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Advanced Math · Rational Expressions

SAT Rational Expressions Practice Questions (Free + Explanations) | Quiz 5

Question 12345 of 5

Question 1 of 5

A community center rents out canoes for a flat equipment fee plus an hourly rate. For a rental lasting hours, the total cost in dollars is modeled by . The average cost per hour of a rental is therefore for . Which expression is equivalent to the average cost per hour?

Explanation

The average cost per hour is total cost divided by the number of hours:

Split the fraction into two parts:

So the equivalent expression is .

Concept summary

To find an average rate from a total modeled by a rational expression, divide the total by the relevant quantity and simplify carefully across each term.

Question 2 of 5

For all values of for which the expression is defined, which expression is equivalent to

Explanation

Factor each part first:

So the expression becomes

Now cancel common factors of and :

Therefore, for every value of where the original expression is defined, the equivalent expression is . Note that the original expression is undefined at and , but that does not change the simplified form on its domain.

Concept summary

To find an equivalent rational expression, factor completely first, then cancel only common factors that are multiplied, while keeping the original domain restrictions in mind.

Question 3 of 5

The graph of the function passes through the point . What is the -coordinate of the point on the graph where ?

Explanation

Since the point is on the graph of , substitute and to find :

So . The function is therefore

Now substitute :

So the -coordinate is .

Concept summary

For a rational function like , use a point on the graph to determine the constant, then evaluate the function at the requested -value.

Question 4 of 5

A science class is tracking a quantity with the model , where and are constants and is measured in hours. The table shows two values of the quantity.

According to the model, what is the value of ?

Explanation

Use the table values to write two equations. Since , we have

so . Since , we have

so . Subtracting the first equation from the second gives , so . Then becomes , so . Now evaluate :

So the correct answer is .

Concept summary

For a rational model with unknown constants, use the data table to create equations, solve for the constants, and then substitute into the expression to find the requested value.

Question 5 of 5

A theater sells snack boxes for a fundraiser. The cost per box, in dollars, is modeled by c={48}{n}, where is the number of boxes made. According to this model, what is the cost per box if the theater makes boxes?

Explanation

Substitute into the model :

So the cost per box is \4

Concept summary

A rational expression can model a quantity that depends on division. To find the value, substitute the given number and simplify the fraction.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice