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.


6. Which equation represents the graph below?

1) y = - 2 sin 2x
2) y = - 2 sin 1/2 x
3) y = - 2 cos 2x
4) y = - 2 cos 1/2 x

Answer: 3) y = - 2 cos 2x

Cosine (0) = 1 and Sine (0) = 0. The function is cosine, so eliminate Choices (1) and (2).

Between 0 and 2π the graph makes two cycles instead of one, so this is cos 2x.

2. What is the graph of the solution set of |2x - 1| > 5?

Answer: 1

First of all, substitute 0 for x. |2(0) - 1| > 5 is NOT a true statement. Zero is NOT a solution, so you can eliminate Choices (2) and (4).

This you only have to check if x = -3 is a solution or not to know the answer.

| 2(-3) - 1 | = | -6 - 1 | = | -7 | = 7, which IS greater than 5, so x = -3 IS a solution. This means that choice (3) is eliminated, and the answer is (1).

Algebraically, break up the equation:

2x - 1 > 5
2x > 6
x > 3

2x - 1 < -5
2x < -4
x < -2

The algebraic solution gives us graph number 1.

8. What is the range of the function shown below?

1) x < 0
2) x > 0
3) y < 0
4) y > 0

Answer:
3) y < 0

Range refers to the y-values, so eliminate choices (1) and (2).

You want all the y values that are less than or equal to 0. There are no y values greater than 0.

9. The expression sin(θ + 90)° is equivalent to

1) -sin θ
2) -cos θ
3) sin θ
4) cos θ

Answer: 4) cos θ

If you recall from rotations in Geometry, a counterclockwise rotation of 90 degrees moved point A(x, y) to point A'(-y, x).

Similarly, a point B(cos θ, sin θ) will have an image B'(-sin θ, cos θ)

So sin θ becomes cos θ

10. The points (2,3), (4, 3/4), and (6,d) lie on the graph of a function.
If y is inversely proportional to the square of x, what is the value of d?

1) 1
2) 1/3
3) 3
4) 27

Answer: 2) 1/3

If y is inversely proportional to x then as x gets bigger y will get smaller. This means that d must be smaller than 3/4. THere is only one possibility.

(2)²(3) = 12

(4)²(3/4) = 12

(6)²d = 12
36d = 12
d = 1/3

More to come. Comments and questions welcome.

More Regents problems.

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