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 III: Each correct answer will receive 3 credits. Partial credit is possible.
Based on the cumulative frequency histogram, determine the number of swimmers who swam
between 200 and 249 yards.
Determine the number of swimmers who swam between 150 and 199 yards.
Determine the number of swimmers who took the swim test.
34. The following cumulative frequency histogram shows the distances swimmers completed in a
recent swim test.
Answer:
There are three questions and each is worth a credit.
For the first question, to find the number of swimmers who swam between 200 and 249 yards, look at the columns labeled "50–249" and "50–299". The difference between those two amounts is what you are looking for. Subtract 20 - 15 = 5. There were 5 swimmers in that range.
Similarly, to find the number between 150 and 199, look at " 50–149" and "50–199". They are both the same, so 12 - 12 = 0. There were 0 swimmers in that range.
The number of swimmers is 20 because the cumulative frequency chart counts everyone, and everyone will be included in the final column.
35. Ashley measured the dimensions of a rectangular prism to be 6 cm by 10 cm by 1.5 cm. The actual dimensions are 5.9 cm by 10.3 cm by 1.7 cm. Determine the relative error, to the nearest thousandth,
in calculating the volume of the prism.
Answer:
Reminder: Relative error is a decimal. Percent of error is a percentage. Should that make a difference? Honestly, I don't think so, but the people who write the rubrics would disagree with me. And their voice is the one that matters, unfortuately.
What this means is, if you do all the work correctly and then express the answer as a correct percentage, you will lose a point, which amounts to 1/3 of the credit for the problem. Or about 33.3%.
To find the relative error, calculate the volume using Ashley's measurements. Then calculate the actual volume with the actual measurements. Find the difference between those two amounts and divide it by the actual volume. Round it to three decimal places.
Ashley's volume: V = L * W * H = 6 * 10 * 1.5 = 90
Actual volume: V = L * W * H = 5.9 * 10.3 * 1.7 = 103.309
Error: (103.309 - 90) / (103.309) = 0.1288...
To the nearest thousandth, the relative error is 0.129.
36. Solve the following system of equations algebraically for all values of x and y.
y = 2x + 1
Answer:
Note that you could graph it or use a table of values, but in doing so, you would only get one point for a correct answer for not solving it algebraically. You can also do this first if you want to know what the answer is before you start solving it algebraically. (There's nothing wrong with doing this.)
To solve the system of equations, set the two equations equal to each other. Since each expression is equation to y, then they are equal to each other. Once you do that, you can solve the quadratic equation that you get.
y = 2x + 1
x2 + 2x - 8 = 2x + 1
x2 - 9 = 0
(x + 3)(x - 3) = 0
x + 3 = 0 or x - 3 = 0
x = -3 or x = 3
Now that you know the values of x, go back and find the matching values of y.
y = 2(-3) + 1 = -6 + 1 = -5. (-3, -5)
y = 2(3) + 1 = 6 + 1 = 7. (3, 7)
End of Part III.
More to come. Comments and questions welcome.
More Regents problems.
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