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Krushang V.

Tutor for three years

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SAT II Mathematics Level 2

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Question:

Given two integers a & b. Also, that $$(a + b) $$=12, $$a^2 + b^2 = 74$$, and $$a^2 - b^2 =24$$. What is $$a-b$$?

Krushang V.

Answer:

SInce we know $$a^2 - b^2 = (a+b)(a-b), (a-b)=\frac{a^2 - b^2}{(a+b)}, we can determine that (a-b)=24/12=2$$

Physics (Electricity and Magnetism)

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Question:

What are the three kinds of symmetries in which you can apply Gauss's law?

Krushang V.

Answer:

Simple. The three kinds of symmetries are: (a) Radial. Given a sphere of charge q, I can create a Gaussian surface surrounding the sphere to find the corresponding Electric Field. (b) Translational. Given an infinite line of charge, I can use a Gaussian cylinder to derive the equation for the Electric Field. (c) Planar. Given a charged sheet, I can use a Gaussian cylinder to derive the Electric Field.

Calculus

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Question:

Evaluate the following indefinite integrals: (a) $$\int x^2 dx$$ (b) $$\int sin(x) dx$$ (c) $$\int x^{-1} dx$$

Krushang V.

Answer:

Answers: Here, n is the power of x. (a) $$\frac{x^{n+1}}{n+1} ; n=2; \therefore \frac{x^{3}}{3}$$ (b) From the formula, $$-cos(x) $$ (c) Notice that n=-1. SO the reverse power rule doesn't apply. $$ln(x)$$

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