SAT Math Problems Thread

<p>8.5, x must be greater than 8 (since the sum of any two sides must be longer than the third side) and less than 9 (since x is the shortest side). I may be wrong here, but if not I’m surprised this is a level 5 question.</p>

<p>@CHD That is completely correct. Most questions that require the triangle rule are Level 5 questions. Most students simply do not know the rule. For everyone’s reference, the full triangle rule says that the third side of a triangle is strictly between the difference and sum of the other two sides. </p>

<p>This one is actually a fairly difficult triangle rule problem. Many students mistakenly think that the answer must be an integer, and even those that know the triangle rule may guess 8 or 9 as the answer.</p>

<p>This is one of those “really difficult” SAT problems that is actually really easy.</p>

<p>I agree, the above problem is really easy but there are several spots where people might make a mistake. I almost didn’t see “where x is the shortest side” and might have guessed anything in (8,26) \ {9, 17}.</p>

<p>DrSteve is right. Triangle inequality questions lurk at the ends of sections where students miss them surprisingly often. That got me thinking: what OTHER topics are level 5 even though they are easy when you know the rule? (I know everything is easy when you know it, but some level 5s require a flash of insight beyond just knowing how to do something.)</p>

<p>Here are the first that popped into mind:</p>

<ol>
<li>Shifting and stretching graphs</li>
<li>Reading a graph to determine the value of a function’s output</li>
<li>Same as #2 but having to repeat the process</li>
<li>Following a given flowchart algorithm to find the output of a process</li>
</ol>

<p>Any others </p>

<ol>
<li>Rate problems where Xiggi’s formula applies</li>
<li>Recognizing that a repeating sequence is just a remainder problem (do a quick division by hand)</li>
<li>Subtract the difference of 2 sums term by term OR apply the arithmetic series formula</li>
</ol>

<p>And for completeness</p>

<ol>
<li>Apply the triangle rule</li>
</ol>

<p>Here is a Logic Problem:</p>

<ol>
<li>At a certain High School, some members of the tennis team are sophomores and some sophomores have a GPA above 1.5. Which of the following statements must be true?</li>
</ol>

<p>A) All members of the tennis team have a GPA above 1.5</p>

<p>B) Some members of the tennis team have a GPA above 1.5</p>

<p>C) More members of the tennis team are sophomores than have a GPA above 1.5</p>

<p>D) More members of the tennis team have a GPA above 1.5 than are sophomores</p>

<p>E) None of these can be determined from the information given.</p>

<p>@DrSteve‌ hi there, can u please define what is the best fit in scatterplot and how to find or know if the best fit is negative or not. And do you have any hard examples related to scatterplot.
Thanks in advance, the scatterplot slope/best fit questions are killing me</p>

<p>I think B is the answer for question 7</p>

<p>Oh i think it’s E</p>

<p>E is correct. It could be that all sophomores on the tennis team have a GPA <1.5, but other sophomores have a GPA > 1.5, and the rest of the members of the tennis team have a GPA <1.5.</p>

<p>I think it’s a good idea here to use specific counterexamples to eliminate answer choices. For example, let’s suppose Bob and John are the only students in the high school. Assume that Bob is on the tennis team and a sophomore, but does not have a GPA above 1.5. Assume that John is not on the tennis team, is a sophomore and does have a GPA above 1.5. Can you use this to eliminate any answer choices?</p>

<p>Level 5 Number Theory</p>

<ol>
<li>In a certain sequence, each term after the second is the product of the two preceding terms. If the sixth term is 32 and the seventh term is 512, what is the second term of this sequence?</li>
</ol>

<p>The fifth term is 512/32 = 16, the fourth term is 32/16 = 2, the third term is 16/2 = 8 and the second term is 2/8 = 1/4. The first term is 8/0.25 = 32.</p>

<p>That’s good. Just be careful…the question is asking for the second term - not the first!</p>

<p>Level 5</p>

<ol>
<li>Let ||x|| be defined as the sum of the integers from 1 to x, inclusive. Which of the following is equal to ||21|| - ||20||?</li>
</ol>

<p>(A) ||1||
(B) ||2||
© ||5||
(D) ||6||
(E) ||21||</p>

<p>(1+2+…+21)-(1+2+…20)=21=1+2+3+4+5+6=||6|| (D). This seems a bit easy for a level 5, no?</p>

<p>I agree - not a hard question. Remember that the level of the question has nothing to do with the actual difficulty - it is determined by how many students got the question wrong on an experimental section of an SAT. There are 2 prominent reasons I can see students getting this question wrong:</p>

<p>(1) They are confused by the notation. In general “Special Symbols” problems tend to be higher level problems because students do not understand the new notation.</p>

<p>(2) They were tricked by the answer choices. I’m sure that many students begin the problem correctly, but carelessly choose choice (E).</p>

<p>More please!!</p>

<p>Level 4 Functions</p>

<ol>
<li>Let the function f be defined for all the values of x by f(x)=x(x+1). If k is a positive number and f(k+5)=72, what is the value of k?</li>
</ol>

<p>f(x)=x(x+1) tells me that they are two consecutive numbers multiplied together. So 8*9=72. x is therefore 8. </p>

<p>k+5=8
k=3</p>

<p>Is that correct? </p>