Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2011)

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

More Regents problems.

Algebra 2/Trigonometry Regents, January 2011

Part I: Each correct answer will receive 2 credits.


25. A four-digit serial number is to be created from the digits 0 through 9. How many of these serial numbers can be created if 0 can not be the first digit, no digit may be repeated, and the last digit must be 5?

1) 448
2) 504
3) 2240
4) 2520

Answer: 1) 448

There are 8 choices for the first digit (not 0 and not 5).

There are 8 choices for the second digit (not 5 and not the 1st digit).

There are 7 choices for the third digit (not 5 and neither of the 1st 2 digits).

There's 1 choice for the fourth digit (5).

8 * 8 * 7 * 1 = 448, which is Choice (1).

Since the fourth digit had to be 5, only three digits were in play, which meant there were less than 1000 possibilities. So Choices (3) and (4) could be eliminated immediately.

26. Which equation represents the circle shown in the graph below that passes through the point (0,−1)?

1) (x − 3)² + (y + 4)² = 16
2) (x − 3)² + (y + 4)² = 18
3) (x + 3)² + (y - 4)² = 16
4) (x + 3)² + (y - 4)² = 18

Answer: 2) (x − 3)² + (y + 4)² = 18

The equation of a circle is (x − h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.

Notice that the radius is a little more than 4, so r² is not 16. The center is at (3,-4) and there is a point on the circle at (0,-1). You can draw a right triangle with legs equal to 3 and 3. That would mean that the hypotenuse, which is the radius of the circle, has a length of √(18). That means that r² = 18. Eliminate Choices (1) and (3).

There are minus signs in the formula, so the numbers are flipped. Choice (2) is correct.

27. Which task is not a component of an observational study?

1) The researcher decides who will make up the sample
2) The researcher analyzes the data received from the sample.
3) The researcher gathers data from the sample, using surveys or taking measurements.
4) The researcher divides the sample into two groups, with one group acting as a control group.

Answer: 4) The researcher divides the sample into two groups, with one group acting as a control group.

An observational study does not have a control group.

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.

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