SAT II Math II : Simplifying Expressions

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

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Example Question #1 : Simplifying Expressions

Decrease  by 40%. Which of the following will this be equal to?

Possible Answers:

Correct answer:

Explanation:

A number decreased by 40% is equivalent to 100% of the number minus 40% of the number. This is taking 60% of the number, or, equivalently, multiplying it by 0.6. 

Therefore,  decreased by 40% is 0.6 times this, or

Example Question #2 : Simplifying Expressions

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Simplifying Expressions

Assume all variables assume positive values.

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : Simplifying Expressions

Assume all variables assume positive values. Simplify:

Possible Answers:

The expression is already simplified.

The expression is undefined.

Correct answer:

Explanation:

Any nonzero expression raised to the power of 0 is equal to 1. Therefore, 

Example Question #5 : Simplifying Expressions

Simplify the following expression:  

Possible Answers:

Correct answer:

Explanation:

Distribute the outer term through both terms in the parentheses.

Multiply each term.

There are no like-terms.

The answer is:  

Example Question #6 : Simplifying Expressions

Simplify the expression:  

Possible Answers:

Correct answer:

Explanation:

Distribute the integers through the binomials.

Combine like-terms.

The answer is:  

Example Question #7 : Simplifying Expressions

Simplify .

Possible Answers:

Correct answer:

Explanation:

We can start by distributing the negative sign in the parentheses term:

Now we can combine like terms.  The constants go together, and the variables go together:

Example Question #51 : Single Variable Algebra

Simplify .

Possible Answers:

Correct answer:

Explanation:

First, we can distribute the negative sign through the parentheses term:

Now we gather like terms.  Remember, you can't gather different variables together.  The 's and 's will still be separate terms:

Example Question #52 : Single Variable Algebra

Simplify .

Possible Answers:

Correct answer:

Explanation:

Start by distributing the negative sign through the parentheses term:

Now combine like terms.  Each variable can't be combined with different variables:

Example Question #53 : Single Variable Algebra

Simplify 

Possible Answers:

Correct answer:

Explanation:

A square root is the inverse of squaring a term, so they cancel each other out:

From there, there's nothing left to simplify.

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