Algebra Problems of the Day (Integrated Algebra Regents, January 2013

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.


21. If x = -3, what is the value of |x - 4| - x²?

(1) -8
(2) -2
(3) 7
(4) 16

Answer: (2) -2

|-3 - 4| - (-3)² = | -7 | - 9 = 7 - 9 = -2

Remember your Order of Operations. Absolute Value is a grouping symbol, like parentheses.

If you got 16 as your answer, you forgot to put parentheses around the -3 before you squared it.

22. Which equation represents a line parallel to the line whose equation is 2x - 3y = 9?

(1) y = 2/3 x - 4
(2) y = -2/3 x + 4
(3) y = 3/2 x - 4
(4) y = -3/2 x + 4

Answer: (1) y = 2/3 x - 4

Parallel lines have the same slope, and the choices are all written in slope-intercept form. So find the slope of the given line.

The given line is in Standard Form Ax + By = C, and the slope of a line written this way is -A/B.

If you weren't aware of that, or didn't remember, you could just rewrite the equation, solving for y in terms of x.

2x - 3y = 9
-3y = -2x + 9
y = 2/3 x - 3

The slope is 2/3.

Note that Choice (4) would be a perpendicular line. The other two would intersect the given line, but are not perpendicular to it.

23. Which ordered pair is in the solution set of the system of inequalities y < 3x + 1 and x - y > 1?

(1) (-1, -2)
(2) (2, -1)
(3) (1, 2)
(4) (-1, 2)

Answer: (2) (2, -1)

You could either plug these in, or put both inequalities into the graphing calculator. (You have to rewrite the second inequality.)

-2 ?< 3(-1) + 1 = -2, true, but -1 - (-2) = 1 ?> 1 is false.

-1 ?< 3(2) + 1 = 7, true, and 2 - (-1) = 3 ?> 1 is true. This is the solution.

2 ?< 3(1) + 1 = 4, true, but 1 - (2) = -1 ?> 1 is false.

2 ?< 3(-1) + 1 =-2, is false, and -1 - (2) = -3 ?> 1 is false.

24. Which equation represents the line that passes through the point (-3,4) and is parallel to the x-axis?

(1) x = 4
(2) x = -3
(3) y = 4
(4) y = -3

Answer: (3) y = 4

Lines parallel to the x-axis are horizontal and have a slope of 0, which means that they have an equation of the form y = b. Since it goes through (-3, 4), it must be y = 4.

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

25. A cube with faces numbered 1 through 6 is rolled 75 times, and the results are given in the table below.

(1) P(odd) <P(even)
(2) P(3 or less) < P(odd)
(3) P(even) < P(2 or 4)
(4) P(2 or 4) < P(3 or less)

Answer: (4) P(2 or 4) < P(3 or less)

Calculate the experimental probabilities and compare the results.

P(odd) = (7 + 14 + 20) / 75 = 41 / 75, which is more than half, so there is no reason to calculate P(even) which must be 1 - 41/75. Eliminate Choice (1).

P(3 or less) = (7 + 22 + 14) / 75 = 43 / 75, which is more than P(odd), or 41/75. Eliminate (2).

P(even) = 1 - 41/75 = 34/75. P(2 or 4) = (22 + 6) / 75 = 28 / 75. Eliminate (3).

P(2 or 4) = 28/75. P(3 or less) = 43/75. This is the correct choice.






More to come. Comments and questions welcome.

More Regents problems.