SAT Math Questions...INsanity!!!

Test Preparation SAT Preparation
1

<p>question one:</p>

<p><a href=“http://i167.■■■■■■■■■■■■■■■/albums/u134/mikedagolfer/Satquestion2.jpg[/url]”>http://i167.■■■■■■■■■■■■■■■/albums/u134/mikedagolfer/Satquestion2.jpg&lt;/a&gt;&lt;/p&gt;

<p>quesiton two:</p>

<p><a href=“http://i167.■■■■■■■■■■■■■■■/albums/u134/mikedagolfer/mathquestionone.jpg[/url]”>http://i167.■■■■■■■■■■■■■■■/albums/u134/mikedagolfer/mathquestionone.jpg&lt;/a&gt;&lt;/p&gt;

2

<p>bumpage…</p>

3

<p>For the first question:</p>

<p>One can easily deduce that the shortest number of blocks one must travel from F to Z is 4 blocks (we define a block as a side of a grid-square). The question defines the “m distance” as the shortest possible distance from F to Z along the grid lines, so there is a restraint on the types of routes we can take, namely only those that take 4 blocks. There are two options initially: going left, or going down. </p>

<p>If we go left from F , there are three options:

  1. Go left two blocks, then down two blocks.
  2. Go left one block, down two blocks, left one block.
  3. Go left one block, down one block, left one block, down one block.</p>

<p>If we go down from F, there are three choices similar to those above:</p>

<ol>
<li>Go down two blocks, left two blocks.</li>
<li>Go down one block, left two blocks, down one block. </li>
<li>Go down one block, left one block, down one block, left one block.</li>
</ol>

<p>So there are 2x3 = 6 different routes from F to Z that take 4 blocks. </p>

<p>A is correct.</p>

4

<p>The second question:</p>

<p>There’s a good reason that circle is answer choice A, because it is what people think of when they think of the set of all points a distance D away from a point P. However, we are not free to draw lines in any direction here. The “m distance” in this problem is defined as the minimum number of blocks traveled from a point A to a point B. By simple inspection, one can draw several points that are an m distance of 3 away from the firehouse and realize that the set of all such points lie on a square. </p>

<p>B is correct.</p>

5

<p>For the third question: </p>

<p>If the circumference of the large circle is 36, we can solve for its radius using the following relationship:</p>

<p>C = 2piR
36 = 2piR
18/pi = R</p>

<p>Now we know the radius of the small circle (let’s call it little r) is 1/2 the radius of the bigger circle (R).</p>

<p>r = (1/2)R = (1/2)(18/pi) = 9/pi
So we can find the circumference of the little circle:
C = 2pir
C = 2pi(9/pi) = 18
We know there are 360 degrees in a circle, and the arc subtends 80 of them, so the length of the arc is simply the ratio of 80/360 multiplied by the circumference of 18. </p>

<p>(80/360)(18) = 80/20 = 4. </p>

<p>D is correct.</p>

6

<p>The arc question.</p>

<p>Since the radius of the small circle is half of the radius of the large circle, circumference of the small circle is half of circumference of the large circle
(circumference is directly proportional to radius).
Circumference of the small circle = 36 / 2 = 18.</p>

<p>Simple proportion:
circumference 18 is 360 deg
arc “a” is 80 deg
a = (18x80)/360 = 4.</p>