At least for Non-Math aspirants, MATH LEVEL-2 is a scary story. Most students sit for the test without understanding the portions included on the test and without gaining the necessary expertise in individual concepts. As a result, we do not hear a lot of students claiming that they got 800/800, even when they can achieve it without getting all the answers right. You’ve read it right! However, the test also has a penalty for wrong answers. How will I attain a balance between the number of questions you should attempt and the number of questions you can skip? Well, that’s exactly the place where we can help you out. Our training and philosophy are well designed for it!
If you are a person scoring 800/800 on the General SAT, with little training you can cross 750, but to attain a perfect score on the examination, you need to do a little bit more work on some areas like Functions (inverses and Odd/Even functions), Logarithmic Functions, Polar coordinates and Parametric Equations, 3-D geometry, Probability, Permutation and combination, Advanced Trigonometry (including sine and cosine rules), Conic sections.
Let’s see how to solve a question from a fairly unfamiliar area known as Conic sections.
What is the length of the major axis of the ellipse given by the equation?
First of all, you need to study the section dealing with ellipses, and then you can tell by looking at the formula that this is an ellipse centered at the origin. Because the general equation of an ellipse is
and here h and k are equal to 0.
You can also say that the ellipse’s major axis is the vertical axis rather than the horizontal because the constant under the y is larger than the one under the x. That means that the ellipse must look something like this:
If you plot it directly on to a graphing calculator (you can use it throughout the exam), you will see that the endpoints of the ellipse’s major axis are (0, –4.472) and (0, 4.472) because the points lie on a vertical line. The distance between the points is equal to 4.472 – (–4.472), or 8.944. This is the length of the ellipse’s major axis. The correct answer is (C).
Hang on. If I do not have a graphing calculator, or if I want to work manually, then how do I proceed?
The major axis is the vertical axis of the ellipse. The endpoints of the major axis are the two points at which the ellipse intersects the y-axis. Since every point on the y-axis has an x-coordinate of 0, then all you have to do to find the coordinates of the endpoints is plug x = 0 into the equation of the ellipse, and see what y-coordinates that produces.
Again you end up with the same answer, which is option choice C.
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