Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.
After a brief hiatus, the Algebra 2 Problems of the Day are back. Hopefully, daily.

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January 2019, Part I

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


1. Suppose two sets of test scores have the same mean, but different standard deviations, σ1 and σ2, with σ2 > σ1. Which statement best describes the variability of these data sets?
(1) Data set one has the greater variability.
(2) Data set two has the greater variability.
(3) The variability will be the same for each data set.
(4) No conclusion can be made regarding the variability of either set.

Answer: (2) Data set two has the greater variability.
A lower standard deviation means that the data is closer to the mean, and a higher standard means that the data is more spread out.

2. If f(x) = log₃ x and g(x) is the image of f(x) after a translation five units to the left, which equation represents g(x)?
(1) g(x) = log₃(x + 5)
(2) g(x) = log₃x + 5
(3) g(x) = log₃(x - 5)
(4) g(x) = log₃x - 5

Answer: (1) g(x) = log₃(x + 5)
Adding 5 inside the parentheses shifts the function 5 units to the left. Subtracting 5 moves it to the right.
Adding 5 outside the parentheses shifts the function 5 units up. Subtracting 5 outside (or without) the parentheses moves it down.

3. When factoring to reveal the roots of the equation x³ + 2x² - 9x - 18 = 0, which equations can be used?

I. x²(x + 2) - 9(x + 2) = 0
II. x(x² - 9) + 2(x² - 9) = 0
III. (x - 2)(x² - 9) = 0
(1) I and II, only
(2) I and III, only
(3) II and III, only
(4) I, II, and III

Answer: (1) I and II, only
If you distribute I, you will get the original four terms.
Likewise, if you distribute II, you will get the four terms, which can be rearranged back into standard form.
If distribute, FOIL, box, or whatever III, you will get -2x² and +18, which are incorrect.



Comments and questions welcome.

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