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.

January 2018
7. 7 There are 440 students at Thomas Paine High School enrolled in U.S. History. On the April report card, the students’ grades are approximately normally distributed with a mean of 79 and a standard deviation of 7. Students who earn a grade less than or equal to 64.9 must attend summer school. The number of students who must attend summer school for U.S. History is closest to

(1) 3
(2) 5
(3) 10
(4) 22

Answer: (3) 10.
If the standard deviation is 7, then 72 is one standard deviation from the mean, and 65 is two standard deviations from the mean. So anyone who scored 64.9 or lower had a score more than 2 standard deviations away from the mean. That would be approximately 2.3% of the 440 students, which is .023 * 440 = 10.12, or about 10.



8. For a given time, x, in seconds, an electric current, y, can be represented by
y = 2.5(1 - 2.7^-10x). Which equation is not equivalent?

Answer: (4)
In each of the four choices, the 25 has been distributed. The Distributive Property gives you choice (1), so eliminate that. In choice (2), you would multiply the exponents (2) and (-.05x) because you have a power of a power, and that gives you -.10x again, so this can be eliminated. Choice (3) removes the negative by inverting the number into its reciprocal, which is what a negative exponent does, so this is eliminated. Choice (4), the only one remaining, shows the product of two expressions with the same base, but the rule would be the add the exponents, not multiply them.

Adding the exponents in choice (4) would yield (-2 + .05x), not (-10x). Choice (4) is not equivalent.



Comments and questions welcome.