## Friday, August 15, 2014

### August 2014 Integrated Algebra Regents Exam, Multiple Choice

The problem with these exams is that they all happen at the same time and leave a lot of time to work on blog posts (and have a life, too!). Then again, whoever said that teachers have lives?

Here are the multiple-choice questions, the quick-and-dirty edition, which may or may not get updated in the near future.

1. What is the product of 3a2b and -2ab3?

(4) -6a32b4. Multiply the co-efficients, add the exponents (no exponent = 1).

2. The value of the expression |-20| - |6| is

(2) 14. (20 - 6 = 14)

3. When 9x2 - 100 is factored, it is equivalent to (3x - b)(3x + b). What is the value of b?

(2) 10. Difference of Squares Rule.

4. Which equation represents the line that passes through the points (1, 1) and (-2, 7)?

(4) y = -1/2 x + 6. Find the slope of the line first, (7-1)/(-2-1) = 6/(-3) = -1/2. Plug in x and y and check the two equations with that slope.

5. The graph below represents the parabolic path of a ball kicked by a young child. What are the vertex and the axis of symmetry for the parabola?

(1) vertex (3, 8); axis x = 3.

6. Which relationship can best be described as causal?

(3) The snow is falling and the stores run out of snow shovels. The others aren't related at all.

7. In a class, which data can be classified as qualitative?

(4) Hair color of students. Qualitative are descriptive, quantitative are amounts. I don't like this question because shoe size is more descriptive than an actual measurement. It is a measurement, but you'll never see it added, subtracted or averaged -- what would the point of knowing the "average" shoe size by, unless by "average" you meant "mode". But that's for another day.

8. Given the following:
..........................................................
What is the intersection of sets A, B, and C?

(4) Jade and Kyle are in all three sets, so they are the intersection.

9. The sun of (3x - 4)/(x + 3) and (2x - 5)/(x + 6) is

(1) (5x - 9)/(x + 3). Add the numerators, leave the denominators alone.

10. If Rosa's age is represented by R, which inequality represents the statement "Rosa is at most 29 years old"?

(3) R < 29

11. What is the slope of a line passing through points (-7, 5) and (5, -3)?

(2) Another slope question! Rise over run gives you (-2/3)

12. A positive correlation always exists on a scatter plot when

(4) y increases as x increases. Also, y decreases as x decreases. It trends up and to the right.

13. A sandwich consists of one type of meat, one type of condiment and one type of cheese. The possible choices are listed below:
.......................................................
In the sample space of all the possible different sandwiches consisting one type of meat, one type of condiment and one type of cheese, how many sandwiches do NOT include provolone cheese?

(1). Use the Counting Principle and multiple 3 * 3 * (4-1) = 27. There were four cheese, remove 1 for provolone.

14. The graph of the equation y = x2 is shown below.
....................................................
Which statement best describes the change in this graph when the coefficient of x2 is multiplied by 4?

(2) The parabola becomes narrower because it would increase higher, faster.

15. A parking lot is 100 yards long. What is the length of 3/4 of the parking lot, in feet. 1 yard = 3 feet.

(2) (3/4) * (100) * 3 = 75 feet

16. What is the solution of the equation (12/7x) + (3/2x) = 15/14

(3) Multiply the entire equation by 14x and you get 24 + 21 = 15x, so 45=15x and x = 3.

17. The expression (2x2 + 10x - 28)/(4x + 28) is undefined when x is

(2) -7, only. The fraction is undefined only if the denominator = 0. If the numerator is 0 (and not the denominator), the fraction is 0, not undefined.

18. In right triangle JKL in the diagram below, KL = 7, JK = 24, JL = 25, and angle K = 90 degrees.
...............................................
Which statement is not true?

(2) cos L = 24/25. That is false because cos L = 7 / 25.

19. A teacher asked the class to solve the equation 3(x + 2) = 21. Robert wrote 3x + 6 = 21 as his first step. Which property did he use?

(3) Distributive property.

20. If the roots of a quadratic equation are -4 and 2, the equation is equivalent to

(1) (x + 4)(x - 2) = 20. Flip the signs.

21. Kelsey scored the following points in her first six basketball games: 22, 14, 19, 22, 8 and 17. What is the relationship between the measures of central tendency?

(1) mode > median > mean

22. Sheba opened a retirement account with \$36,500. Her account grew at a rate of 7% per year compounded annually. She made no deposits or withdrawals on the account. At the end of 20 years, what was the account worth, to the nearest dollar?

(3) \$141,243. Exponential growth/compounded interest: Balance = 36500 (1.07)20

23. Which equation represents a vertical line?

(4) x = 12. Set x = to any constant, and you have a vertical line. In this case the line contains the points {... (12, -2), (12, -1), (12, 0), (12, 1), (12, 2), ... }

24. Byron has 72 coins in his piggy bank. The piggy bank contains only dimes and quarters. If he has \$14.70 in his piggy bank, which equation can be used to determine q, the number of quarters he has?

(3) 0.10(72 - q) + 0.25q = 14.70

25. Which graph represents the equation y = |x - 2|?

(4) The V shape in on the x-axis at (2,0). The -2 shifts the graph to the right.

26. If ax + 3 = 7 - bx, what is x expressed in terms of a and b?

(3) Subtract 3 from both sides. Add bx to both sides: ax + bx = 4.
Factor: (a + b)x = 4.
Divide: x = 4/(a + b)

27. Which equation represents a line that is parallel to the line whose equation is y = -3x?

(3) 6x + 2y = 4. Another slope question, but this time you had to work out which of the choices has a slope of -3 so it can be parallel to the given line.

28. What is the result when 6x2 - 13x + 12 is subtracted from -3x2 + 6x + 7?

(4) When you subtract 6 from -3 you get -9, and only choice (4) has that.

29. What is the solution set of the equation x / 3 = 8 / (x + 2).

(2). Cross multiply to get x2 + 2x = 24, subtract 24 from each side, factor and solve. Or plug in the choices and see what works. {-6, 4} both work.

30. Which set of integers is included in (-1, 3]?

(1) -1 is NOT included, but 3 IS included because of the square bracket. (I just went over this when I subbed last week. I hope they remembered!)

That's it for part one.
I will try to clean this up a bit over the weekend.