SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #2851 : Sat Mathematics

If  and , what is ?

Possible Answers:

Correct answer:

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function. Since this is multi-function, whichever answer we get for the inside function, we plug it into the outer function.

 ; 

 

Example Question #1082 : Algebra

If  and , then what is ?

Possible Answers:

Correct answer:

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function. Since this is multi-function, whichever answer we get for the inside function, we plug it into the outer function.

 and 

Example Question #1081 : Algebra

If , then what value of  will make  true?

Possible Answers:

Correct answer:

Explanation:

We know  and . Just set them equal to each other.

 Subtract  on both sides.

 Divide  on both sides.

Example Question #1084 : Algebra

If , then what value of  will make  true?

Possible Answers:

Correct answer:

Explanation:

We know  and . Just set them equal to each other.

 Subtract  on both sides.

 Take square root on both sides and account for also negative answers.

Example Question #1085 : Algebra

If  then what value of  will make  true?

Possible Answers:

Correct answer:

Explanation:

We know that  and . Just set them equal to each other.

 Remember to account for negative values.

 Subtract  on both sides.

 Subtract  on both sides.

Example Question #1081 : Algebra

If  and  then what value of  will make  true?

Possible Answers:

Correct answer:

Explanation:

We know  so we need to apply substitutions to solve for .

 Subtract  on both sides.

 Take square root on both sides and account for negative values.

Example Question #1087 : Algebra

If , then what value of  will make 

Possible Answers:

Correct answer:

Explanation:

We know  so let's make the substitution.

 This is a quadratic so subtract  on both sides.

 Factor.

 Solve individually.

Example Question #1081 : Algebra

Define .

How can  be defined so that  ?

Possible Answers:

Correct answer:

Explanation:

By definition,

so

If

,

it follows that 

,

and, substituting, 

Solving for  by isolating this expression:

.

Example Question #1089 : Algebra

Define .

How can  be defined so that  ?

Possible Answers:

Correct answer:

Explanation:

By definition,

so

If

,

it follows that 

,

and, substituting, 

Solving for  by isolating this expression:

Taking the square root of both sides:

Either , which is not among the given choices, or , which is.

Example Question #1090 : Algebra

Define .

How can  be defined so that  ?

Possible Answers:

Correct answer:

Explanation:

By definition,

so

If

,

it follows that 

,

and, substituting, 

Solving for  by isolating this expression:

Applying the Power of a Product Rule:

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