Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, June 2013)

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 2013

Part I: Each correct answer will receive 2 credits.


21. The expression log 4m² is equivalent to

1) 2(log 4 + log m)
2) 2 log 4 + log m
3) log 4 + 2 log m
4) log 16 + 2 log m

Answer: 3) log 4 + 2 log m

When you multiply to expressions with the same base you add the exponents. If you have a log of two things being multiplied, you can add the logs. When you raise a power to another power, you multiply the exponents. If you have a log of a variable with an exponent, you can multiply the log by the exponent.

In other words:

log 4m²
= log 4 + log m²
= log 4 + 2 log m

22. In triangle PQR, p equals

1) r sin P / sin Q
2) r sin P / sin R
3) r sin R / sin P
4) q sin R / sin Q

Answer: 2) r sin P / sin R

Use the Law of Sines:sin P / p = sin Q / q = sin R / r

Split this into sin P / p = sin Q / q or sin P / p = sin R / r

Solving for p gives either p = q sin P / sin Q or p = r sin P / sin R.

23. If tan ( Arc cos Sqrt(3)/k ) = Sqrt(3) / 3, then k is

1) 1
2) 2
3) SQRT (2)
4) 3 SQRT (2)

Answer: 2) 2

In you take Tan ^-1 SQRT(3)/3, you get π/6.

Cos &pi/6 = SQRT(3)/2, so k = 2.

24. Which expression is equivalent to 2x^-2y^-2 / (4 y^-5)

1) y³ / (2 x²)
2) 2y³ / (x²)
3) 2x² / (y³)
4) x² / (2 y³)

Answer: 1) y³ / (2 x²)

A variable in the numerator with a negative exponent gets moved to the denominator and its exponent is switched to positive. If it's in the demoninator, it comes up to the numerator.

2x^-2y^-2 / (4 y^-5)
= 2y⁵ / (4 x² y²)

Now simplify the factors:

2y⁵ / (4 x² y²)
= 1 y³ / (2 x²)

More to come. Comments and questions welcome.

More Regents problems.

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