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.

*26. Given:*

*
*

A = {perfect square integers from 4 to 100, inclusive}

B = {16, 36, 49, 64}*
*

The complement of set B in the universal set A is

(1) {9, 25, 81}

(2) {4, 9, 25, 81, 100}

(3) {1, 4, 9, 25, 81, 100}

(4) {4, 16, 36, 49, 64, 100}

**Answer: (2) {4, 9, 25, 81, 100} **

If A is the set of perfect square integers between 4 and 100, inclusive (meaning 4 and 100 are part of the set), then the complement of B in set A would be all the perfect squares between 4 and 100 that are NOT in set B.

Choice (1) does not include 4 and 100, so it is eliminated.

Choice (3) includes 1, but 1 is not an element of set A, so it is eliminated.

Choice (4) includes all the members of set B, along with 4 and 100. Eliminate it.

*27. The expression (2x*^{2} + 10x - 28) / (4x + 28) is equivalent to

(1) (x - 2) / 2

(2) x - 1

(3) (x + 2) / 2

(4) (x + 5) / 2

**Answer: ((1) (x - 2) / 2 **

Factor the numerator and denominator and cross out common factors.

(2x^{2} + 10x - 28) / (4x + 28)

= ( (2)(x^{2} + 5x - 14) ) / ( (4)(x + 7) )

= ( (2)(x + 7)(x - 2) ) / ( (4)(x + 7) )

= ( (x - 2) ) / ( (2) )
*28. Which value of x is the solution of the equation 1/7 + 2x / 3 = (15x - 3) / 21
*

(1) 6

(2) 0

(3) 4 / 13

(4) 6 / 29

**Answer: (1) 6 **

You can combine the fractions and cross-multiply, or you can multiply the entire equation by 21 to get rid of all the denominators:

[ 1/7 + 2x / 3 = (15x - 3) / 21 ] (21)

(21)(1/7) + (21)(2x/3) = ((15x - 3) / 21 ) (21)

3 + 14x = 15x - 3

6 = x
You could all try the choices to see which one works. It's fairly obvious that 0 incorrect ( 1/7 =/= -1/7), and 6 is the correct choice. The only problem is if the answer had been one of the fractions -- then plugging in values might've been a problem.

*29. Which statement is true about the data set 4, 5, 6, 6, 7, 9, 12?
*

(1) mean = mode

(2) mode = median

(3) mean < median

(4) mode > mean

**Answer: (2) mode = median **

The median and the mode are both 6, because 6 is the middle number of the 7 listed, and there are two of them.

The mean is the Sum / N, and N = 7. The Sum is 49, and 49 / 7 = 7, so the mean = 7.

The mean =/= mode. Eliminate (1)

The mode = median. This is the answer.

The mean is greater than the median, not less. Elinimate (3).

The mode is less than the mean, not greater. Eliminate (4).

Vertical lines, which are parallel to the y-axis, will have equations in the form x = a, like choices (1) and (2).

*30. How is the graph of y = x*^{2} + 4x + 3 affected when the coefficient
of x^{2} is changed to a smaller positive number?

(1) The graph becomes wider, and the y-intercept changes.

(2) The graph becomes wider, and the y-intercept stays the same.

(3) The graph becomes narrower, and the y-intercept changes

(4) The graph becomes narrower, and the y-intercept stays the
same.

**Answer: (2) The graph becomes wider, and the y-intercept stays the same. **

The coefficient of x

^{2} determines whether the parabola opens up or down and how narrow or wide the parabola will be. It has nothing to do with the y-intercept, which is determined by the constant (in this case, + 3).

Making the coefficient smaller, but still positive, means that the parabola will become wider as the y values will not increase as quickly.

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.