Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, August 2010)

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, August 2010

Part I: Each correct answer will receive 2 credits.


1. The product of (3 + √(5)) and (3 − √(5)) is

1) 4 − 6 √(5)
2) 14 − 6 √(5)
3) 14
4) 4

Answer: 4) 4

The product of two conjugates is the Difference of the Two Squares.

(3 + √(5))(3 − √(5)) = 3² - (√(5))² = 9 - 5 = 4

2. What is the radian measure of an angle whose measure is −420°?

1) −7π/3
2) −7π/6
3) 7π/6
4) 7π/3

Answer: 1) −7π/3

The conversion rate is 180° = π radians.

-420π/180 simplifies to −7π/3, which is Choice (1)

3. What are the domain and the range of the function shown in the graph below?

1) {x | x > −4}; {y | y > 2}
2) {x | x ≥ −4}; {y | y ≥ 2}
3) {x | x > 2}; {y | y > −4}
4) {x | x ≥ 2}; {y | y ≥ −4}

Answer: 2) {x | x ≥ −4}; {y | y ≥ 2}

The domain is all the valid x values, which are x x ≥ −4. The range is all the value y values, which are y ≥ 2.

This is Choice (2).

4. The expression 2i² + 3i³ is equivalent to

1) −2 − 3i
2) 2 − 3i
3) −2 + 3i
4) 2 + 3i

Answer: 1) −2 − 3i

i² = -1 and i³ = -i.

Therefore, 2i² + 3i³ = -2 - 3i.

5. In which graph is θ coterminal with an angle of −70°?

Answer: 4) [SEE IMAGE]

The angle −70° is shown in Choice (4).

More to come. Comments and questions welcome.

More Regents problems.

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