Algebra Problems of the Day (Integrated Algebra Regents, June 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

June 2012

Part I: Each correct answer will receive 2 credits.


6. Which situation is an example of bivariate data?

1) the number of pizzas Tanya eats during her years in high school
2) the number of times Ezra puts air in his bicycle tires during the summer
3) the number of home runs Elias hits per game and the number of hours he practices baseball
4) the number of hours Nellie studies for her mathematics tests during the first half of the school year

Answer: 3) the number of home runs Elias hits per game and the number of hours he practices baseball

Bivariate means that there are two pieces of data being tracked and compared. In Choice (3), there is data for Elias scoring hits and for the hours he practices. These can be compared.

In Choice (1), only the number of pizzas is being counted.

In Choice (2), just the number of times air in put into tires is tracked.

In Choice (4), the hours studying for tests is measured, but not, say, the scores on those tests.

7. Brianna’s score on a national math assessment exceeded the scores of 95,000 of the 125,000 students who took the assessment. What was her percentile rank?

1) 6
2) 24
3) 31
4) 76

Answer: 4) 76

Given the choices provided, you don't have to do much math at all. If you beat 95,000 of 125,000, you are well above the halfway point. I could do the math to see if that would be 76 percent, but the other three numbers are so low, why bother. Choices (1), (2) and (3) are just silly.

Anyway, 95000 / 125000 = 0.76, which is the 76th percentile.

8. 8 If A = {0, 1, 3, 4, 6, 7}, B = {0, 2, 3, 5, 6}, and C = {0, 1, 4, 6, 7}, then A ∩ B ∩ C is

1) {0, 1, 2, 3, 4, 5, 6, 7}
2) {0, 3, 6}
3) {0, 6}
4) {0}

Answer: 3) {0, 6}

The intersection of two sets in the set of all elements that are present in both the first and the second set. The intersection of three sets is the set of all elements that are present in every one of the three individual sets. You can do one intersection at a time to make it less confusing, if you want to.

The intersection A ∩ B = {0, 1, 3, 4, 6, 7} ∩ {0, 2, 3, 5, 6} = {0, 3, 6}

The intersection A ∩ B ∩ C = {0, 3, 6} ∩ {0, 1, 4, 6, 7} = {0, 6}

9.Which graph represents a function?

Answer: 1)

For a graph to be a function, it must pass the vertical-line test, which states that no vertical line can be drawn through any part of the graph so that it touches more than one point on the graph.

In Choice (2), a vertical line can be drawn between, for example, (2, 2) and (2, -2). The same x-value (the input) has two different y-values (output). This is not allowed in a function.

Similarly, Choices (3) and (4) fail the test.

10. What is the product of (3x + 2) and (x - 7)?

1) 3x² - 14
2) 3x² - 5x - 14
3) 3x² - 19x - 14
4) 3x² - 23x - 14

Answer: 3) 3x² - 19x - 14

If the four choices, the first and last terms are the same. You only need to concern yourself with the middle term.

If you use the Area Model, you can see that the four products that you need to find are:

(3x)(x) = 3x²

(3x)(-7) = -21x

(2)(x) = 2x

(2)(-7) = -14

When you combine the like terms, you see that -21x + 2x = -19x, which is Choice (3).

More to come. Comments and questions welcome.

More Regents problems.