Friday, September 10, 2021

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 a7 = 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

an = 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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