Wednesday, November 24, 2021

Algebra Problems of the Day (Integrated Algebra Regents, August 2011)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones. The Integrated Algebra Regents covered most of the same material as the current Algebra Regents, with a few differences.

More Regents problems.

Integrated Algebra Regents, August 2011

Part I: Each correct answer will receive 2 credits.

1. The number of calories burned while jogging varies directly with the number of minutes spent jogging. If George burns 150 calories by jogging for 20 minutes, how many calories does he burn by jogging for 30 minutes?

1) 100
2) 180
3) 200
4) 225

Answer: 4) 225

If it varies directly, then the amounts will be proportional. So write a proportion.

150 / 20 = x / 30

20x = 4500

x = 225

2.The scatter plot below represents the relationship between the number of peanuts a student eats and the student’s bowling score.

Which conclusion about the scatter plot is valid?

1) There is almost no relationship between eating peanuts and bowling score.
2) Students who eat more peanuts have higher bowling scores.
3) Students who eat more peanuts have lower bowling scores.
4) No bowlers eat peanuts.

Answer: 1) There is almost no relationship between eating peanuts and bowling score.

The graph doesn't show any positive or negative trends. The points appear to be randomly scattered about the graph. So eating peanuts doesn't raise or lower bowling scores.

Choice (4) is the most obviously incorrect. Almost all of the bowlers are peanuts.

3. If the universal set is {pennies, nickels, dimes, quarters}, what is the complement of the set {nickels}?

1) {}
2) {pennies, quarters}
3) {pennies, dimes, quarters}
4) {pennies, nickels, dimes, quarters}

Answer: 3) {pennies, dimes, quarters}

The complement of a set is everything that is in the universal set that is NOT in the set.

So the complement of {nickels} is {pennies, dimes, quarters}

4. Which situation does not describe a causal relationship?

1) The higher the volume on a radio, the louder the sound will be.
2) The faster a student types a research paper, the more pages the paper will have.
3) The shorter the distance driven, the less gasoline that will be used.
4) The slower the pace of a runner, the longer it will take the runner to finish the race.

Answer: 2) The faster a student types a research paper, the more pages the paper will have.

First of all, the word is "causal", as in one thing causes another. It is not "casual", which is commonly misread.

In Choice (1), turning up the volume increases the sound. That is cause and effect. Eliminate Choice (1).

In Choice (2), the speed the student types doesn't affect the length of the paper. It may affect how soon the paper is completed, but not the length. Choice (2) is the answer.

In Choice (3), if you don't drive as far, you won't need as much gas as you would for a longer drive. Eliminate Choice (3).

In Choice (4), running slower will take longer to finish than running faster. Unlike Choice (2), this one doesn't mention the length of the course being run. Eliminate Choice (1).

5. A cylinder has a diameter of 10 inches and a height of 2.3 inches. What is the volume of this cylinder, to the nearest tenth of a cubic inch?

1) 72.3
2) 83.1
3) 180.6
4) 722.6

Answer: 3) 180.6

The volume of a cylinder is given by the formula V = πr2h, and the radius is half of the diameter.

So V = (3.141592)(5)2(2.3) = 180.64154, which is about 180.6.

More to come. Comments and questions welcome.

More Regents problems.

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