Mimi B.

Third-year Medical School Student

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SAT II Mathematics Level 2

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Question:

Mary deposits $500 into her savings account that earns 5% interest compounded annually. If she makes no additional deposits or withdrawals, how many years will it take for the amount in her account to double?

Mimi B.

Answer:

To arrive at our answer, we need to use the equation, amount=principal*(1+interest rate in decimal form/number of times interest is compounded per year)^number of times interest is compounded per year*time in years [A=P(1+r/n)^nt]. Replacing the proper variables, you get 1000=500(1+0.05/1)^1*t (Why 1000? Because we want to know how long it will take to DOUBLE the principle, which is $500; 500*2=1000). Continuing on, we get 2=1.05^t. Then taking the log of both sides of the equation, we get log(2)=log(1.05)*t. Divide log(2) by log(1.05) and you get t=14.2 years.

Spanish

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Question:

Fill in the blank with the proper conjugated form of the verb, (hacer): Estoy _______ mi tarea ahora.

Mimi B.

Answer:

We want to insert the proper form of "to do" (hacer) in the sentence. To conjugate, we take off the "-er" ending and change it to "-iendo", which is the proper ending to make it "doing" (because the event is currently taking place, "ahora"). The verb is coming after a conjugated form of "estar", so the sentence reads: I am _______ my homework now. >> I am doing my homework now.

Algebra

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Question:

Expand the following factors (to polynomial form): (3x^2+5)(2x+3).

Mimi B.

Answer:

To expand, we must FOIL the factors: First, Outside, Inside, Last First: 3x^2*2x=6x^3 Outside: 3x^2*3=9x^2 Inside: 5*2x=10x Last: 5*3=15 Put it all together and we get: 6x^3+9x^2+10x+15 (All are plus signs because all of the FOIL outcomes are positive.)

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