Integrated Algebra Regents Exam (August 2013) Discussion, Part 1

I've been itching to do this for a few days now, just to get my mind off other things.

Comments are welcome and encouraged!

EDIT: I've added the questions to the answers listed below because students are using search engines to find the answers, and that will lead them here!

Part 1: Multiple Choice

As there are 30 questions, I will be brief about them. The questions and answers are online, so I'm restrict my comments to the "tricky" ones. I won't retype the entire type or restate what is (hopefully) obvious.

1. Which situation describes a negative correlation?
Amount of gas used and the amount of gas left make a negative correlation. The others are positive.

2. The sum of 8n - 3n + 10 and -3n² - 6n - 7 is
Watch the signs. Choice (1).

3. Which event is certain to happen?
Certainty in probability means 100% of the time. As much as I'd like to say "The Yankees" (but that would be boring), it's "the sun rises in the east."

4. Noj is 5 years older than Jacob. The product of their ages is 84. How old is Noj?
(x)(x+5)=84. The older brother is 12. (3)
You don't have to solve a quadratic equation to get this. You can look at the choices. Multiply each number by the number that is five less. Which product is 84? (6)(1), (7)(2), (12)(7) or (14)(9)?

5. Marie currently has a collection of 58 stamps. If she buys s stamps each week for w weeks, which expression represents the total number of stamps she will have?
Seriously, this question looks recycled. Not "similar", I mean "recycled". 58 + sw.

6. Given: A  {all odd integers from 1 through 19, inclusive} B  {9, 11, 13, 15, 17} What is the complement of set B within set A?
They want the members of A that are NOT in B. "Inclusive" means that 1 and 19 are elements of set A. Answer is (4).

7. Which equation represents a line that is parallel to the line whose equation is y = - 3x - 7?
This is a "gimme". Parallel lines have the same slope. You didn't even have to find the slope because the question and the choices were all in slope-intercept form.

8. Which graph does not represent the graph of a function?
Choice (3) fails the Vertical Line Test and is not a function. The others are linear, quadratic and absolute value functions.

9. Which value of x is in the solution set of -3x + 8 ≥ 14?
Plug in the choices one at a time and the answer is the first one. In an inequality such as this one, the answer almost always has to be the highest or the lowest number. It's the lowest.

10. What is the slope of the line that passes through the points (4,-7) and (9,1)?
Slope of a line = rise / run or "change in y" / "change in x". (2) 8/5

11. Simplify the fractions by cancelling common factors. (3) and (4) aren't simplest form, and there are more factors of x in the denominator than in the numerator, so it's choice (2).

12. The box-and-whisker plot below represents a set of grades in a college statistics class. [GRAPH OMITTED] Which interval contains exactly 50% of the grades?
My tutoring class just went over box-and-whisker plots (see the comic on Quartiles), so I hope they all got this one. Each section represent 25% of the data, so two sections is 50%. (4) includes exactly two quartiles.

13. An art studio has a list of information posted with each sculpture that is for sale. Each entry in the list could be classified as quantitative except for the
"Quantitative" is an answer to "how much" or "how many". (It's numeric.) The name of the artist is not quantitative. (Note: Remember, not all numeric data is quantitative, but that's for another day.)

14. Which graph represents the inequality y ≥ x + 3?
">" means greater than or equal to. Solid line and shaded above. (2)

15. Using the substitution method, Ken solves the following system of equations algebraically
2x - y = 5
3x + 2y = - 3
Which equivalent equation could Ken use?

Okay, this one is just EVIL! When given a choice, it's easier to solve a problem like this through elimination. I don't force my students to use substitution when a different method is better and simpler. In problem solving you are supposed to come up with a plan of action. This goes against the plan.

Anyway . . . rewrite 2x - y = 5 as 2x - 5 = y and substitute and you get 3x + 2(2x - 5) = -3, which is (1).

