Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

Welcome back. After a long pause, the Problems of the Day are back. And I'll be honest, the reason I haven't been posting is because I forgot that I hadn't finished all the New York State Regents exams. Otherwise, I would have continued after I posted the January 2020 exam. As far as I can tell, I left off in Part I of the January 2017 exam.
Update: After doing a deep dive on my blog, I discovered that I have answered these questions before -- except that I used the tag "Algebra" instead of "Algebra 2", even though "Algebra 2" was in the title of the posts. Next project: update all those old tags.

January 2017, Part I

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


7. The expression [SEE IMAGE BELOW] is equivalent to

[SEE IMAGE]

Answer: 2) SEE IMAGE BELOW
The rules of exponents. A negative exponent indicates a reciprocal. A fractional exponent indicates a root (square, cube, fourth, etc). An exponent outside of the parentheses multiplies all the exponents inside the parentheses (even if those are 1). Exponents appearing in the numerator and denominator of a fraction mean that, if the base is the same, the exponents are subtracted.

Some of the operations shown below could have been done in a different order, but the result should be the same. (If it isn't, then a mistake was made. Please, check your work.)

The -1/2 exponent is resolved by taking the reciprocal of the fraction and changing the -1/2 to +1/2.

The 1/2 exponent is resolved by multiplying, producing m^1/6 in the numerator and m^2/2, which is just m, in the denominator.

Subtract 1/6 - 1, which is -5/6.

Negative exponent. Take the reciprocal and make it +5/6.

Finally, take the sixth root of m⁵, which is Choice (2).

8. What is the inverse of the function y = log₃ x?

1) y = x³
2) y = log_x 3
3) y = 3^x
4) x = 3^y

Answer:(3) y = 3^x then x = 3^y.

The inverse of that would switch the x and the y, so the inverse is y = 3^x.



9. Gabriel performed an experiment to see if planting 13 tomato plants in black plastic mulch leads to larger tomatoes than if 13 plants are planted without mulch. He observed that the average weight of the tomatoes from tomato plants grown in black plastic mulch was 5 ounces greater than those from the plants planted without mulch. To determine if the observed difference is statistically signifi cant, he rerandomized the tomato groups 100 times to study these random differences in the mean weights. The output of his simulation is summarized in the dotplot below.
Given these results, what is an appropriate inference that can be drawn?

1) There was no effect observed between the two groups.
2) There was an effect observed that could be due to the random assignment of plants to the groups.
3) There is strong evidence to support the hypothesis that tomatoes from plants planted in black plastic mulch are larger than those planted without mulch.
4) There is strong evidence to support the hypothesis that tomatoes from plants planted without mulch are larger than those planted in black plastic mulch.

Answer: 2) There was an effect observed that could be due to the random assignment of plants to the groups.
There was an effect, but there isn't strong evidence. It could be random.

Comments and questions welcome.

More Algebra 2 problems.

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