Algebra 2 Problems of the Day

Algebra 2 is not my usual subject, but I do get asked about the problems occasionally. So I've decided to run a couple of Regents problems daily for a while. If there's a positive reaction (or at least, a lack of negative reaction), I may continue it.

More Algebra 2 problems.

January 2018
1. The operator of the local mall wants to find out how many of the computations. mall’s employees make purchases in the food court when they are working. She hopes to use these data to increase the rent and attract new food vendors. In total, there are 1023 employees who work at the mall. The best method to obtain a random sample of the employees would be to survey
(1) all 170 employees at each of the larger stores
(2) 50% of the 90 employees of the food court
(3) every employee
(4) every 30th employee entering each mall entrance for one week

Answer: (4)
The only one of the choices that has a random element to it is the last one: every 30th employee who works at the mall. Notice that choices (1) and (2) only survey people working in certain location, leaving out the rest. "Every employee" is a terrible way to get a "sample".



2. What is the solution set for x in the equation below?

(1) {1}
(2) {0}
(3) {-1,0}
(4) {0,1}

Answer: (3) {-1, 0}
If you try each of the solution sets, you will quickly see that {1} is bad, so (1) and (4) are eliminated, and {0} is good. Next check {-1}, which is also good.

If you needed to actually solve it, as you might in part II, solve for x, as in the image below.
Move the -1 to the other side of the equation. Square both sides. Move the x + 1 to the other side of the equation, leaving 0. Factor the quadratic on the right side.

Comments and questions welcome.