16. A fraction is "undefined" when the denominator is zero, so the real question here is "Solve for x when x² - 2x - 15 = 0. That happens when x = 5 or x = -3. The correct choice is (4). (Again, you could have substituted for each of the choices, which may have been faster for you.)

17. The statement |-15| < x < |-20| is true when x is equal to
Definition of absolute value. Notice that x does not have absolute value symbols, so the only correct answer is (3).

18. Which equation is true?
A little involved, but easily done. You have evaluate the left side to see if it equals the right side. When dividing fractions you flip the second fraction over and multiply. c⁵ * c is not equal to c⁴, so (1) is wrong. Choice (2) applies the exponent to everything inside the parentheses, so (2) is the answer. In (3), (t⁸/t⁵)² would have an exponent of 6 not 5. In (4), the product of the co-efficients (-2)(3) is (-6), not 1 (which is omitted).

19. The equation 3(4x)  (4x)3 illustrates which property?
Switching the order of two multiplicands is commutative.

20. Monique has three sons who play football, two sons who play baseball, and one son who plays both sports. If all of her sons play baseball or football, how many sons does she have?
I hate the wording of this problem because the word "only" might be inferred by students reading it, and they would be incorrect for doing that. One son plays both sports, so one son just plays baseball, and two just play just football, so she has four sons. (4)

21. Written in set-builder notation, S = {1, 3, 5, 7, 9} is
Even if you didn't know what set-builder notation was, you could infer the correct answer by knowing that "1 < x < 9, where x is an odd number" means "1, 3, 5, 7, 9".

22. Which is the equation of a parabola that has the same vertex as the parabola represented by y = x², but is wider?
To widen a parabola, you need a smaller (in this case, fractional) co-efficient. If you change the y-intercept, you will change the vertex. Choice (4).

23. In right triangle ABC, m∠C = 90, AC = 7, and AB = 13. What is the length of BC?
Since angle C is the right angle, side AB is the hypotenuse. The length of BC is the square root of (13² - 7² = 169 - 49 = 120). Choice (3). If you added, you incorrectly got (4) as your answer.

24. A cube, with faces numbered 1 to 6, is rolled, and a penny is tossed at the same time. How many elements in the sample space consist of an even number and a tail?
Three elements: 2T, 4T, 6T. I hope you did NOT try using the Counting Principle on this one.

25. If the volume of a cube is 8 cubic centimeters, what is its surface area, in square centimeters?
Volume of a cube is s³ = 8, so s = 2. The surface area is 6s², which is 24. (2) Fixed

26. A designer created a garden, as shown in the diagram below. The garden consists of four quarter-circles of equal size inside a square. The designer put a fence around both the inside and the outside of the garden.

Which expression represents the amount of fencing, in yards, that the designer used for the fence.
Four quarter-circles is one full circle. The circumference of the circle is 10pi (not 5pi or 25pi). The perimeter of the square is (4)(10) = 40. Answer (1) 40 + 10pi.

27. Mr. Taylor raised all his students’ scores on a recent test by five points. How were the mean and the range of the scores affected?
Curveball! They included the range. I went over this question with my students, but I didn't include the range (which wasn't included in previous tests). The mean goes up by five because the all the scores went up by five; however, the range remains the same because the highest score and the lowest score were increased by the same amount.

28. The common denominator between 3a and 2a is 6a. Multiply the first fraction by (2/2) and the second by (3/3) and you get (8/6a) - (15/6a), which is (-7/6a). Choice (3). No exponents!

29. Which ratio represents the cosine of angle A in the right triangle below?
What did I tell everyone about their overuse of 3-4-5 triangles? Cosine is adjacent/hypotenuse, 3/5. (1). Cosine can't be greater than 1, so (2) and (4) are right out.

30. If 2y + 2w = x, then w, in terms of x and y, is equal to
Subtract 2y from both sides and then divide by 2. You get (x - 2y)/2. (2)

How did you do? Be honest. Fifteen correct answers is a passing grade and everything else is extra, but we're all hoping for a lot better than merely passing, right?

Parts II, III and IV to come.