YoungProdigy's Math Thread

Test Preparation SAT Preparation
1

<p>So I have a lot of math questions, and instead of bombarding the forum page, I'm going to list all of my questions in this thread. If you have any math questions, you are welcome to post them here.</p>

<p>BB. Pg. 861 #15</p>

<ol>
<li>A store charges 28 dollars for a certain type of sweater. This price is 40 percent more than the amount it costs the store to buy one of these sweaters. At an end-of-season sale, store employees can purchase any remaining sweaters at 30 perfect of the store's cost. How much would it cost an employee to purchase a sweater of this type at this sale?</li>
</ol>

<p>A. $8.40
B. $14.00
C. $19.60
D. $20.00
E. $25.20</p>

<ol>
<li>Practice Test #3 in the BB, Section 5 #8</li>
</ol>

<p>(x-8)(x-k) = x^2-5kx+m</p>

<p>In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?</p>

<p>A. 8
B. 16.
C. 24
D. 32
E. 40</p>

<ol>
<li>Test 3 problem 17 section 5</li>
</ol>

<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>

<ol>
<li>Test 2 section 2 #12</li>
</ol>

<p>In the figure above, what is the value of PT/PS?</p>

<ol>
<li>Test 8 section 9 #12</li>
</ol>

<p>a.jpg</a> picture by talaltq - Photobucket</p>

<p>In the figure above, points P, A and B are equally spaced on line l and points P, Q and R are equally spaced on line m. If PB = 4, PR = 6 and AQ = 4, what is the perimeter of quadrilateral QABR?</p>

<p>a) 13
b) 14
c) 15
d) 16
e) 17</p>

<p>I have a lot more questions, but I'll post them after these have been explained. I am grateful to anyone who helps me with these question</p>

<p>BTW, I have looked all of these questions up on Google and on CC, but I did no fully understand the explanations. Hence, my re-posting of these questions.</p>

<p>I have two questions that I don't actually have SAT questions from the BB, but here they are:</p>

<ol>
<li>When you have a proportion how do you know whether the cross-multiplication of the opposite numerator and denominator or equal or if the numerators of the two fractions are equal (or the denominators).</li>
</ol>

<p>Ex: 5/6=3/4 </p>

<p>I am not even sure if that is the right type of example, but I hope you understand what I am trying to ask. :)</p>

<ol>
<li>When you multiply a number by a percent (that you have converted into a decimal) how do you know if you should subtract the answer you get after multiplying the two numbers from the original number, or if the answer you got after multiplying the two numbers is the answer you need? (This mostly comes up on discount and percent questions)</li>
</ol>

<p>Ex: $40 * .35=? </p>

<p>Is the number you get after multiplying the two numbers the answer? Or, do you need to subtract the answer you get from muliplying these two numbers from $40?</p>

2

<p>All right here we go</p>

<ol>
<li><p>Let X be the price the store pays to buy one sweater
X + 0.4X=28
1.4X=28
X=$20
Now, you made a typo, you should have said employees can purchase any remaining sweaters at 30 perfect “off” the store’s cost, not of the store’s cost.
So 70% of $20=$14
Therefore, the answer is B</p></li>
<li><p>Let’s expand this: (x-8)(x-k)=x^2-xk-8x+8k=x2-5kx+m
cancelling out the x^2 gives you -xk-8x+8k=-5kx+m
You see those xk and you want to have both sides look similar.
Take out -x and you will ahve -x(k+8)+8k=-5kx+m, which means k+5=-5k and 8k=m
-5k=-k-8, -4k=-8, k=2…8k=m, 8(2)=16
Therefore, the answer is B</p></li>
<li><p>This is easy questian if you look at it in a simple way.
It is an 80 inch long paper and at every 3 inch, there is a triangular empty space cut out. Instead of it being 1inch, it becomes 2inches (because its equilateral triangle).
Let’s assume that the paper did not have the triangular empty spaced, then this will give you 20 of 4 inches. (4inches and the paper is 20 inches long, so there will be 20 of 4 inches).
It became 5 inches, so you should 20 x 5 instead of 20 x 4, and this gives you 100
Therefore, the answer is 100 (Sorry I suck at explaining)</p></li>
<li><p>It is #10 not #12 =)
I’m not sure what the name of the rule is but we learned it in grade 9 or 10.
Length of QT=8, and RS=10, we see that angle T and angle S are same, therefore we get the ratio of smaller triangle to bigger triangle: 4/5.
PT=length of smaller triangle, PS=length of bigger triangle
Therefore, the answer is 4/5 (You should note that this ratio works for length that shares same angles. For example, in the same question, you cannot use length of PQ to find the length of SR, but you can find the length of PR. If length of PQ was 4, length of PR=5)</p></li>
<li><p>This question is very similar to that of #4 (the previous question)
Let’s look at the figure and we can find out from the passage that PA=PB, PQ=QR
We have length of PB, PR, AQ and we can find out PA=AB=2, PQ=QR=3, AQ=2.
Using the method we used in #4, use the length of AQ to find out the length of BR.
Ratio of PA to AQ= 1:2. You now know that ratio of PB to BR= 1:2, which gives you BR=8.
2+3+4+8=17
Therefore, the answer is 17.</p></li>
</ol>

<p>For the questions that you brought, I am not sure what you meant with number 1
For question number 2, I will give you an exmaple.
When you are finding out the price of a sweater, which is $80 at original price, that is on 30% disccount, you just need to $80(0.7)=$56 to find out the price of sweater AFTER the sale. But let’s look at this question in different way. If you want to use the 30% in the equation, you can use $80(0.3)=$24, which is the price that is discounted. It is NOT the price after the sale, its how much you will save when you buy the sweater. Therefore, you have to subtract 24 from 80 to find the answer $56.</p>

<p>Hope you understood what I meant and hope it helped you. Sorry for bad grammar, I was really sleepy while typing. XD</p>

3

<p>Opps for # 2, -(k+8)=-5k, not k+5=-5k, sorry about that</p>

4

<p>MoonTuHon said it all, but I think that there is an easier way to solve number 2.</p>

<p>(x-8)(x-k) = x^2-5kx+m</p>

<p>In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?</p>

<p>A. 8
B. 16.
C. 24
D. 32
E. 40</p>

<p>We know that if m = 8, k = 1; if m=16, k=2; and so forth.
Therefore, we can just plug in the respective k values into the equation:
(x-8)(x-1) = x^2 - 9x + 8
Does -9 = -5(1)? No.
(x-8)(x-2) = x^2 - 10x + 16
Does -10 = -5(2)? Yes!
Therefore, we know that the answer is B without having to go into any messy algebra.</p>

5

<p>If p^2 – r^2 = 18 and p – r = 2, what is p + r?</p>

<p>(A) 5
(B) 9
(C) 13
(D) 16
(E) 18</p>

6

<p>Let me remind you that.
a^2 - b^2 = (a+b)(a-b)
Also useful, though unrelated, is the fact that.
(a+b)^2 = a^2 + 2ab + b^2
You can always find those out for yourself pretty easily on the day of the test.</p>

<p>First you must simplify the equation as follows:
(p - r)(p + r) = 18
2(p + r) = 18
(p + r) = 9
The answer is (B) 9.</p>