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.
What is the surface area, in square centimeters?
16. The rectangular prism shown below has a length of 3.0 cm, a width of 2.2 cm, and a height of 7.5 cm.
1) 45.6
2) 49.5
3) 78.0
4) 91.2
Answer: 4) 91.2
The surface area is the sum of the areas of the six sides of the prism. Since it is a rectangular prism, the opposite sides have the same area.
You have find the L * W, L * H, and W * H, double each of those, and find the sum.
L * W = 3 * 2.2 = 6.6
L * H = 3 * 7.5 = 22.5
W * H = 2.2 * 7.5 = 16.5
2 * (6.6 + 22.5 + 16.5) = 91.2
17. Which set of coordinates is a solution of the equation 2x - y = 11?
1) (-6, -1)
2) (-1, 9)
3) (0, 11)
4) (2, -7)
Answer: 4) (2, -7)
You can try each of the choices to see which makes a true statement, or you can rewrite the equation, solving for y, and put that into your graphing calculator and look at the Table of Values for the correct entry.
2x - y = 11
2x - 11 = y, or y = 2x - 11
Ironically, it wasn't until I typed the above equation just now that I noticed that the first three choices are all solutions to y = 2x + 11. I would've just did the mental math.
18. The graph of a parabola is represented by the equation y = ax2
where a is a positive integer. If a is multiplied by 2, the new parabola
will become
1) narrower and open downward
2) narrower and open upward
3) wider and open downward
4) wider and open upward
Answer: 2) narrower and open upward
Since a is positive, it opens upward. Eliminate Choices (1) and (3).
If you double a, then the y values will increase more rapidly. That will cause the parabola to become thinner, or narrower.
19. Which equation represents a line that has a slope of 3/4 and passes through the point (2,1)?
1) 3y = 4x - 5
2) 3y = 4x + 2
3) 4y = 3x - 2
4) 4y = 3x + 5
Answer: 3) 4y = 3x - 2
The choices given are not in any familar form. However, they could easily be put into slope-intercept form by dividing by the coefficient of y to get y = mx + b.
If you divide Choices (1) and (2) by 3, then the value of m will be 4/3 instead of 3/4. Eliminate choices (1) and (2).
Next, substitute x = 2 into Choices (3) and (4).
4y = 3(2) - 2 = 6 - 2 = 4; 4y = 4, y = 1. This is the solution we are looking for.
4y = 3(2) + 5 = 6 + 5 = 11; 4y = 11, y = 11/4. This is NOT the solution we are looking for.
20. What is the value of | ( 4(-6) + 18 ) / 4! | ?
1) 1/4
2) - 1/4
3) 12
4) -12
Answer: 1) 1/4
I hate questions like this. I had a student come up to me after the exam and ask me, "Mr. Burke, what does an exclamation point in a math problem mean?" That's not to say that he shouldn't have known it, but the notation wasn't used as much as the concept it stands for. However, the reason I hate this problem is because it's meaningless and bizarre. There is no reason to put a factorial symbol in an equation like this other than to see if students were paying attention. It's a meaningless Order of Operations question with an added twist to it that only makes it longer, but not more challenging or interesting.
Order of Operations: Evaluate the numerator, multiply and add. Then evaluate the factorial, 4!, which is 4*3*2*1. Then simplify the fraction. Finally, take the absolute value.
Note that the Absolute Value is the final step, so the answer cannot be negative. Eliminate Choices (2) and (4).
= | ( -24 + 18 ) / 4! |
= | -6 / 4! |
= | - 6/24 |
= | -1/4 |
= 1/4
I'm a little curious where they got 12 from. That should come from an "obvious" mistake, but I'm not seeing it.
More to come. Comments and questions welcome.
More Regents problems.
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