Quite a few math questions

Test Preparation SAT Preparation
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<p>Well i just did a math section and didn't do as good as i excepted to. Anyways i got quite a few math questions. Here is the link: <a href="http://www.collegeboard.com/prod_downloads/sat/sat-practice-test.pdf%5B/url%5D"&gt;http://www.collegeboard.com/prod_downloads/sat/sat-practice-test.pdf&lt;/a&gt;&lt;/p>

<p>Starting from page 13.</p>

<p>Here are the questions i need help in:
5. (b)
11. (e)
13. (e)
15. (a)
16. (b)
17. (b)
19. (c)
20. (d)</p>

<p>Now i know these are a lot of questions, but would really appreciate if some helps =D</p>

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<p>For 5, simply plug in any integer and you will get a total of 36. Divide that by 3 and you will get 12.</p>

<p>For 11, make a=2 or any integer. Plug in a value that would make both expressions equal to each other. In all cases, the solution is 5.</p>

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<p>13) Classic system of equations! Always try adding and subtracting these before using substitution. Multiply the second equation by -1 so you can subtract it from the first equation:</p>

<p>3x + 2y + 2z = 19
-3x - y - z = -14</p>

<hr>

<pre><code> y + z = 5
</code></pre>

<p>15) When the SAT gives you a rule, satisfy it. Here the rule is x < 2. So make x = 1. Therefore, y = 2x + 3 becomes y = 2(1) + 3 or y = 5. If y = 5, you can eliminate (C), (D), and (E) because they show y being less than or greater than 5, and we’ve proven that it can actually equal 5. We can also eliminate (B), as 5 is not greater than 7.</p>

<p>16) The graph of f(x) becomes identical to g(x) when you move f(x) up 1. This is a translation. A graph shifts up 1 when you add 1 to f(x). Note: It shifts down one with f(x) - 1, it moves right one with f(x - 1) and it moves left one with f(x + 1).</p>

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<p>17) answer is NINE</p>

<p>The 4 sided polygon that you can see has a total of 360 degrees contained in the 4 interior angles (x+y+ the other two angles). This is because the formula for the sum of interior angles of a polygon is 180<em>(n-2). For example, a triangle has n=3 sides, so it has a total of 180 degrees inside 180</em>(3-2)=180. A rectangle has 360 degrees =(180)*(4-2) because a rectangle has 4 sides</p>

<p>Since x+y=80, then the other two angles must total 280 degrees, since 360 degrees -80 degrees =280 degrees.</p>

<p>Because the big polygon that is covered by the paper is a regular polygon, each angle must equal 140 degrees. So we know that all of the angles inside the big polygon covered in paper also must equal 140 degrees. The only question left is: how many sides does the big polygon have?</p>

<p>Remember, 180(n-2)=sum of all angles inside.</p>

<p>So we know that the sum of all angles inside MUST equal a number evenly divisible by 140 degrees, because each angle is 140 degrees. So the “sum of all angles inside” is 140, or 280, or 420, or 560, etc.</p>

<p>If we “guess” that the polygon has 9 sides, this works out: 180*(9-2)=1260 total degrees inside</p>

<p>1260 total degrees/ 9 angles = 140 degrees in each angle</p>

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<p>17) The shaded quadrilateral has interior angles that add up to 360. Since x + y = 80, the other two (call them a and b for the sake of the discussion) must add up to 280 (x+y+a+b=360, so 80+a+b=360, so a+b=280). Since a and b are from a regular polygon, they are equal (280/2 = 140). </p>

<p>Some students will have memorized that a nonagon, a 9-sided regular figure, has interior angles with a sum of 1260 and each is 140. If you didn’t memorize this, you can use a formula: interior angle = 180(n-2)/n, where n is the number of sides:</p>

<p>140 = 180(n-2)/n
140n = 180n - 360
-40n = -360
n = 9</p>

<p>19) The graph shows a decrease of 2 feet from 3:00 to 4:00. Use translation:
2 feet is 10 percent of how many feet?
2 = .10 (x)
20 = x</p>

<p>Be careful! This is the height at 3:00. The height at 4:00 is 20 - 2 = 18.</p>

<p>20) Oh, joy. This is a long one!</p>

<p>Start with I:
aOb = ab + a + b
Part 1: xOy = xy + x + y
Part 2: yOx = yx + y + x</p>

<p>xy + x + y = yx + y + x TRUE
This eliminates (B) and (C)</p>

<p>Now work on II:
aOb = ab + a + b
Part 1: (x-1)O(x+1) = (x-1)(x+1) + (x-1) + (x+1) >>> (x^2 - 1) + 2x >>> x^2 +2x - 1
Part 2: (xOx) - 1 = [(x)(x) + x + x] - 1 >>> (x^2 + 2x) - 1 >>> x^2 +2x - 1</p>

<p>x^2 +2x - 1 = x^2 +2x - 1 TRUE
This eliminates (A). </p>

<p>Finally, III:
aOb = ab + a + b
Part 1: xO(y+z) = x(y+z) + x + (y+z) >>> xy + xz + x + y + z
Part 2a: xOy = xy + x + y
Part 2b: xOz = xz + x + z
Part 2c: (xOy) + (xOz) >>> (xy + x + y) + (xz + x + z) >>> xy + xz + 2x + y + z</p>

<p>xy + xz + x + y + z = xy + xz + 2x + y + z FALSE</p>

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<p>Question 17 is a really tough SAT question, but there is another way to do it: the exterior angles of any polygon add to 360. Since the exterior angle here is 180-140=40, that must mean that there are 360/40 = 9 sides.</p>

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<p>It is indeed a tough problem. While not much different from the suggestions above, one shortcut is provided by noticing (when x is number of sides) that </p>

<p>140 … x-2 … 7
---- = ---- = -----
180 … x … 9</p>