Sat blue book problems

Test Preparation SAT Preparation
1

<p>Test 3 problem 15 section 5;
15)In the figure above,six segments intersect at O; OD bisect AOF, OC bisects AOE, and OB bisect AOD. IF x = 40 and y = 30, what is the measure of BOE? </p>

<p>I solved this long way,but I wonder how can you solve this fast here is how I solved it.</p>

<p>AOF = AB + BC +CD = DE + EF;</p>

<p>40 + BC + CD = DE + 30;</p>

<p>AOE = AB + BC = CD + DE;</p>

<p>40 + BC = CD + DE;</p>

<p>AOD = AB = BC + CD;</p>

<p>40 = BC + CD;</p>

<p>then we know BC + CD = 40;</p>

<p>We can use that in first equation 40 + 40 = DE + 30;
DE = 50;</p>

<p>then DE + BC + CD = 50 + 40 = 90;</p>

<p>But is there faster way to solve this ??</p>

<p>Test 3 problem 17 section 5;</p>

<p>On end of an 80 inch long paper strip is shown in the figure above. The notched edge, shown in bold, was formed by removing an equilateral triangle from the end of each 4-inch length of one edge of the paper strip. What is the total length, in inches, of the bold notched edge on the 80-inch paper strip ?</p>

<p>I don't understand this question if we only need the length of the bold line then I did
4 * 3 + 3 = 15; but answer is quite different.</p>

<p>Test 3 problem 18 section 5;</p>

<p>I solved this,but I don't know where did I do wrong.</p>

<p>In the figure above, PQRS is a square and points Q,R,and O lie on the graph of y = ax^2,where a is a constant. If the area of the square is 64, what is the value of a?</p>

<p>we know each side of square should be 64^1/2 = 8; then point S downstairs should be (4,0) and up should be (4,4);</p>

<p>then y = ax^2 = 4 = 16a;</p>

<p>a = .25,but answer is .5 I don't understand I must have done something wrong !!,but I don't see what did I do wrong.</p>

<p>Thanks in advance for help.</p>

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<p>Sorry I had to edit page until someone reply or else it would go to page 2.</p>

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<p>I just did test 3 tonight and was stuck on the same questions… I also made the same mistake for problem 17 but I think they expected you to continue the “bold line” to the length of the 80 inch ruler which would give you 100 as the answer. </p>

<p>split 80 inches into 4 because each triangle occurs every 4 inches. there are 20 triangles each 2 inches… 20x2=40</p>

<p>there are twenty 3 inch lines 20x3=60
60+40=100
i believe thats how to get the right answer</p>

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<p>@elcrew thanks alot mate for explanation for problem 17.</p>

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<p>I remember this question. Well, I didn’t use algebraic equations whatsoever. I marked over the figure itself and stated which angles were bisected i.e. which angles are equal to each other. Then, after I finished dissecting the figure, I grouped angles together and finally came up with the answer. I hope you understand anything. I hate algebraic equations in any case, unless the answer is required in the form of an algebraic equation. Even then though, I tend to substitute numbers and still get the right answer in the shortest amount of time possible. I score 700+ in Math consistently.</p>

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<p>^Yeh I see what you mean when solving this question I thought about which way to use to solve it like visually like what you said or algebrically,but you see for this type of questions that ask for alot of angles sometimes I get scared coz your visual way of solving it could be wrong,so I just end up doing algebric equations in order to be sure I am right took sometime though.</p>

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<p>In order to counter that possibility, you have to mark up the drawing while you’re visually dissecting it. If x = 40, and it was one of two equal bisected angles, then mark the other angle as well as 40. And make symbols for equal angles on the drawing, such as X, Y, Z etc. Then add up whichever symbols form the angle required to get the degree of measure.</p>

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<p>^I see yes that wouldn’t waste time and its faster than doing it in algebrically.</p>

<p>Thanks.</p>

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<p>For the {y=ax^2} question: The up shd be (4,8) because the the length of each side is 8
so, 8=16a…a=.5</p>

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This is what I did for the one with the paper strip.
Well the paper strip measurement that they gave was 12 inches. So then divide 80 by 12 to see how many of those paper strips there are in the 80 inch paper strip. You will get 6.666666666… Now since they said that the notched edge was formed by an equilateral triangle, then each side of the triangle in bold is 1 so that would be 15 inches of the bold. So now just multiply 15 by 6.666666666 = 100.

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Aarea of rectangle PQRS= 64,so RS= 8, OS =4
at point R: x=4,y=8
y= ax^2, a=y/ x^2=8/16=1/2