Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
August 2012
Part I: Each correct answer will receive 2 credits.
1. A system of equations is graphed on the set of axes below.
The solution of this system is
1) (0, 4)
2) (2, 4)
3) (4, 2)
4) (8, 0)
Answer: 3) (4, 2)
The solution to a system of equations is the point where the two lines intersect. That point is (4, 2). If you thought it was (2, 4), then you need to review which is the x coordinate and which is the y coordinate. Hint: the x comes first.
2. A cell phone can receive 120 messages per minute. At this rate, how many messages can the phone receive in 150 seconds?
1) 48
2) 75
3) 300
4) 18,000
Answer: 3) 300
Change minutes to seconds by dividing by 60 and then multiplying by 150 seconds.
120 / 60 * 150 = 300
If you multiplied by 60 and then divided by 150, you would've gotten 48. If you did 60 times 150 and then divided by 120 (I don't know why you would do that), you would get 75. If you just multiplied 120 by 150, you would have gotten 18,000. (It's rarely that easy when there's so much going on in a problem.)
3. The value of y in the equation 0.06y + 200 = 0.03y + 350 is
1) 500
2) 1,666.666...
3) 5,000
4) 18,333.333...
Answer: 3) 5,000
Note: On the actual exam, they used the repeater bar to indicate the repeating decimal.
0.03y + 200 = 350
0.03y = 150
y = 150/0.03 = 5,000
You can check your answer by substituting 5000 for y:
0.06(5000) + 200 = 0.03(5000) + 350
500 = 500 (check)
4. The scatter plot shown below represents a relationship between x and y.
This type of relationship is
1) a positive correlation
2) a negative correlation
3) a zero correlation
4) not able to be determined
Answer: 1) a positive correlation
First of all, we wouldn't say a "zero correlation". We'd say that there was no correlation. Is this splitting hairs? Maybe, but consider the difference between a zero slope and no slope. Words have meanings.
As the x values increase, the y values generally increase. So it is a positive correlation.
5. The sum of 3x2 + 5x - 6 and -x2 + 3x + 9 is
1) 2x2 + 8x - 15
2) 2x2 + 8x + 3
3) 2x4 + 8x2 + 3
4) 4x2 + 2x - 15
Answer: 2) 2x2 + 8x + 3
When you add polynomials, you combine like terms. The variables and their exponents do not change. Eliminate Choice (3).
The sum of the leading coefficients 3 and -1 is 2, so eliminate Choice (4).
5x + 3x = 8x and -6 + 9 = +3, so Choice (2) is the answer.
As the x values increase, the y values generally increase. So it is a positive correlation.
More to come. Comments and questions welcome.
More Regents problems.
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