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 IV: Each correct answer will receive 4 credits. Partial credit is available.


37. An oil company distributes oil in a metal can shaped like a cylinder that has an actual radius of 5.1 cm and a height of 15.1 cm. A worker incorrectly measured the radius as 5 cm and the height as 15 cm.

Determine the relative error in calculating the surface area, to the nearest thousandth.

Answer:

Remember that they are asking for relative error, which is a decimal, not the percent of error. If you give the answer as a percentage, you will lose a point. (No, I don't agree with that, but I don't write the rubric.)

The relative error is the difference between the actual amount and the measured amount, divided by the actual amount.

You don't actually have to find the two surface areas, but you need to have the factors in your equation. Why would you do this? Because you can eliminate pi from the equation.

Surface area of a cylinder is equal to 2 π r² + 2 π r h

( (2 π (5.1)² + 2 π (5.1)(15.1)) - (2 π (5)² + 2 π (5)(15) )
(2 π (5.1)² + 2 π (5.1)(15.1))

2π( ((5.1)² + (5.1)(15.1)) - ((5)² + (5)(15) )
((2 π)((5.1)² + (5.1)(15.1)))

( ((5.1)² + (5.1)(15.1)) - ((5)² + (5)(15) )
((5.1)² + (5.1)(15.1))

( 103.02 - 100 )
103.02

3.02
103.02

Which is approximately equal to 0.029 to the nearest thousandth.

38. The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund.
Each year the fund will decrease by 5%. Determine the amount of money, to the nearest cent, that will be left in the sports fund after 4 years.

Answer:

You can use the equation for exponential decay and get it in one shot, or you can you the calculate 5% of the total, subtract it and then repeat that three more times. You will get the same answer.

Do the long one if you don't remember how to do the quick method.

A = 30000(1.00 - 0.05)⁴ = 24435.19, to the nearest cent.

The longer way:

100 - 5% = 95% that remains, which is .95.

30000 * 0.95 = 28500

28500 * 0.95 = 27075

27075 * 0.95 = 25721.25

25721.25 * 0.95 = 24435.1875 = 24435.19

Note: According to the Answer Key, a result of 24435.20 was also acceptable because different models and brands of calculators yield slightly different results.

39. Graph the following system of inequalities on the set of axes shown below and label the solution set S.

y > −x + 2
y ≤ 2/3 x + 5

Answer:

Thankfully, the inequalities are already in slop-intercept form and are ready to be entered into your graphing calculator, if you have one.

Most that the first inequality says greater than. The line will be broken (dashed, dotted) and the graph will be shaded Above the line. The second inequality says less than or equal to. This line will be solid (part of the solution). The graph will be shaded below the line.

Make sure that you label the two lines, even if it looks "obvious" to you. Look at the graph below:

End of Exam.

More to come. Comments and questions welcome.

More Regents problems.

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