SAT Rational Expressions Practice Questions (Free + Explanations)

Advanced Math · Rational Expressions

SAT Rational Expressions Practice Questions (Free + Explanations) | Quiz 2

Question 12345 of 5

Question 1 of 5

The table shows values of a function f . x 248 f (x) \frac{5}{2} \frac{5}{4} \frac{5}{8} Which expression could represent f (x) ?

Explanation From the table, each output is 5 divided by the input: f (2) = \frac{5}{2}, f (4) = \frac{5}{4}, and f (8) = \frac{5}{8} . So the expression that matches the data is f (x) = \frac{5}{x} . Concept summary For a rational expression model, compare how each input and output are related. Here, the output equals 5 divided by the input, so the rule is \frac{5}{x} .

Question 2 of 5

For all values of x such that the expression is defined, which statement must be true about \frac{x ^{2} - 9}{x - 3} ?

Explanation Factor the numerator: x^{2} - 9 = (x - 3) (x + 3) . For values of x where the expression is defined, x \neq = 3, so the factor x - 3 cancels. The expression becomes x + 3 . Therefore, the statement that must be true is that it is equal to x + 3 . Concept summary A rational expression can often be simplified by factoring and canceling common factors, but values that make the original denominator 0 are still excluded.

Question 3 of 5

A rectangular garden has length x + 4 feet and width x feet, where x > 0 . The ratio of the garden's width to its length is \frac{x}{x + 4} . If the width is 6 feet, what is this ratio?

Explanation Substitute x = 6 into the ratio \frac{x}{x + 4} : \frac{6}{6 + 4} = \frac{6}{10} = \frac{3}{5} . So the correct ratio is \frac{3}{5} . Concept summary For a rational expression in a measurement context, identify what each part represents and substitute the given value carefully before simplifying.

Question 4 of 5

A plumber charges a flat fee of \40\ per hour for a repair. The total cost of the repair is represented by , where is the number of hours worked. Which expression represents the number of hours worked in terms of the total cost ?

Explanation Start with the given equation C = 40 + 60 h . Subtract 40 from both sides to get C - 40 = 60 h . Then divide both sides by 60 : h = \frac{C - 40}{60} . So the expression for the number of hours worked is \frac{C - 40}{60} . Concept summary To rewrite a linear cost equation for one variable, undo the operations in reverse order. For C = 40 + 60 h, subtract first, then divide.

Question 5 of 5

For x \neq = 4, the expression \frac{x ^{2} - 16}{x - 4} is equivalent to which of the following?

Explanation Factor the numerator: x^{2} - 16 = (x - 4) (x + 4) . Then \frac{x ^{2} - 16}{x - 4} = \frac{( x - 4 ) ( x + 4 )}{x - 4} = x + 4 for x \neq = 4 . So the expression is equivalent to x + 4 . Concept summary To simplify a rational expression, factor the numerator and denominator, then cancel any common factors that are allowed by the domain restriction.

Your results

0of 5 correct

Estimated SAT Math band

500-550

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

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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.

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Your results

2of 5 correct

Estimated SAT Math band

600-650

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

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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.

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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.

Download on the App Store Get it on Google Play

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.

Download on the App Store Get it on Google Play

More SAT Math practice

Practice outline (enable JavaScript for interactive mode)

Q1. The table shows values of a function f . x 2 4 8  f ( x ) 2 5  4 5  8 5    Which expression could represent f ( x ) ?

Q2. For all values of x such that the expression is defined, which statement must be true about x − 3 x 2 − 9  ?

Q3. A rectangular garden has length x + 4 feet and width x feet, where x &gt; 0 . The ratio of the garden's width to its length is x + 4 x  . If the width is 6 feet, what is this ratio?

Q4. A plumber charges a flat fee of \ 40 pl u s \ 60 per hour for a repair. The total cost of the repair is represented by C = 40 + 60 h , where h is the number of hours worked. Which expression represents the number of hours worked in terms of the total cost C ?

Q5. For x  = 4 , the expression x − 4 x 2 − 16  is equivalent to which of the following?