Test 2 Section 2 - #15 (page 456)

This is a function question, which means you're going to need to follow directions very closely. Start by understanding the definition:

x▲ = (x + 1)(x - 1)

All that means is that whatever we find to the left of the ▲, we put it through the same machinery:

x▲ = (x + 1)(x - 1)

p▲ = (p + 1)(p - 1)

[dog]▲ = ([dog] + 1)([dog] - 1)

I'm having a bit of fun with the definition, but you get the point. Let's solve this problem:

6▲ - 5▲

= (6 + 1)(6 - 1) - (5 + 1)(5 - 1)

= (7)(5) - (6)(4)

= 35 - 24

= 11

So we're looking for the answer choice that gives us the same result. Which answer choice gives you 11? Try them all to make sure, but for the sake of saving space I'm just going to do out the correct one:

3▲ + 2▲

= (3 + 1)(3 - 1) + (2 + 1)(2 - 1)

= (4)(2) + (3)(1)

= 8 + 3

= 11

Nice. That's choice (B).

Test 2 Section 2 - #10 (page 455)

The key here is to recognize that these are similar triangles, so their sides are all in the same ratios.  How do we know they're similar?  Well, they both have the same angle at P (I labeled it z°), and we know angles QTP and RSP are also the same (the diagram says they're both x°). So their third angles also have to be the same (marked y° on the graph).

Since the corresponding sides of similar triangles are always in the same ratio, we know that PT/PS will be the same as QT/RS, or 8/10. 8/10 simplifies to 4/5, so our answer is (E).

Test 2 Section 2 - #18 (page 457)

The question is basically asking for which answer will be the smallest volume that is BIGGER than the cylinder ("the smallest box that completely contains the cylinder" means "the smallest box that the cylinder could fit inside"). Plug in values for the variables to help start. Let's call d=4 and h=3.

Since the volume of a cylinder is (π)(radius²)(height), the volume would be (π)(2²)(3), which becomes 12π, which equals about 38. Now just see which of the 5 answer choices is the smallest number that is BIGGER than 38. (A) gives us 12, which is too small. (B) gives us 48, which is bigger than 38, so that works. All the other answers end up being bigger than 48, so they're not correct, since the question asks for the smallest box that will hold the cylinder.

Test 2 Section 2 - #4 (page 453)

This question is basically asking what percent of the total car sales April represents. We know there were 30 cars sold in April (from the given graph), but how many cars were sold total? Using the graph, that would be 20+18+22+30+48+42, which equals 180. So April had 30 of the 180 cars, which is equal to 1/6. Since a circle graph has 360 degrees, 1/6 of that would be 60 degrees, and the answer is (C).