Algebra 2 Problems of the Day

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June 2017, Part I

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


1. The graph of the function p(x) is sketched below.

Which equation could represent p(x)?
1) p(x) = (x² − 9)(x − 2)
2) p(x) = x³ − 2x² + 9x + 18
3) p(x) = (x²2 + 9)(x − 2)
4) p(x) = x³ + 2x² − 9x − 18

Answer: 1) p(x) = (x² − 9)(x − 2)
The zeroes are -3, 2, and 3, so the factors are (x + 3)(x - 2)(x - 3).
(x + 3)(x - 3) = x² - 9.
Choice 3 is bad because it has x² + 9, which doesn't have zeroes.
Choice 4 is bad because (3)(-2)(-3) = 18, not -18.

2. What is the solution to 8(2^{x + 3}) = 48?
1) x = ln6/ln2 - 3
2) x = 0
3) x = ln48/ln16 - 3
4) x = ln4 - 3

Answer: 1) x = ln6/ln2 - 3

8(2^{x + 3}) = 48
2^{x + 3} = 6
(x + 3)ln 2 = ln 6
x + 3 = ln6/ln2
x = ln6/ln2 - 3

3. Cheap and Fast gas station is conducting a consumer satisfaction survey. Which method of collecting data would most likely lead to a biased sample?
1) interviewing every 5th customer to come into the station
2) interviewing customers chosen at random by a computer at the checkout
3) interviewing customers who call an 800 number posted on the customers' receipts
4) interviewing every customer who comes into the station on a day of the week chosen at random out of a hat

Answer: 3) interviewing customers who call an 800 number posted on the customers' receipts
Self-selection introduces bias because those with stronger opinions are more likely to call the number. You would not get a random sample.

Comments and questions welcome.

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