Algebra Problems of the Day (Integrated Algebra Regents, June 2013)

And now for something completely different.

While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


6. The roots of a quadratic equation can be found using the graph below.

What are the roots of this equation?

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

Answer: (3) -1 and 4
The roots of the equation are the points where the line crosses the x-axis. This occurs at -1 and 4.

It should have been obious that choices (1) and (4) were incorrect because there are two places where the lines crosses the x-axis.

7. If the area of a rectangle is represented by x² + 8x + 15 and its length is represented by x + 5, which expression represents the width of the rectangle?

(1) x + 3
(2) x - 3
(3) x² + 6x + 5
(4) x² + 7x + 10

Answer: (1) x + 3
Since the formula for the Area of a rectangle is A = LW then x² + 8x + 15 = (x + 5) W.

Factor x² + 8x + 15 and you get (x + 5)(x + 3). You can check this by multiplying, which will give you x² + 5x + 3x + 15.



8Which set of data describes a situation that would be classified as qualitative?

(1) the colors of the birds at the city zoo
(2) the shoe size of the zookeepers at the city zoo
(3) the heights of the giraffes at the city zoo
(4) the weights of the monkeys at the city zoo

Answer: (1) the colors of the birds at the city zoo
Color is a character trait and is descriptive. That makes it a quality of the object, or qualitative data.

The other three are measurable, or quantifiable, so they are quantative data. You could make an argument about shoe size, as that is an arbitrary scale, and it different measures are usually used for male and female, but it is a size that is quantifiable by some scale.

Color is the better choice.

9. The value of the expression 6! + (5!)(3!)/4! - 10 is

(1) 50
(2) 102
(3) 740
(4) 750

Answer: (3) -1
I will come straight out and say: This is a STUPID Question.

It doesn't mean anything. It is an attempt to see if you understand what a factorial is (the exclamation point) and then can properly perform the Order of Operations.

I remember a student asking me after the exam, "Mr. Burke, what does an exclamation point in a math problem mean?" He, apparently, had never seen it.

For those who don't know what a Factorial (!) is, a number like 6! is calculated as 6 * 5 * 4 * 3 * 2 * 1. Start with that number and multiply it by every integer down to 1. This is something that gets used with combinations and permutations.

But this isn't a combination problem. It's just a mess.

Okay, let's solve it now:

6! + (5!)(3!)/4! - 10
= 720 + (120)(6)/(24) - 10
= 720 + (5)(6) - 10
= 720 + 30 - 10
= 740

If there was a hint, it was that 740 and 750 were both answers. If you forgot to subtract that final 10, you got 750.



10. Which interval notation represents -3 < x < 3?

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

Answer: (1) [-3, 3]
When you see "<", you want to use a square bracket like [ or ]. When you see just <, you want to use a rounded bracket or parenthesis, like ( or ).

There are two < symbols, so both symbols are square brackets.



More to come. Comments and questions welcome.

More STAAR problems.