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Only 39% right on today’s SAT question

By Murray Bourne, 23 Jun 2007 have a "SAT Question of the Day". [SAT is the Scholastic Aptitude Test, which is something you have to pass before entering colleges in the US.]

Today's question is:

A manager estimates that if the company charges p dollars for their new product, where 0 ≤ p ≤ 200, then the revenue from the product will be r(p) = 2,000p − 10p2 dollars each week. According to this model, for which of the following values of p would the company's weekly revenue for the product be the greatest?

a. 10
b. 20
c. 50
d. 100
e. 200

You can enter your answer on the site and see if you got it right.

Out of 52,833 attempts so far today, 61% got it wrong. Oh dear.

I would argue that this is quite a good question. It is an example of mathematical modeling, where we estimate some future behaviour using a mathematical expression (aka function). Modeling is one of the most important branches of mathematics, but most students don't get to experience the process of developing a model. (The usual situation is that students are just given some confusing formula and they start plugging in values, having no idea where it comes from or why they are doing it...)

Interestingly, the rating for this question is Hard. I'm wondering if this rating is by the SAT question writers, or by the site because so many got it wrong.

The question is multiple choice. Is that good, or does that guarantee and encourage a "lottery approach" to answering mathematics questions?

[If you're dying to know how to solve the problem, go to Quadratic functions or see an almost identical problem solved using differentiation.]

See the 2 Comments below.

2 Comments on “Only 39% right on today’s SAT question”

  1. Jackie says:

    Oh, how sad (the % correct, not the question). Do the questions rotate among the SAT topics?

    I didn't know this existed - so I thank you. I'm not sure my students will though!

  2. Murray says:

    As far as I can tell Jackie, the questions are randomly chosen from past SATs.

    You can access hundreds of SAT math questions from there.

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