While I'm waiting for new Regents exams to come along, I'm revisiting some of the older NY Regents exams.
More Regents problems.
Administered January 2013
Part I: Each correct answer will receive 2 credits.
16. What is 24x2y6 - 16x6y2 + 4xy2 divided by 4xy2?
(1) 6xy4 + 4x5
(2) 6xy4 + 4x5 + 1
(3) 6x2y3 + 4x6y
(4) 6x2y3 + 4x6y + 1
Answer: (2) 6xy4 + 4x5 + 1
When you divide a trimonimal by a monomial, the result will still be a trinomial. You will not reduce the number of terms. So Choices (1) and (3) are eliminated.
When you divide 4xy2 by 4xy2, the result is 1, not 0, so the answer must end with + 1.
The rule for division of variables with exponents is that you subtract the exponent values: if you have six factors of y and you divided by two factors of y, then four factors of y would remain, which would be y4.
You do NOT divide the exponents as is the case in Choices (3) and (4).
17. Which expression can be used to change 75 kilometers per hour to
meters per minute?
Answer: (3) (75 km) / (1 hr) X (1,000m) / (1 km) X (1 hr) / (60 min)
Units can be canceled in fractions the same way that factors can. If the same unit appears in both the numerator and the denominator, it is divided by itself with a result of 1 (that is, it goes away). On the other hand, if the same unit appear twice on the top or the bottom of a fraction, it gets multiplied and becomes squared (that is, it doesn't go away).
You want kilometers and hours to go away, leaving you with just meters on top and minutes on the bottom.
Choices (1) and (2) have km on top twice and meters on the bottom. Eliminate them.
Choice (4) has hr on the bottom twice and minutes on the top. Eliminate it.
18. The inequality -2 < x < 3 can be written as
(1) (-2, 3)
(2) [-2, 3)
(3) (-2, 3]
(4) [-2, 3]
Answer: (4) [-2, 3]
If should be obvious that since the inequality symbol < was used twice that the two brackets should be the same.
Since they both say less than or equal to, the square brackets are used to indicate that the numbers shown are part of the solution.
19. The expression (6 X 10-7) / (3 X 10-3) is equivalent to
(1) 2 X 104
(2) 2 X 1010
(3) 2 X 10-4
(4) 2 X 10-10
Answer: (3) 2 X 10-4
Did you notice the parentheses I added to the problem so I could type it out without any ambiguity to the problem? You need those parentheses if you are using a calculator to solve this but its Operating System does not have actual fractions in the display window.
If you didn't include the parentheses in the denominator, you would have gotten an incorrect solution becuase the Order of Operations would take over, and you might never realize the mistake you made.
That said, there is no reason to use a scientific or graphing calculator for this problem!
The factors are lined up nicely for you: 6 / 3 = 2 and 10-7 / 10-3 = 10(-7 - -3). The rule is to subtract the exponents, and -7 - -3 = -4, so it will be 10-4.
20.The roots of the equation x2 - 14x + 48 = 0 are
(1) -6 and -8
(2) -6 and 8
(3) 6 and -8
(4) 6 and 8
Answer: (4) 6 and 8
The factors of x2 - 14x + 48 are (x - 6) and (x - 8).
If x - 6 = 0 then x = 6.
If x - 8 = 0 then x = 8.
Note that the final term is + 48, so you should have known immediately that the two roots were both positive or both negative and eliminated Choices (2) and (3).
More to come. Comments and questions welcome.
More Regents problems.
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