Algebra Problems of the Day (Integrated Algebra Regents, January 2011)

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, January 2011

Part III: Each correct answer will receive 3 credits. Partial credit is available.


34. A line having a slope of 3/4 passes through the point (−8,4).

Write the equation of this line in slope-intercept form.

Answer:

You can write the equation in point-slope form and then convert it to slope-intercept form.

In point-slope form, it's either

y - 4 = 3/4(x + 8) or y = 3/4(x + 8) + 4

depending upon which way you learned it. If you wrote the first one, the first step is to add 4 to both sides and get the second one.

Then use the Distributive Property.

y = 3/4x + 6 + 4

y = 3/4x + 10

35. The test scores for 18 students in Ms. Mosher’s class are listed below:

86, 81, 79, 71, 58, 87, 52, 71, 87, 87, 93, 64, 94, 81, 76, 98, 94, 68
Complete the frequency table below:

Draw and label a frequency histogram on the grid below.

Answer:

Record a tally mark for each score in an interval. Then count them up to get the Frequency.

Next, use the table to make the histogram.

Things to take note of: the bars on your histogram need to be the same width, whatever that width is (2 boxes, 3 boxes); there needs to be a space on the x-axis and a squiggle to indicate a break because the x-axis is a number line and the bottom left corner is zero; each bar needs to be labeled with its interval; each of the axes needs to have a label; the histogram needs a title.

If any of those are missing or inconsistent, you can leave a point. Multiple mistakes will cost you two points from a three-point problem. That's a lot of credit to give up for silly mistakes after putting in all the effort.

36. Solve algebraically for x: (x + 2) / 6 = 3 / (x - 1)

Answer:

It's a proportion, so you can cross-multiply. Then solve the resulting quadratic equation by setting it equal to 0 and factoring.

(x + 2) / 6 = 3 / (x - 1)

(x + 2)(x - 1) = (3)(6)

x² + x - 2 = 18

x² + x - 20 = 0

(x + 5)(x - 4) = 0

x + 5 = 0 or x - 4 = 0

x = -5 or x = 4

End of Part III.

More to come. Comments and questions welcome.

More Regents problems.

I also write Fiction! You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Preorder the softcover or ebook at Amazon. Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.