Sherry Z.

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SAT II Mathematics Level 2

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Question:

If x is a positive, even integer, y is a negative number, and z is an odd integer, what is a possible value of xyz?

Sherry Z.

Answer:

If you thought of any negative even number, you're correct!! Let's take this step by step. Let's first figure out if it is positive or negative. Since x is positive and y is negative, when they are multiplied, it becomes negative. Great! step one complete. Next, let's figure out if it even or odd. Since x is even and z is odd, when they are multiplied, it has to be even. Think about it, if you double anything, it is always even. So 4 times something is just 2 doubles. Even times odd is always even. Tada! Now you know that the answer must be a negative even number.

SAT

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Question:

Two 6-sided dice are tossed. What is the probability that the sum of the two dice is greater than 4?

Sherry Z.

Answer:

Since each dice has 6 possibilities, that means there is a total of 6x6 = 36 possible outcomes. Of those 36 outcomes, all of them will be greater than four except for the following combinations - ( 1 ; 1 ), ( 1 ; 2 ), ( 1 ; 3 ), ( 2 ; 1 ), ( 2; 2 ), ( 3 ; 1 ). Therefore 36 - 6 = 30 possible combination that will be greater than 4. 30/36 = 5/6 probability that the sum of the two dice is greater than 4.

Calculus

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Question:

True or False: If F(x) is an antiderivative of f(x) and c is any constant, then F(x) + C is also an antiderivative of f(x).

Sherry Z.

Answer:

True!! The opposite of an antiderivative is a derivative, so to make sure you understand why this is true, differentiate F(x) + c. This is always true because the derivative of a constant is always 0.

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