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

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

More Regents problems.

Integrated Algebra Regents, January 2012

Part I: Each correct answer will receive 2 credits.


11. Which set of data can be classified as quantitative?

1) first names of students in a chess club
2) ages of students in a government class
3) hair colors of students in a debate club
4) favorite sports of students in a gym class

Answer: 2) ages of students in a government class

Qualitative data is descriptive, and Quantitative data is countable or measurable. In most cases, numeric data is Quantitative. (Zip codes, phone numbers and shoe sizes, for example, would not be.)

Qualitative can be shown on bar graphs. Quantitative can be shown on histograms and cumulative histograms.

If you weren't sure which was which, you could also look at the choices and play "one of these things is not like the others."

Names, colors and favorite sports are qualitative. Ages are quantitative.

12. Three fair coins are tossed. What is the probability that two heads and one tail appear?

1) 1/8
2) 3/8
3) 3/6
4) 2/3

Answer: 2) 3/8

There are eight possible outcomes when flipping three coins. Three of them involve one head with the other two coins being tails. So the probability is 3/8, which is three positive outcomes out of eight possible outcomes.

Note that there is no question you can ask about flipping three coins where the answer will be 2/3. Likewise, you could formulate a question that has an answer of 1/2, but you wouldn't get 3/6 in your calculations.

13. What is the sum of -3x² - 7x + 9 and -5x² + 6x - 4?

1) -8x² - x + 5
2) -8x⁴ - x + 5
3) -8x² - 13x + 13
4) -8x⁴ - 13x² + 13

Answer: 1) -8x² - x + 5

When adding two binomials, just combine the like terms. Note that the like terms do not change -- that is, the exponents are not increased when adding the coefficients. Two squares plus three squares would be five squares not five tesseracts (which is a four-dimensional square).

Add -3x² and -5x² for -8x². Add - 7x + 6x to get -1x or -x. Add 9 and -4 to get 5.

14. For which values of x is the fraction (x² + x - 6) / (x² + 5x - 6) undefined?

1) 1 and -6
2) 2 and -3
3) 3 and -2
4) 6 and -1

Answer: 1) 1 and -6

The fraction is undefined when the denominator is equal to 0. Set the quadratic expression equal to 0 and solve.

x² + 5x - 6 = 0
(x + 6)(x - 1) = 0
x + 6 = 0 or x - 1 = 0
x = -6 or x = 1

15. What is the slope of the line that passes through the points (2,-3) and (5,1)?

1) -2/3
2) 2/3
3) -4/3
4) 4/3

Answer: 4) 4/3

Simple question. No tricks or curve balls.

Delta y divided by delta x.

(1 - -3) / (5 - 2) = 4 / 3

More to come. Comments and questions welcome.

More Regents problems.

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