<p>Okay. For me, the hardest part of the ACT is math (and science). I do okay up until the last 15 questions or so. I have time, even more than enough time for a minute for each problem. But I lose my focus and my determination, and I start to make stupid mistakes. Any ideas on how to fix/help this? I've also got a couple of practice tests questions I don't understand...Here they are.</p>
<ol>
<li><p>(Real ACT Prep, Practice Test 3)
If (x-7) is a factor of 2x^2-11x + k, what is the value of k?
Here's what I know you do.
(x-7)(2x + b) = 2x^2-11x + k
2x^2 + (b-14)x - 7b = 2x^2 - 11x + k
THEN, somehow, they get b-14 = -11 and that -7b = k. Can anyone explain how they get that?</p></li>
<li><p>(Real ACT Prep, Practice Test 3)
This one has a picture, but all I don't understand is this:"What is the measure of <COD measured in the direction of the arrow shown?"</p></li>
</ol>
<p>I figured that (bi14) must equal -11 and that -7b must equal k, but why? I swear I’ve never seen that happen in math before? What is the “rule” for that? Thanks!</p>
<p>the quadratic expression that would yield a and b as roots is:</p>
<p>(x-a)(x-b) which is, once expanded, x^2-ax-bx+ab=>x^2-(a+b)+ab.</p>
<p>you will notice that the opposite of the sum of the roots is the coefficient of the x term and the product of the roots is the constant term.</p>
<p>Things get a bit complicated when the coefficient of the x^2 term is not 1.</p>
<hr>
<p>So in your scenario: if (x-7) is a factor, this means 7 is a root. So, let’s call the other root b. So the product of the roots, 7b must equal k</p>
<p>so 7b=k
and b-14=-11</p>
<p>This is essentially Vieta’s formula applied to a quadratic equation.</p>
<p>Ugh, I still can’t get it! haha. I basically don’t understand the “root” part. Are you referring to roots where a root makes a function = 0? Thanks for all of the help so far!</p>
<p>I looked at your problems in the question. I have a few suggestions that if you follow them, your score will increase vastly. </p>
<p>In your school work, you practiced a lot of the problems with the expansions of (x-a)(x-b) etc. On ACT, you need to do the reverse process, with which you are not familar. So in your own practice now, you need to think about how you do the expansions, that will remind you most of your prior practices. If you can do that visually in your mind, your score will increase greatly. </p>
<p>I remember that there is a function problem solved in a 3-D animated video format, if you can visualize according to what the video describes, then you will understand the process well. The video is at FTL Math site. You can just use your Facebook or Yahoo account to sign in to watch the different videos. Oh, it is at</p>
<p>Another suggestion is that you can use a different way to solve the problem and then verify your answers with the one your got already. The videos also show different ways to solve the problems.</p>
<p>Few will write that much stuff for an ad. The title of the site automatically showed up when you type a url. I didn’t write that. You only wrote a few words. I just try to help you. You need to write more about what you think, so people can help you more. You need to say where you got stucked. </p>
<p>What you can do is</p>
<p>expanding this </p>
<p>( x - 7) ( 2x + 3) = </p>
<p>Then go through your mind how this is expanded. Then you can tell me how you did it, where is your problem.</p>
<p>That part is easy. It just equals 2x^2 -11x -21. My problem is how you get from this: 2x^2 + (b-14)x - 7b = 2x^2 - 11x + k to this: b-14 = -11 and that -7b = k.
Sorry about accusing you of advertising.</p>
<p>Ok, I don’t mean to interrupt the discussion of this thread, but to be efficient, I have a different math question. Ok here it is:</p>
<p>The radio signal from the transmitter site of radio station WGGW can be received only within a radius of 52 miles in all directions from the transmitter. A map of the region of coverage of the radio signal is shown below in the standard (x,y) coordinate plane, with the transmitter site at the origin and 1 coordinate unit representing 1 mile.</p>
<p>The transmitter site of radio station WGGW and the transmitter site of another radio station, WGWB, are on the same highway 100 miles apart, the radio signal from the transmitter site of WGWB can be received only within a radius of 60 miles in all directions from the WGWB transmitter site. For how many miles along the highway can the radio signals of both stations be received? (Note: Assume the highway is straight)</p>
<p>a) 8
b) 12
c) 40
d) 44
e) 48</p>
<p>I said the answer was A, but the answer is B. Could someone explain this?</p>
<p>I will teach you to fish rather than give you a fish, so be patient with me. </p>
<p>You know it is easy bc you did many times at school. In 2x^2 -11x -21, think and tell me how you get 2, -11, -21. Then I will show you the reverse part. </p>
<p>zslavitz, </p>
<p>Sorry, I don’t have time to read your question now.</p>
<p>-21 is K, although we did not know that before we do the problem backwards. We know for sure -7 Y = K. Y is 3 as we know now, but we did not know yet. So far so good?</p>
<p>If (x-7) is a factor of 2x^2-11x + k, what is the value of k?
Here’s what I know you do.
(x-7)(2x + b) = 2x^2-11x + k
2x^2 + (b-14)x - 7b = 2x^2 - 11x + k</p>