Blue Book Math Question Help?

Test Preparation SAT Preparation
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<p>Need to know how to solve some of these questions from the newer blue book's 1st practice test (on page 400, section 3). If someone asked these already or something, do link it to me!</p>

<p>Pg. 400-</p>

<h1>16- If 3a + 4b = b, which of the following must equal 6a + 6b?</h1>

<p>A) 0, B) 12, C) 2b, D) 12b, E) 6b - 8
The answer is A) 0, but how do you get that?</p>

<h1>18- The table shows some values for the function f. If f(x)=ka^x for some constants k and a, what is the value of a?</h1>

<p>x -1 0 1
f(x) 1/8 1/2 2
A) 1/2, B) 1/4, C) 2, D) 4, E) 16
Answer is D) 4</p>

<h1>19- The pyramid has altitude h and a sq. base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m?</h1>

<p>(if some of you have the BB, please look this one up! answers and the pyramid sketch are hard to get on this)</p>

<h1>20- A salesperson's commission is k percent of the selling price of a car. Which of the following represents the commission, in dollars, on 2 cars that sold for $14,000 each?</h1>

<p>A) 280k, B) 7,000k, C) 28,000k, D) 14,000/100+2k, E) 28,000+k/100
Answer is A)280k, and I have NO idea how, I thought this was a pretty easy question to be at the back until I read the answer and got confused... what's going on with this? I really thought it was C. </p>

<p>Thanks again, math's one of my weaker sections but at least all of you own it.</p>

2

<p>18-
3a + 4b = b
3a + 3b = 0 (subtract b from both sides)
6a + 6b = 0 (multiply by 2)</p>

3

<p>Pg. 400-</p>

<h1>16- If 3a + 4b = b, which of the following must equal 6a + 6b?</h1>

<p>A) 0, B) 12, C) 2b, D) 12b, E) 6b - 8</p>

<p>Subtract b from both sides of the equation to get 3a + 3b = 0.
Multiply both sides of the equation by 2 to get 6a + 6b = 0, choice (A).</p>

4

<p>^ that was 16</p>

5

<h1>18- The table shows some values for the function f. If f(x)=ka^x for some constants k and a, what is the value of a?</h1>

<p>x -1 0 1
f(x) 1/8 1/2 2
A) 1/2, B) 1/4, C) 2, D) 4, E) 16</p>

<p>Let’s use the second point first since it’s easiest. When x=0, f(x)=1/2.</p>

<p>f(x)=ka^x
1/2 = ka^0 = k. So k = 1/2 = .5</p>

<p>f(x)=.5a^x</p>

<p>Now let’s use the third point. When x=1, f(x)=2</p>

<p>2=.5a^1. So 2=.5a. Thus, a = 2/.5 = 4, choice (D).</p>

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<h1>19- The pyramid has altitude h and a sq. base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m?</h1>

<p>(if some of you have the BB, please look this one up! answers and the pyramid sketch are hard to get on this)</p>

<p>I don’t have the BB in front of me, but most likely you’re going to want to form a right triangle in 3 dimensions and use the Pythagorean theorem.</p>

7

<h1>20- A salesperson’s commission is k percent of the selling price of a car. Which of the following represents the commission, in dollars, on 2 cars that sold for $14,000 each?</h1>

<p>A) 280k, B) 7,000k, C) 28,000k, D) 14,000/100+2k, E) 28,000+k/100</p>

<p>Let’s plug in a value for k, say k = 100. The 2 cars sold for 28,000 together. The commission is then 100% of 28,000 which is 28,000. Now plug 100 in for k in each answer choice, and you’ll see that only choice (A) gives the correct answer.</p>

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<p>Thanks for the speedy response, DrSteve! But I’m still confused. I think what you mean is that k (the percent), doesn’t refer to 50% or .50, but just the whole number 50. So obviously 28,000(50) isn’t his commission, but 280(50) is. You kind of get what I mean?</p>

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<p>I think you’re confusing what it means to pick a value for k, and what percentage k represents. Once you pick k, this is the value you plug in whenever you see a k (in the answer choices in this case), but the commission is k percent of 28000. So you have to take a percentage of 28,000. Let’s use your number 50 (although 100 is usually a better choice in a percentage problem). See if this clears things up a bit:</p>

<p>Let’s plug in k = 50. The 2 cars sold for 28,000 together. The commission is then 50% of 28,000 which is 14,000. Now plug 50 in for k in each answer choice (because we CHOSE k=50), and you’ll see that only choice (A) gives the correct answer of 14,000.</p>

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<h1>20</h1>

<p>A method using proportions.
The commission is k percent i.e k dollars for every 100 dollars
How many dollars commission for 28000 dollars</p>

<p>k/100 = ?/28000
? = (k/100) (28000) = 280k</p>

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</p>

<p>Oh, I think I get what you mean. I’m guessing in the future, any problems like this will require guess and check?</p>

<p>

</p>

<p>I thought it involved twisting the volume formula somehow using the same variable for e and m (base and diagnol hypotnuses)</p>

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<h1>19- The pyramid has altitude h and a sq. base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m?</h1>

<p>Consider the square base of side m. Its diagonal would be,</p>

<p>d = square root(m^2 + m^2) = square root(2) x (m) {by Pythagoras theorem}</p>

<p>Draw a line from the altitude marked h to the edge marked e. This line is half of the above diagonal d.</p>

<p>Now you have a right triangle with 3 sides, e, h, and (square root(2) x (m))/2</p>

<p>It is given e = m and e is the hypotenuse in the right triangle.</p>

<p>So, e^2 = m^2 = h^2 + ((square root(2) x (m))/2) ^2
=> m^2 = h^2 + (m^2)/2
=> h^2 = (m^2)/2
=> h = m/(square root(2))</p>

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<p>If there are letters in the answer choices, then picking numbers is a strategy that should always get you the right answer. It is a more time consuming strategy. On easy and medium questions you should use it as a last resort, but on hard questions (last few in a section) you should ALWAYS use this strategy - doing the problem algebraically will most likely get you the wrong answer (since these tend to have subtle tricks that you might miss).</p>

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<h1>20 is basically asking you what is k percent of 28,000? If it asked for 7% of 28,000 what would you do? Multiply 28,000 by .07 or 7/100. So to find k percent by multiplying 28,000 by k/100. 280k.</h1>