Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

January 2017, Part I

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


1. Relative to the graph of y = 3 sin x, what is the shift of the graph of y = 3 sin(x + π/3)?

1) π/3 right
2) π/3 left
3) π/3 up
4) π/3 down

Answer: 2) π/3 left
This is the same as it was with functions in Algebra 1. If the change is inside the parentheses, the shift occurs to the left (if there is a plus sign) or right (if there is a minus sign). Outside of the parentheses, the shift occurs up (plus) or down (minus).

By adding to the x value, you are getting y values sooner than you would have with the original function, so the shift is to the left.

2. A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in weeks, and P(t) is the population of rabbits with respect to time, about how many rabbits will there be in 98 days?

1) 56
2) 152
3) 3668
4) 81,920

Answer: 1) 56
Change 98 days to 14 weeks (divide by 7). The population doubles every 4 weeks, so divide 14 by 4 and get 3.5. The rabbit population doubles "three and a half" times.
At this point, you can estimate an answer, if you wanted to:
5 doubles once to 10, twice to 20, three times to 40 and four times to 80.
There is only one choice between 40 and 80 and that's Choice (1) 56.

Mathematically, enter the following into the calculator:
5*2^3.5 = 56.56854... Even though this would round to 57, the only possible choice is 56.

Also, you could have just entered 5*2^(98/28), just remember the parentheses if you have an older operating system. The only reason I don't like doing this is that it relies completely on the calculator, and my "Number Sense" probably won't alert me that I made a mistake entering the equation unless it's a completely ridiculous answer. I can picture what doubling three and a half times might mean.

3. When factored completely, m⁵ + m³ - 6m is equivalent to

1) (m + 3)(m - 2)
2) (m³ + 3m)(m² - 2)
3) m(m⁴ + m² - 6)
4) m(m² + 3)(m² - 2)

Answer: 4) m(m² + 3)(m² - 2)
Each term has a factor of m, so there must be a factor of m in the answer. This eliminates Choices (1) and (2). Choice (3) can be factored further, so it wasn't "factored completely".

Comments and questions welcome.

More Algebra 2 problems.