January 2014 Algebra Regents, Part IV

Day 20 of the 30-day blogging challenge. In the homestretch!

Finishing the January 2014 Integrated Algebra Regents, which started with the multiple-choice, the rest of the multiple choice, and Parts II and III.

This is Part IV, the last three questions. (Two and a half, really, as you'll see.)

37. On the set of axes below, solve the following system of equations graphically for all values of x and y. State the coordinates of all the solutions. y = x² + 4x - 5, y = 2x + 3

As I've stated in the past, the graph is the easiest four points you'll ever get, especially because you are given a graphing calculator. Type in the equations, hit Graph, check the Table and you're good.

Points get lost when people don't label the lines and state the co-ordinates of the points of intersection. Note: Even if you graph a line incorrectly, you still need to state an "appropriate" solution, even if you have to estimate a fraction.

Graph the lines, you'll get the correct answer.

38. Solve algebraically for all values of x:

To solve this proportion, cross multiply. Use the Distributive Property. Here's a hint: if they saw to find all solutions to an equation, there's a good chance that this will be a quadratic equation with two solutions. You need to find both of them.

After distributing, get all the terms on one side of the equation, leaving only a zero on the other side. Factor the polynomial into two binomials. Using the Zero Product Property, we know that one of the two terms must equal zero, so we can solve for x, as illustrated below:

39. Doug has four baseball caps: one tan, one blue, one red, and one green. He also has three jackets: one blue, one red, and one white. Draw a tree diagram or list a sample space to show all possible outfits consisting of one baseball cap and one jacket.

Sample space: tan/blue, tan/red, tan/white, blue/blue, blue/red, blue/white, red/blue, red/red, red/white, green/blue, green/red, green/white.

A tree diagram would have four branches with the cap colors and each of those branches would have three branches repeating the jacket colors.

Find the number of Doug’s outfits that consist of a cap and a jacket that are different colors.

There are 12 outfits, only two are the same color (blue/blue, red/red). 12 - 2 = 10. If you have a tree diagram or sample space, you are not required to show work for this problem. It will be assumed that you counted from the work you did above. If you do show work, it has to be relevant and correct. If you're tree or sample is incorrect, this answer must be consistent.

On Spirit Day, Doug wants to wear either green or white, his school’s colors. Find the number of his outfits from which he can choose.

Again, they will assume that you counted: there are 6 combinations. If you calculated without a tree diagram, remember not to count the green/white outfit twice.

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And that's it. Sorry it took so long to cover this, but for those of you who are currently reviewing for June, I'm hoping that it worked into your schedule.