<p>I found some of these kind of hard and still struggling with a good explanation for the sequence and function questions.</p>
<p>Help would be much appreciated.</p>
<p>For number one 1) It is E)</p>
<p>Imagine a square. The length is x+4 and the diagonal is x+8. Cut the square in half by the diagonal and you get a triangle (right triangle to be precise). </p>
<p>Do the Pythagorean theorem.</p>
<p>(x+4)^2 + (x+4)^2 = (x+8)^2</p>
<p>So…</p>
<p>2x^2+36 = x^2 +64</p>
<p>x^2 = 28</p>
<p>Square root both sides…</p>
<p>E) is the answer.</p>
<p>For 20)</p>
<p>Immediately cut out A) since FE=CE, then 1/2CE=BC NOT 1/3</p>
<p>I am not soo sure about my answer, but can you tell me if it is E. I am pretty sure it is that, and if you can tell me it, I can explain it a little better.</p>
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<p>Here are the questions written out:
9. If a square has a side length of x+4 and a diagonal length x+8, what is the value of x?</p>
<p>(A) 4
(B) 8
(C) 16
(D) 4 sqrt (2)
(E) 8 sqrt (2)</p>
<ol>
<li>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?</li>
</ol>
<p>(A) f(10)=1
(B) f(0)= -5
(C) f(0)=5
(D) f(1)= -h
(E) f(-1)=h</p>
<ol>
<li>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 of the following?</li>
</ol>
<p>(A) A
(B) A^2
(C) A^3
(D) A^2/3
(E) A^3/2</p>
<p>For this one, I understand how to get the answer, but i don’t know why, in this context, they are saying “directly proportional”. The answer is (D).</p>
<ol>
<li>1/(1)(2), 1/(2)(3), 1/(3)(4)</li>
</ol>
<p>The first three terms of a sequence are given above. The nth term of the sequence is 1/(n)(n+1), which is equal to 1/n-1/n+1. What is the sum of the first 50 terms of this sequence?</p>
<p>(A) 1
(B) 50/51
(C) 49/50
(D) 24/50
(E)1/(50)(51)</p>
<p>"For number one 1) It is E)</p>
<p>Imagine a square. The length is x+4 and the diagonal is x+8. Cut the square in half by the diagonal and you get a triangle (right triangle to be precise). </p>
<p>Do the Pythagorean theorem.</p>
<p>(x+4)^2 + (x+4)^2 = (x+8)^2</p>
<p>So…</p>
<p>2x^2+36 = x^2 +64</p>
<p>x^2 = 28</p>
<p>Square root both sides…</p>
<p>E) is the answer."</p>
<p>It’s actually D, but I see how to get it now, thanks for the help. You just made a mistake squaring the 4’s; 4^2 + 4^2 would equal 32 not 36.</p>
<p>
</p>
<p>In simple terms, directly proportional means that both variables increase or decrease in the same ratio.</p>
<p>I understand what directly proportional means, but I think I’m confused on this question now that I try to go back and solve it. The correct answer is actually E, I wrote that wrong in the original post.</p>
<p>Assume that the face of the cube (A) is 4 square inches, and subsequently the cube (V) is 8 cubic inches. A, or 4, to the 2/3 power is 8. The questions asks what is proportional to V. To me, that is equal to V, not directly proportional. I’m confused on that aspect of it, if anyone could clarify.</p>
<p>15 is B, if h and k and a are positive. then f(0)=a(-h)^2+k or ah^2+k which is greater than 0 because h, k and a are positive.
16 is E, i’ll try to explain to the best of my ability. Let the side length of a cube be s, so the surface area is A=6s^2 and the volume is V=s^3, thus A<em>s/6=V and s=(A/6)^(1/2) So V=A/6</em>(A/6)^1/2 or V=(A/6)^3/2
for 19.
We can decompose 1/[n(n+1]) into partial fractions by the following process:
1/[n(n+1)]=A/(n)+B/(n+1), if we multiply both sides by n(n+1) we get 1=A(n+1)+B(n)
plugging in n=0 we get 1=A(1)+B(0)=>A=1 and plugging in n=-1 we get B=-1, thus we can decompose 1/[n(n+1)] into 1/n-1/(n+1), therefore, we can write our sum as 1-1/2+1/2-1/3+1/3…+1/49-1/50+1/50-1/51 and all of hte terms cancel except the 1 and the -1/51 so the sum is 50/51 or B
heh, I didn’t realize that the way to rewrite the sum was included in the question :P</p>
<p>@nothingto im pretty sure the answer to number 9 is D</p>
<p>^ It is, I just made a calculation error (I put 36 rather then 32) by mistake, since I wanted to do that question before I go to work, so I was in a rush.</p>
<p>Nice solution Astro Blue. I would’ve done the exact same method if I took the June SAT.</p>
<p>Number 19 is one of the hardest problems I’ve ever seen on the SAT math</p>
<p>Which month SAT test is this from?</p>
<p>
</p>
<p>It is not an easy problem, but one that is not so hard when you remember that this is the SAT and not high school math.</p>
<p>Here are two ways</p>
<p>The first approach does focus on the successive elimination of terms in the pattern.
1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 … -1/50 +1/50 - 1/51
At the end, you have 1 - 1/51 or 51/51 - 1/51 = 50/51</p>
<p>Pretty simple stuff, in fact.</p>
<p>The second one is a bit trickier and requires trusting ETS to stay true to its typical devious ways: </p>
<p>Take a look at the answers. </p>
<p>(A) 1
(B) 50/51
(C) 49/50
(D) 24/50
(E) 1/(50)(51)</p>
<p>The given sequence starts with 1/2 and adds increasingly smaller fractions. The solution cannot only be higher equal of higher than 1, but also not smaller than 1/2 (because of the additions)</p>
<p>This means that 1, 24/50, and 1/50*51 are impossible answers. </p>
<p>Now we have two choices (B and C) that are very close to 1. Since we are down to two answers, one could guess randomly, and some dumb books advocate. However, if one remembers that ETS loves to include a “trick answer” that is usually very similar to the correct one. In this case, there is a trick answer in the form of 1/(50)(51) </p>
<p>So pick, B and move on!</p>
<p>xiggi…can u please explain number 16 to me^ :)</p>
<p>@xiggi + astroblue Thanks for the explanations guys. Does anyone know if this could this also be solved by using the sum of a geometric series equation?</p>
<p>What are authoritative websites?</p>
<p>@Beatzzz
It’s not geometric, so no. :p</p>
<p>@OtherWindow</p>
<p>A boy can dream</p>
<p>@Beatzzz what QAS test date is this for anyways?</p>