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 I: Each correct answer will receive 2 credits.
26. Right triangle ABC has legs of 8 and 15 and a hypotenuse of 17, as
shown in the diagram below.
The value of the tangent of ∠B is
1) 0.4706
2) 0.5333
3) 0.8824
4) 1.8750
Answer: 2) 0.5333
The tangent of angle B is the ratio of the side opposite B, which is AC, and the side that is adjacent to angle B, which is CB. Do not use side AB -- that is the hypotenuse.
tan B = opp/adj = 8/15 = 0.53333...., which is Choice (2).
27. What is (2 + x) / (5x) - (x - 2) / (5x) expressed in simplest form?
1) 0
2) 2/5
3) 4/(5x)
4) (2x + 4) / (5x)
Answer: 3) 4/(5x)
The two fractions have a common denominator, so you can just subtract the numerators
(2 + x) - (x - 2) = 2 + x - x + 2 = 4
The correct answer is Choice (3) 4/(5x).
Note that I have to use parentheses to represent these fractions correctly. They are not in the original problem.
28. How many different four-letter arrangements are possible with the
letters G, A, R, D, E, N if each letter may be used only once?
1) 15
2) 24
3) 360
4) 720
Answer: 3) 360
There are six choices for the first letter, five for the second, four for the third and three for the fourth.
There are 6 * 5 * 4 * 3 = 360 ways to select 4 letters from the six, without repeats.
This is 6P4.
Choice (4) 720 is equal to 6! = 6 * 5 * 4 * 3 * 2 * 1, which is the number of SIX letter arrangements.
29. What is an equation of the line that passes through the points (1,3)
and (8,5)?
1) y + 1 = 2/7 (x + 3)
2) y - 5 = 2/7 (x - 8)
3) y - 1 = 2/7 (x + 3)
4) y + 5 = 2/7 (x - 8)
Answer: 2) y - 5 = 2/7 (x - 8)
All four choices have slope = 2/7, so you don't have to calculate the slope of the line.
The Choice are written in Point-Slope Form, which can be written as
Notice the minus signs in the formula. There should be two minus signs in the answer because all of the coordinates are positive.
Choice (1) has two plus signs. Eliminate it.
Choice (2) has two negative signs, which go with the positive coordinates (8,5).
Choice (3) and (4) make no sense. They each have one positive and one negative. That should tell you something is off.
I found it surprising that they didn't have any choices where the x-coordinate and y-coordinate were flipped around, or one that used, say, the two x-coordinates.
30. An example of an algebraic expression is
1) x + 2
2) y = x + 2
3) y < x + 2
4) y = x2 + 2x
Answer: 1) x + 2
An algebraic expression has only variables, constants and operators. It doesn't have an equal sign or any inequalities.
Choice (1) is an algebraic expression. It's the correct answer.
Choice (2) is an algebraic equation because it has an equal sign.
Choice (3) is an algebraic inequality because it has a less than sign.
Choice (4) is an algebraic equation because it has an equal sign. It's also a quadratic equation.
End of Part I.
More to come. Comments and questions welcome.
More Regents problems.
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