Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones. The Integrated Algebra Regents covered most of the same material as the current Algebra Regents, with a few differences.
More Regents problems.
Integrated Algebra Regents, August 2010
Part III: Each correct answer will receive 3 credits. Partial credit is available. One computational error will cost 1 credit. A conceptual error will usually cost 2 credits.
State the values of the minimum, 1st quartile, median, 3rd quartile, and maximum.
Using these values, construct a box-and-whisker plot using an appropriate scale on the line below.
34. The number of songs fifteen students have on their MP3 players is:
Answer:
The numbers are already in order, so the first step is down for you. Next, you need to find the Five-Number Summary. There are so few pieces of data that it will be quicker to do by hand than if you put it in your calculator. (If you use your calculator, double-check your data entry.)
There are 15 pieces of data. The first, 120, is the Minimum. The last, 452, is the Maximum. The number in the middle of the 15 is the 8th piece of data, is the Median, 292.
There are 7 pieces of data less than the median and 7 more that are greater than the median. The middle number of the lower 7, the fourth number, is the First Quartile (Q1), 145. The middle number of the upper 7, the fourth from the end, or the 11th, is the Third Quartile (Q3), 407.
You can now make the box-and-whisker plot above the number line. Before you do this, you have to decide upon a scale to use to number it. The Range = Maximum - Minimum = 452 - 120 = 332. Since there are only 21 tick marks on the number line, you need to use a scale of 20 or larger. Don't make it too large, or you wrote be able to plot the points accurately.
DO NOT DRAW THE BOX AND WHISPER PLOT AND THEN NUMBER THE LINE. YOU WILL LIKELY LOSE 2 OUT OF THE 3 POINTS.
Look at the image below:
35. Find the volume, in cubic centimeters, and the surface area, in square centimeters, of the
rectangular prism shown below.
Answer:
The volume of a rectangular prism is the product of the Length times the Width times the Height. The surface area is the total area of the six rectangles: the front and back, the left and right, and the top and bottom. Each pair listed in the previous sentence are congruent, so you find one and double it.
V = 10 * 2 * 4 = 80 cm3.
S = 2(10)(2) + 2(10)(4) + 2(2)(4) = 136 cm2.
SHOW YOUR SUBSTITUTIONS. Don't just put the numbers in the calculator and write the answers.
You don't need to include the units because they are in the question. HOWEVER, if you include the units, and you make a mistake, such as writing cm2 for Volume, you will lose a point.
36. Find the roots of the equation x2 = 30 − 13x algebraically.
Answer:
Algebraically means that if you do it some other way, like sketching a graph or using your calculator, you will not get full credit. You would likely get only 1 credit out of the 3.
That said, if you make a graph, you will know the answer that you need to find when you do it algebraically, and you'll know if you've made a mistake.
x2 = 30 − 13x
x2 + 13x - 30 = 0
(x + 15)(x - 2) = 0
x + 15 = 0 or x - 2 = 0
x = -15 or x = 2
End of Part III.
More to come. Comments and questions welcome.
More Regents problems.
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