MATHS 2 unclear questions - solution needed

Test Preparation SAT Subject Test Preparation
1

<ol>
<li>The set of points (x,y,z) such that x^2+y^2+z^2=1
is</li>
</ol>

<p>A)Empty
b) point
c)sphere
d)circle
e)plance</p>

<ol>
<li><p>The only prime factors of a number n are 2,5,7,17. Which of the following could NOT be a factor of n?
a)10 b)20 c)25 d)30 e)34</p></li>
<li><p>Portions of the graphs of f and g are shown below. Which of the following could be a portion of the graph of fg?
<a href="http://img850.imageshack.us/img850/247/40ppp.jpg%5B/url%5D"&gt;http://img850.imageshack.us/img850/247/40ppp.jpg&lt;/a&gt;&lt;/p&gt;&lt;/li>
</ol>

<p>The answer is:
<a href="http://img809.imageshack.us/img809/6818/203p41.jpg%5B/url%5D"&gt;http://img809.imageshack.us/img809/6818/203p41.jpg&lt;/a&gt;&lt;/p>

<p>how should I get this?</p>

<ol>
<li><p>If matrix A has dimensions m x n and matrix B has dimensios n xp , where m ,n,p are distinct positive integers, which of the following statements must be true?</p></li>
<li><p>The product BA does not exists</p></li>
<li><p>The product AB exists and has dimensions m x p
3.The product AB exists and has dimensions n x n.</p></li>
</ol>

<p>A) 1 ONLY
B) 2 ONLY
C) 3 ONLY
D) 1 AND 2
E) 1 AND 3</p>

<p>I know why 2 is ok but why 1 is ok as well as answer is D.</p>

<p>All these are taken from official SAT book, so I appreciate help!</p>

2

<ol>
<li><p>C. You know that x^2+y^2=1 is the most basic circle, so to put in the third dimension you just add z^2.</p></li>
<li><p>D. 30 is divisible by 3 but n is not, so n can’t be divisible by 30. The best way to go about this is to start going through the primes that aren’t on that list and see if any of the answers are divisible by them.</p></li>
<li><p>If it really is written “fg,” then all you have to do is multiple the values of f(x) and g(x) at each x. When x is -1, f(x) is -1 and g(x) is 1, so multiplying yields -1. The same result comes at x=1. At 0, both f and g are 0, so fg is 0.</p></li>
<li><p>Unlike when you multiple numbers, order matters when you multiply matrices. To multiply BxA, you really have to put them in that order. That would mean multiplying an n x p matrix by an m x n matrix, which you know doesn’t work because p and m aren’t equal.</p></li>
</ol>

<p>Hope I helped! Let me know if you need more clarification.</p>