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

Part III: Each correct answer will receive 4 credits. Partial credit is available.


36. Express as a single fraction the exact value of sin 75°.

Answer:

If you're one of those people who have memorized, sine and cosine for 15 and 75 degrees, then you know the answer, but they still want to see the work. You can use the formula for the Sum of Two Angles.

sin(A + B) = sin A cos B + cos A sin B

sin (45 + 30) = sin 45 cos 30 + cos 45 sin 30

sin (75) = (√(2)/2)(√(3)/2) + (√(2)/2)(1/2)

= (√(6)/4) + (√(2)/4)

= (√(6) + √(2)) / 4

37. Solve the inequality −3|6 − x| < −15 for x. Graph the solution on the line below.

Answer:

Divide both sides by -3 and flip the inequality. Then split the equation in two to solve the Absolute Value

−3|6 − x| < −15

|6 − x| > 5

6 - x < -5 or 6 - x > 5

-x &t -11 or -x > -1

x > 11 or x < 1

Your number should look like the one below:

38. The probability that a professional baseball player will get a hit is 1/3. Calculate the exact probability that he will get at least 3 hits in 5 attempts.

Answer:

The probability that he will get at least 3 hits is equal to the probability that he will get 3 plus the probability that he will get 4 plus the probability that he will get 5.

P(3) = ₅C₃(1/3)³(2/3)² = 10(4/243)

P(4) = ₅C₄(1/3)⁴(2/3) = 5(2/243)

P(5) = ₅C₅(1/3)⁵ = 1/243

P(3 or 4 or 5) = 51/243

End of Part III

More to come. Comments and questions welcome.

More Regents problems.

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