Math Level 5 questions and some Level 4 questions - Let us share the knowldege

Test Preparation SAT Preparation
1

<p>I will start with one which came in released PSAT exam.</p>

<p>In a certain parking lot that contains 200 cars, 50 percent of the cars are red, 60 percent are four-door cars, and 70 percent have alloy trims. What is the greatest number of cars in the parking lot that could be green two-door cars with alloy trims?</p>

2

<p>If there are 200 cars, 100 of them are red, 120 of them have 4 doors and 140 of them have alloy trims. So 100 of them are green, 80 of them have two doors, and 140 of them have alloy trims.</p>

<p>We look for the least possible number here for the greatest possible number (sounds weird, but it doesn’t say or, it says and, all 3 attributes combined). So isn’t it 80? Am I missing something?</p>

3

<p>It should be 80 :/</p>

4

<p>answer is 80.</p>

5

<p>My turn? This is a level 5.</p>

<p>The graph above (can’t draw, but the vertex is at -4) shows the function g, where g(x) = k(x+3)(x-3) for some constant k. If g(a - 1.2) = 0 and a > 0, what is the value of a?</p>

<p>I’ll explain if needed.</p>

6

<p>is the answer 4.2?</p>

7

<p>Yes, also 1.2.</p>

8

<p>I’m confused by how 1.2 works as an answer.</p>

<p>if a = 1.2, g(a - 1.2) = g(0).
g(0) = k(0+3)(0-3) = k(3)(-3) = -9k</p>

<p>So when a = 1.2, g(x) doesn’t equal 0.</p>

9

<p>Sorry, I remembered the other answer incorrectly.</p>

<p>The constant k is irrelevant and serves only to confuse. I’ll explain to people just in case.</p>

<p>1. Replace the x with a - 1.2</p>

<p>g(a - 1.2) = k(a - 1.2 + 3)(a - 1.2 - 3)
g (a - 1.2) = k(a + 1.8)(a - 4.2) =></p>

<p>2. Multiply the brackets</p>

<p>a^2 - 4.2a + 1.8a - 7.56 = a^2 - 2.4a - 7.56 = 0</p>

<p>3. Complete the square. In order to do this, divide b (which in this equation is -2.4) then square it, add it and subtract it.</p>

<p>a^2 - 2.4a + 1.44 - 7.56 - 1.44 = 0
(a - 1.2)^2 - 9 = 0
(a - 1.2)^2 = 9</p>

<p>4. Square root both sides then solve.</p>

<p>a - 1.2 = +/- 3
a1 = 4.2
a2 = -1.8</p>

<p>a > 0, so it can’t be -1.8. It’s 4.2.</p>

10

<p>This will help me visualize. Thanks</p>

11

<p>Attempt to draw it yourself first (you should know how, it might help in the SAT, yes I know you don’t draw on the SAT and it sure as hell will help in high school), if you can’t, click for my drawing:</p>

<p><a href=“http://img.■■■■■■■■■■■■■■■/albums/v322/DarkV/satgraphstuff.jpg[/url]”>http://img.■■■■■■■■■■■■■■■/albums/v322/DarkV/satgraphstuff.jpg&lt;/a&gt;&lt;/p&gt;

<p>I suck super hard at drawing by the way. If you don’t know how to draw (plotting and etc.), I can explain.</p>

12

<p>Rectangle ABCD lies in the xy-coordinate plane so that its dies are NOT parallel to the axes. What is the product of all four sides of rectangle ABCD?</p>

<p>A) -2
B) -1
C) 0
D) 1
E) 2</p>

13

<p>I believe you wrote the question wrong. It seemed so impossible to me I searched a part of it on Google to find the real question.</p>

<p>sides > dies (typo)
slopes > sides</p>

<p>If that is the case, 1 perpendicular = -1.</p>

<p>Two perpendiculars = -1 x -1 = 1.</p>

<p>So D.</p>