Tuesday, November 30, 2021

Algebra Problems of the Day (Integrated Algebra Regents, August 2011)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones. The Integrated Algebra Regents covered most of the same material as the current Algebra Regents, with a few differences.

More Regents problems.

Integrated Algebra Regents, August 2011

6. Based on the box-and-whisker plot below, which statement is false?

1) The median is 7.
2) The range is 12.
3) The first quartile is 4.
4) The third quartile is 11.

Answer: 2) The range is 12..

What we can identify from the graph is that the minimum value is 2, the first quartile is 4, the median is 7, the third quartile is 11, and the maximum value is 12. We can calculate that the range is 12 - 2 = 10 and the interquartile range (IQR) is 11 - 4 = 7.

Choice (2) is the only statement that is false.

7. The ninth grade class at a local high school needs to purchase a park permit for \$250.00 for their upcoming class picnic. Each ninth grader attending the picnic pays \$0.75. Each guest pays \$1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?

1) 0.75x − (1.25)(200) ≥ 250.00
2) 0.75x + (1.25)(200) ≥ 250.00
3) 0.75x + (1.25)(200) ≥ 250.00
4) 0.75x + (1.25)(200) ≥ 250.00

Answer: 4) 0.75x + (1.25)(200) ≥ 250.00

Obviously, the sum has to be greater than \$250.00, so eliminate the two subtraction answers, Choices (1) and (3).

If 200 ninth graders are paying \$0.75 each then (200)(0.75) needs to appear in the solution. That's Choice (4). The x number of guests will each pay 1.25, so 1.25x is added to the (200)(0.75) already collected.

8. Which equation represents the line that passes through the point (1,5) and has a slope of −2?

1) y = -2x + 7
2) y = -2x + 11
3) y = 2x - 9
4) y = 3x + 3

Answer: 1) y = -2x + 7

A slope of -2 means that the equation is y = -2x + b, and you have to find b. Eliminate Choices (3) and (4).

You can solve for b, or you can substitute 1 for x and see which equation gives you y = 5.

y = -2(1) + 7 = 5. Choice (1) is your answer.

y = -2(1) + 11 = 9. Not the equation we're looking for.

9. What is the solution of the system of equations 2x − 5y = 11 and −2x + 3y = −9

1) (−3,−1)
2) (−1,3)
3) (3,−1)
4) (3,−1)

You could solve algebraically, or you could work backward from the choices.

Algebraically, if you add the two equations together, you get -2y = 2, so y = -1. That eliminates Choices (2) and (4).

Again, you could solve for x, or you could substitute x = 3 and see if it works:

2(3) - 5(-1) ?= 11
6 + 5 = 11. Choice (3) is correct.

2(-3) - 5(-1) ?= 11
-6 + 5 != 11. Choice (1) was incorrect.

10. Which algebraic expression represents 15 less than x divided by 9?

1) x/9 - 15
2) 9x - 15
3) 15 - x/9
4) 15 - 9x

Only two of the choices have division in them. The other two have multiplication and subtraction. Eliminate choices (2) and (4).

If it is "15 less than", then you are taking 15 away from x/9, so it is choice (1).

More to come. Comments and questions welcome.

More Regents problems.

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