## Wednesday, May 30, 2018

### Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

More Algebra 2 problems.

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(2x + 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(2x + 3) = 48
2x + 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.

More Algebra 2 problems.