Algebra 2 Problems of the Day (Algebra 2 Regents, June 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, June 2012

Part I: Each correct answer will receive 2 credits.


6. If m∠θ = -50, which diagram represents θ drawn in standard position?

Answer: 4) (see image)

If θ has a negative value, you drop down below the x-axis, in a clockwise direction, starting from the right side of axis.

Choice (3) is 50 degrees. Choices (1) and (2) are not standard positions because they start on the left.

7. If log_b x = 3 log _b p - (2 log _b t + 1/2 log _b r), then the value of x is

Answer: 4) See image

Sometimes I think the Regents people just want to give me a headache.

8. Which equation has roots with the sum equal to 9/4 and the product equal to 3/4?

1) 4x² + 9x + 3 = 0
2) 4x² + 9x - 3 = 0
3) 4x² - 9x + 3 = 0
4) 4x² - 9x - 3 = 0

Answer: 3) 4x² - 9x + 3 = 0

The rule for the Sum of the Roots is −b/a, and for the Product of the Roots is c/a. Note that the Sum has a minus sign and the Product does not.

If -b/a = +9/4 then either a or b must be negative. Since a = 4 in all four choices, b must be -9. Eliminate Choices (1) and (2).

If c/a = +3/4 then either a and c are both positive or they are both negative. Since a must be +4, then c must be +3. Eliminate Choice (4).

9. Which graph represents the solution set of | (4x - 5) / 3 | > 1?

Answer: 3) see image

You have to remove the absolute value symbols and then solve TWO inequalities: one for > 1 and one for < -1

(4x - 5) / 3 > 1 4x - 5 > 3 4x > 8 x > 2

(4x - 5) / 3 < -1 4x - 5 < -3 4x < 2 x < 1/2

10. Which expression is equivalent to (x^-1y⁴) / (3x^-5y^-1)

1) x⁴y⁵ / 3
2) x⁵y⁴ / 3
3) 3x⁴y⁵
4) y⁴ / (3x⁵)

Answer: 1) x⁴y⁵ / 3

When you have the same variable in the numerator and the denominator, you can SUBTRACT the exponents.

x^-1 / x^-5 = x^{-1 - -5} = x⁴

y⁴ / y^-1 = y^{4 - -1} = y⁵

The 3 in the denominator doesn't move. It remains 1/3 because there is no exponent affecting it.

The final result is 1/3 x⁴ y⁵

More to come. Comments and questions welcome.

More Regents problems.

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