math 2c last minute questions

Test Preparation SAT Subject Test Preparation
1

<p>(these are from the current collegboard real sat 2 book)</p>

<li>if x = y, then x2 = y2
if x and y are real numbers, which of the following CANNOT be inferred from the statement above?</li>
</ol>

<p>a) in order for x2 to be equal to y2, it is sufficient that x be equal to y
b) a necessary condition for x to be equal to y is that x2 be equal to y2
c) x is equal to y implies that x2 is equal to y2
d) if x2 is not equal to y2, then x is not equal to y
e) if x2 is equal to y2, then x is equal to y</p>

<li><p>the set of all real numbers x such that sq root of x2 = -x consists of
a) zero only
b) nonpositive real numbers only
c) positive real numbers only
d) all real numbers
e) no real numbers
please explain</p></li>
<li><p>if matrix A has dimensions m x n and matrix B has dimensions n x p where m, n, and p are distinct positive integers, which of the following is true?
I.the product of BA doesnt exist
II. the product of AB exists and has dimensions m x p
III. the product of AB exists and has dimensions n x n</p></li>
</ol>

<p>a) I only
b) II only
c) III only
d) I and II only
e) I and III</p>

<p>please explain</p>

<p>thankss (test tmrw)!</p>

<p>49.</p>

2

<ol>
<li>(E)</li>
</ol>

<p>If x^2 = y^2 = 4, then it is possible that x = -2 and y = 2.</p>

<ol>
<li>(B)</li>
</ol>

<p>If x is less than or equal to 0, ONLY then will sqrt(x^2) = -x. Think about it; for a real number n, sqrt(n^2) is greater than or equal to 0. But if n < 0, then the equation holds.</p>

<ol>
<li>(D)</li>
</ol>

<p>Really simple linear algebra here:</p>

<p>For a matrix AB to exist, A must have dimension mxn and B must have dimension nxp; the important part is that the columns of matrix A MUST equal the rows of matrix B. So, BA would be impossible because p is not equal to m.</p>

<p>Also, for a matrix AB, it will have dimension mxp. (It takes the rows of A and the columns of B).</p>

<p>And based on what I just said above, III is wrong.</p>

3

<p>
[quote]
29. if x = y, then x2 = y2
if x and y are real numbers, which of the following CANNOT be inferred from the statement above?</p>

<p>a) in order for x2 to be equal to y2, it is sufficient that x be equal to y
b) a necessary condition for x to be equal to y is that x2 be equal to y2
c) x is equal to y implies that x2 is equal to y2
d) if x2 is not equal to y2, then x is not equal to y
e) if x2 is equal to y2, then x is equal to y

[/quote]
</p>

<p>isn't this a logic problem?
if P-> Q
then ~Q -> ~P</p>

<p>so its D</p>

4

<p>i thought sqrt of x^2 was always positive</p>

<p>sqrt of x^2 is the same thing as abs value of x?</p>

5

<p>
[quote]
i thought sqrt of x^2 was always positive

[/quote]

If x^2 = 4, sqrt x^2 can be 2 or -2.
(2)^2 = (-2)^2 = 4</p>

6

<p>do we need to know arithmetic and geometric sequences???? I just happened upon them in a kaplan book and I have never seen such a thing before!</p>

7

<p>Yes, that's correct. For real numbers, the sqrt of x^2 is always positive. It's not exactly the same as abs (abs x is defined as a piecewise function), but in basically every case, they're equivalent.</p>

<p>But if you think about x = -2,</p>

<p>sqrt((-2)^2) = 2, which is equal to -x.</p>

8

<p>^ Ya you do. It's a very simple concept though. Put the formulas in your calculator and look over some sample problems and you'll be fine.</p>

9

<p>Rupac: you are right! that's what I was missing!
thanks</p>