Friday, September 17, 2021

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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