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

While I'm waiting for new Regents exams to come along (AND THEY ARE COMING SOON!), I'm revisiting some of the older NY Regents exams.

More Regents problems.

Administered January 2013

Part II: Each correct answer will receive 2 credits. Partial credit can be earned.


31. Express in 4 SQRT(75) simplest radical form.

Answer:

Factor the 75 into 3 * 5 * 5. The square root of (5 * 5) is simply 5. So we can remove the two factors of 5 from beneath the radical and put one factor of 5 in front of it.

So 4 * SQRT(75) = 4 * SQRT(3 * 5 * 5) = 4 * 5 * SQRT(3) = 20 SQRT(3)

Note 1: Write this with a radical sign. Don't use the letters "SQRT". I'm a little limited on this blog.

Note 2: If you wrote a decimal for an answer, you scored 0 points, even if you're answer was accurate to a dozen places.

32. Factor completely: 5x³ - 20x² - 60x

Answer:

A general rule of thumb is that when the question says "Factor completely" then there will be more than one step involved. In this case, each term has a factor of x that can be removed, and each coefficient is a multiple of 5. So start by factoring 5x from each term.

5x³ - 20x² - 60x
= 5x(x² - 4x - 12)
= 5x(x - 6)(x + 2)

You can check your answer by multiplying. You should get the original expression back.



33. On the set of axes below, graph y = 2|x + 3|. Include the interval 7 < x < 1.

Answer:

First, an absolute value graph is V shaped, assuming that you graph its vertex. Second, if it says to show the interval then you must only show that interval, closed at the ends. No arrows. Arrows would be a graphing error.

You can use the graphing calculator to see what it looks like, but you might realize from the equation that the vertex will be at (-3, 0) and the slopes of the two sides will be -2 and 2.

More to come. Comments and questions welcome.

More Regents problems.