Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2014)

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 2014

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


32. Solve |-4x + 5| < 13 aglebraically for x.

Answer:

You need to split the inequatily into two, one < 13 and one > -13.

-4x + 5 < 13
-4x < 8
x > -2

-4x + 5 > -13
-4x > -18
x < 4.5

x > -2 OR x < 4.5
or -2 < x < 4.5

33. Express 4xi + 5yi⁸ + 6xi³ + 2yi⁴ in simplest a + bi form.

Answer:

Since i² = -1, then i³ = -i, and i⁴ = 1. Since i⁴ * i⁴ = i⁸, then i⁸ = 1 * 1 = 1.

4xi + 5yi⁸ + 6xi³ + 2yi⁴
= 4xi + 5y(1) + 6x(-i) + 2y(1)
= 4xi + 5y - 6xi + 2y
= 7y - 2xi

34. In an arithmetic sequence, a₄ = 19 and a_{7 = 31. Determine a formula for an, the nth term of this sequence.}

Answer:

Finding the common difference of an aritmetic sequence is like finding the slope of a linear equation.

d = (31 - 19) / (7 - 4) = 12 / 3 = 4

Substitute this into the formula for an arithmetic sequence, and solve for a₁.

a₄ = (4)(4 - 1) + a₁
19 = 12 + a₁
a₁ = 7

a_n = 4(n - 1) + 7

35. 5 Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of 83°50′.

Answer:

The circumference of the circle is 2πr, so x is a fraction of that amount and that fraction will be (83°50′)/360°

(83 5/6) / 360 = (503/6) / 360 = 503 / 2160

x = (2)(3.141592)(12)(503/2160) = 17.558... or 17.6 cm.

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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