as shown in the graph.

The correct choice is (1).

24. The expression log₅(1/25) is equivalent to

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

Answer: 4) -2

If x = log₅(1/25) then 5^x = 1/25.

So x = -2, which is Choice (4).

More to come. Comments and questions welcome.

More Regents problems.

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