More Algebra 2 problems.

__August 2017, Part I__

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.

*7. Which diagram represents an angle, α, measuring 13π / 20 radians drawn in standard position, and its reference angle, θ?
*

**Answer: 4) **

The reference angle is always measured from the x-axis and will not be greater than 90 degrees. In choice 1, the supplement of the reference angle is shown. In choice 3, the measure from the y-axis is shown.

Choices 1, 3, and 4 shown a correct angle measuring 13π / 20 radians. Choice 2 shows *a* measured in a clockwise, instead of counterclockwise, direction.

*8. What are the zeros of P(m) = (m ^{2} - 4)(m^{2} + 1)?
*

1) 2 and − 2, only

2) 2, − 2, and − 4

3) −4, i, and − i

4) 2, − 2, i, and − i

**Answer: 4) 2, − 2, i, and − i**

(m^{2} - 4) is the difference of two perfect squares and can be factored into two conjugates:

(m + 2)(m - 2), which means that P(m) has zeroes at -2 and 2.

Likewise, if (m^{2} - 4) = 0

Then m^{2} = 4

and m = __+__2

(m^{2} + 1) has no *real* roots, but does have imaginary roots.

m^{2} = -1

m = __+__(-1)^.5 = __+__*i*

*9. The value of a new car depreciates over time. Greg purchased a new car in June 2011. The value, V, of his car after t years can be modeled by the equation log _{0.8}( V/17000) = t.
What is the average decreasing rate of change per
year of the value of the car from June 2012 to June 2014, to the nearest ten dollars per year??
1) 1960
2) 2180
3) 2450
4) 2770
*

**Answer:3) 2450**

In 2014, t = 3 years, and in 2012, t = 1 year.

Find the value of the function when t = 3 and t = 1, and then divide by the change in t, which is 3 - 1 = 2.

(17000(0.8)^{3} - 17000(0.8)^{1})/(3-1) = -2448 = -2450, to the nearest ten.

Comments and questions welcome.

More Algebra 2 problems.

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