Algebra Problems of the Day (Integrated Algebra Regents, August 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, August 2011

Part II: Each correct answer will receive 2 credits. Partial credit is available.


31. Solve for c in terms of a and b: bc + ac = ab

Answer:

You have to factor c from each of the terms on the left before you can isolate it.

bc + ac = ab

c(b + a) = ab

c = ab / (b + a)

32. Ms. Hopkins recorded her students’ final exam scores in the frequency table below.

On the grid below, construct a frequency histogram based on the table.

Answer:

Rules for histograms: the bars must be the same size, the bars must be next to each other, there cannot be any gaps (excpet for when the data value is 0, which doesn't happen here). Also since the data doesn't start at zero, there needs to be a break on the x-axis, which can be indicated by a little squiggle. Also, there needs to be a title and labels for everything.

Your final chart should look like this one. Yours may have been skinnier or fatter, as long as the bars are the same size, and the title and labels make sense.

33. Mrs. Chen owns two pieces of property. The areas of the properties are 77,120 square feet and 33,500 square feet.

43,560 square feet = 1 acre

Find the total number of acres Mrs. Chen owns, to the nearest hundredth of an acre.

Answer: 1) 22 + 6π

Add the area of the properties and divide them by 43,560. I'm surprised that they didn't make this one a little more complicated, but it's only worth two points.

(77,120 + 33,500) / 43,560 = 2.5394...

Mrs. Chen owns are 2.54 acres.

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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