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

Part II: Each correct answer will receive 2 credits. Partial credit is possible.


32. Solve the equation 6x²> - 2x - 3 = 0 and express the answer in simplest radical form.

Answer:

Telling you to answer in simplest radical form is a sure sign that you need to use the Quadratic Formula.

x = ( -b + SQRT(b² - 4ac) ) / (2a)

= ( -(-2) + SQRT((-2)² - 4(6)(-3)) ) / (2(6))

= ( 2 + SQRT(4 - (-72) ) / (12)

= ( 2 + SQRT(76) / (12)

= ( 2 + SQRT(4)SQRT(19) / (12)

= ( 2 + 2SQRT(19) ) / 12

= ( 1 + SQRT(19) ) / 6

You could have also split the fraction.

33. The number of bacteria present in a Petri dish can be modeled by the function N = 50e^3t, where N is the number of bacteria present in the Petri dish after t hours. Using this model, determine, to the nearest hundredth, the number of hours it will take for N to reach 30,700.

Answer:

50e^3t = 30700
e^3t = 614
ln e^3t = ln 614
3t = ln 614
3t = 6.4199...
t = 2.1399...

t = 2.14 hours

34. 4 Determine the solution of the inequality |3 - 2x | > 7.
[The use of the grid below is optional.]

Answer:

This can be solved algebraically, or you could use the grid to graph y = |3 - 2x |, and mark off where y > 7. However, if you graph, you still need to state a solution. The graph will not stand on its own.

|3 - 2x | > 7
3 - 2x > 7 or 3 - 2x < -7
-2x > 4 or -2x < -10
x < -2 or x > 5

35. Convert 3 radians to degrees and express the answer to the nearest minute.

Answer:

There are 180 degrees in &pi radians, and there are 60 minutes in 1 degree. Note that Pi is about 3.14, so 3 radians should be close to (but less than) 180 degrees.

180 / &pi = x / 3
&pi x = 540
x = 540/&pi
x = 171.8873 degrees

.8873 * 60 = 53.24, approximately 53 minutes.

So 3 radians is about 171 degrees 53 minutes.

More to come. Comments and questions welcome.

More Regents problems.

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