M@th

Test Preparation SAT Preparation
1

<ol>
<li><p>the pyramid shown above has altitude h and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e=m, what is the value of h in terms of m? Figure not drawn to scale.
a)m/(2)^1/2
b)(m(3)^1/2)/2
c)m
d)2m/(3)^1/2
e)m(2)^1/2</p></li>
<li><p>A salesperson's commission is k percent of the selling price of a car. Which of the following represents the commission, in dollars, on 2 cars that sold for 14,000 each?
a)280k
b)7000k
c)28000k
d)(14000)/(100+2k)
e)((28000)+k)/100</p></li>
</ol>

2

<p>for 20. </p>

<p>2 X 14000 = 28000</p>

<p>28000 X k/100 = 280k ANSWER is A -</p>

<p>I found that on yahoo answers because honestly i don’t really understand why its not just C. I plug in numbers and that works just fine</p>

3

<p>

</p>

<p>1.) Realize what the question is asking.
2.) The question is asking for in $ how much the salesperson made on two cars that each cost $14,000 with respect to k, which is in PERCENTAGE form.
3.) Let k = 10 percent.
4.) Let k = 10 percent of (14,000 + 14,000) = 28,000 x 10/100 = $2,800
5.) Plug 10 in for k.
(a) = 280 x 10 = $2,800
6.) Answer = A.</p>

<p>The “trick” in this question is being able to differentiate between percentages and decimals. Answer “C” is very tantalizing because if you set k to .1 (decimal form) it will yield the correct answer in $ form.</p>

4

<p>For 19, did you type the answer choices in exactly?
Since a) means m / sqrt(2) right now.
Is is sqrt(m/2)?
(No, I don’t think a is the answer right now)</p>

5

<p>no its m over squareroot of 2</p>

6

<ol>
<li><p>A (M/sqrt2)</p></li>
<li><p>Draw a pyramid (to-scale helps) so the square has sides m,m,m,m and the 4triangles have lengths m,m,m,m (since m=e). The “h” is the unknown still.</p></li>
<li><p>Draw a diagonal from the base of the square, and you know it has to be a 45-45-90 triangle so x, x, x<em>sqrt2. Diagonal = m</em>sqrtrt2. Then, divide in half and connect it to the altitude h and the edge of the pyramid (m).</p></li>
<li><p>Use Pythagorean theorem a^2 + b^2 = c^2</p></li>
</ol>

<p>h^2 + [(m<em>sqrt2)/2]^2 = m^2
h^2 = m^2 - [(m</em>sqrt2)/2]^2
h^2 = m^2 - 2m^2/4
h^2 = m^2 - m^2/2
h^2 = m^2*(1 - 0.5)
h^2 = m^2/2
h = m/sqrt2, therefore A</p>