January 2014 Algebra Regents Discussion Thread

It's Day 6 of my 30-Day blogging challenge, and I was thinking: I didn't get around to starting a discussion thread for the January Algebra Regents until long after anyone who had taken it cared any longer.

However, tutoring sessions have started and testing season is almost upon us. And I'm trolling for pings on search engines. A lot of my hits come from students looking for answers to specific questions.

So without further ado:

January 2014 Algebra Regents

1. An example of an equation is...

An equation has an equal sign. An expression does not. Only choice (4) does.

2. The greatest common factor of 3m²n + 12mn² is

Both terms have co-efficients which are multiples of 3. Both have at least one factor of m and at least one factor of n. So the answer is (3) 3mn.

3. Jeremy is hosting a Halloween party for 80 children. He will give each child at least one candy bar. If each bag of candy contains 18 candy bars, which inequality can be used to determine how many bags, c, Jeremy will need to buy?

The number of candy bars in c bags of 18 bars is 18c. This number must be > 80. ("At least" means greater than or equal to.) The answer is (1) 18c > 80.

4. Which statement regarding biased sampling is false?

The answer is (3) "A survey handed to every third person leaving a library is biased because everyone leaving the library was not asked to participate."

When you are taking a sample, you don't want everyone to participate. By taking every third person, regardless of who that person is, bias is reduced.

(I won't go as far as to say that there is no bias, but you're doing what you can to reduce/avoid it.)

5. Which relation is not a function?

A function is not a relation if any x co-ordinate has two different values for the y co-ordinate. Choice (4) repeats x=2. If this set of points were graphed, it would fail the vertical-line test.

6. What is an equation of the line that passes through the point (-2,-8) and has a slope of 3?

Same yourself some trouble and work backward from the answers. The slope is 3, so the answer is in the form y = 3x + b. Unfortunately, all 4 choices look like this. Substitute -2 for x. Which equation gives you -8 for y? You didn't have to go far: (1) y = 3x - 2.

7. A figure consists of a square and a semicircle, as shown in the diagram below.

If the length of a side of the square is 6, what is the area of the shaded region?

The area of the entire square is 36 (which is in all four choices). The diameter of the circle is 6. The area of a semicircle is half the area of a whole circle, making it 1/2 * pi * r². The radius is 3 (half of 6), so the area of the area of the semicircle is 9/2 * pi. The answer is (2) 36 - 4.5*pi.

8. The box-and-whisker plot shown below represents the number of magazine subscriptions sold by members of a club.

Which statistical measures do points B, D, and E represent, respectively?

A, B, C, D, and E refer to the minimum, the first quartile, the median, the third quartile, and the maximum, respectively. This is known as the Five-Number Summary.

9. What is the slope of a line represented by the equation 2y = x - 4?

Divide the entire equation by 2 to get it into slope-intercept form. The slope will be 1/2, which is what the co-efficient of x will become.

10. What is the solution of the system of equations below?

2x + 3y = 7
x + y = 3

You can work backward from the choices, which quickly eliminate choice (4) because x and y don't add up to 3. Or you can solve the system of equations. It's fairly quick and painless, so let's give it a try.

Doubling the second equation gives up 2x + 2y = 6. Subtract that from 2x + 3y = 7 and we get y = 1. That gives us choice (2) (2, 1) because we eliminated (4) already.
If you substitute y=1 in either equation, you will find that x=2.

to be continued . . .