<p>Hi, new to CC. These 2 questions appeared at the end of the math section in an old SAT from which I was studying. They are HARD, well, at least for me! Both are L5.</p>
<p>1.) For all values of y, let y* be defined as y* = y² -1. Which of the following is = to (y<em>)</em>?
The answer is y⁴ - 2y²
But how??? I need proof to satisfy myself:)</p>
<p>2.) A club is buying boxes of candy bars to sell for a fundraiser. If each box contains c candy bars, and each member sells x bars each day, how many boxes are needed to supply enough candy bars for 3c members to sell for 5 days?
The answer is 15x
Again, I need to know how.</p>
<p>I’ll do the first one for you. Try to think of y* as f(x) (I’m assuming you’ve learned function composition in your math classes) and (y<em>)</em> is f(f(x)) so you would do (y² -1)(y² -1)-1
which multiplies out to y⁴-2y²+1-1 and then the 1s cancel</p>
<p>Each member sells x bars each day. In other words:
Each member sells x/c boxes each day
Therefore each member sells 5 * x/c boxes that is 5x/c boxes in 5 days.
Therefore 3c members sell 3c * 5x/c boxes that is 15x boxes in 5 days.</p>
<p>I am pretty certain that these are both from real college board tests. I don’t remember which ones – maybe 1st edition blue book, maybe old psat, maybe QAS. But I remember them both and I never use anything other than college board material when I work with students. </p>
<p>BTW, both of these questions are nicely vulnerable to the “make-up-numbers” approach. I think OP wanted to see the algebra, but if you are not fussy about that, making up numbers is helpful. For example, pick a y value, say 4. 4<em>=16-1=15. Then 15</em>=225-1=224. Now plug y = 4 into each answer…rule out any that don’t match the 224.</p>
<p>Same kind of thing works on the candy bars…</p>
<p>Xiggis method is valid and should be implemented, but in moderation. One should practice from only official matderial but if You encounter something from an outside source that seems like a possible test question, then we should definitely try It. That being said, official tests are the best source of preparation</p>
<p>And, the second problem that is similar is from the 2011 PSAT. I am not sure about the first.</p>
<p>Possibly, but it serves little to no purpose if the question is poorly written, is mostly irrelevant to the scope of the SAT, and more importantly has no provided answer or a … wrong one.</p>
<p>The problem with synthetic tests and unverified question is that they can (and do) mislead students. With the wealth of official questions available, why waste precious time honoring a test writer who probably knows less than you do about the test!</p>
<p>@PeterAP and @xiggi, These were both on an actual SAT from 2001-2004 era. The link to these tests is actually on CC’s Past SAT Tests post. I am in accordance with the fact that only real SAT material is key to success.</p>
<p>1.
The piramid has altitude h and a square base of m.The four edges that meet at V,the vertex of the piramid,each have length e.If e=m what is the value of h in terms of m?
Correct answer is : 2m/√3
I tried to solve it by finding the diagonal of the base as m√2 and than use pythagoras theorem like this: the edge m^2 - half the base daigonal(m√2/2)^2=h but thats not correct i guess.Can someone explain me why and how to solve it?</p>
<p>2.
The letters S H O W E R repeat indefinitely with letter S as the first term in the sequence.
What will be the 117th term in the sequence? I have no idea how to solve this or similar questions so please explain me the principle of doing this type of questions.</p>
<ol>
<li><p>In your solution, h should be replaced by h^2. However, this yields m^2 - (m sqrt(2)/2)^2 = h^2, h = (sqrt(2)/2)m. May want to check the problem again (hopefully I didn’t screw up).</p></li>
<li><p>The sequence repeats every 6, so every multiple of 6 letter will be an R. 114 is a multiple of 6, so the 114th letter is R and the 117th letter is O.</p></li>
</ol>