A Few Math Questions

Test Preparation SAT Preparation
1

<p>1) The product of a and b is equal to x, and the sum of a and b is equal to y. If x and y are positive numbers, what is 1/a + 1/b in terms of x and y?</p>

<p>a) x/y
b) y/x
c) xy
d) 1/x + 1/y
e) 1/x+y</p>

<p>2) If a square has a side length of x+4 and a diagonal of length x+8, what is the value of x?</p>

<p>a) 4
b) 8
c) 16
d) 4sqrt(2)
e) 8sqrt(2)</p>

<p>3) For all x, let the function f be defined by f(x) = a(x-h)^2 + k, where a, h and k are constants. If a and k are positive, which of the following CANNOT be true?</p>

<p>a) f(10) = 1
b) f(0) = -5
c) f(0) = 5
d) f(1) = -h
e) f(-1) = h</p>

<p>4) For any cube, if the volume is V cubic inches and the surface area is A square inches, then V is directly proportional to which if the following?</p>

<p>a) A
b) A^2
c) A^3
d) A^2/3
e) A^3/2</p>

<p>Thanks for the help. :]</p>

2

<ol>
<li>b
1/a+1/b=(b+a)/ab=y/x
2.d
(x+4)<em>sq.rt2=x+8
x=(8-4sqrt2)/(sqrt2-1)=4sqrt2
3.b
if a>0, k>0, and ()^2>=0,then fx=positive</em>positive+positive
so no matter b is pos or neg, fx should be positive
thus, b is the only impossible answer.
4 e
V=side^3, A=side^2
thus, V=A^(3/2)</li>
</ol>

3

<p>An easy way to solve one is to substitute numbers in for A and B. Say A=1 and B=1. Therefore, X = 1 and Y = 2. The only equation that comes out to 2 since 1/1+1/1=2, is B, Y/X.</p>

4

<p>In number 4, A=6x^2 where x is the length of a side (not x^2).</p>

5

<p>2-a</p>

<p>3-didn’t get.</p>

<p>ftrzruth:how can you assume a,k>0 ?</p>

<p>4-b</p>

<p>1-b (substitute in options)</p>

6

<p>DrSteve: since we are looking at proportionality,shouldn’t 6 be avoided?
so a=s2
squaring,a2=s3
now v=s3
thus v=a2</p>

<p>is this correct?</p>

7

<p>@nseries: In this particular question, if you drop the 6 you will get the correct answer. I would be a bit cautious about this though. The harder questions can be quite tricky, and making simplifying assumptions can sometimes lead to a wrong answer. In this particular case it is okay.</p>

8

<p>nseries, your post #5, question 3 includes “If a and k are positive.”</p>

9

<p>DrSteve: i agree with you.</p>

<p>QuantMech:sorry i missed that part and got stuck up.got it now.
ty.</p>

10

<p>OP:can you give the correct answers?</p>

11

<p>These are the correct answers</p>

<p>1) B
2) D
3) B
4) E</p>

12

<p>nseries–no problem. When you’re preparing for the SAT, it’s really useful to be aware that you might “read past” some of the information. Happens to everyone. If you are aware of that possibility, and a problem seems weird, it’s always worthwhile to go back and re-read the entire question. Near the top of the SAT M curve, a difference of 2 questions could easily make a 50 point difference in the score.</p>

13

<p>Im pretty sure my answers are correct and my explanations are very clear…</p>

14

<p>Thanks for posting @ThaMan it helps me as well. I knew how to do 3/4 of them but I looked at others’ explanations for the one I didn’t understand. :)</p>