SAT Rational Expressions Practice Questions (Free + Explanations)

Advanced Math · Rational Expressions

SAT Rational Expressions Practice Questions (Free + Explanations) | Quiz 1

Question 12345 of 5

Question 1 of 5

A car rental company charges a one-time fee of \24\ per mile driven. If the total cost of a rental is represented by , where is the number of miles driven, which expression represents the number of miles driven in terms of the total cost ?

Explanation Start with the given equation C = 24 + 0.20 m . To solve for m, subtract 24 from both sides: C - 24 = 0.20 m . Then divide both sides by 0.20 : m = \frac{C - 24}{0.20} So the expression for the number of miles driven is \frac{C - 24}{0.20} . Concept summary To rewrite a linear equation for a different variable, undo each operation in reverse order. For a cost model with a fixed fee plus a per-unit rate, subtract the fixed fee first, then divide by the rate.

Question 2 of 5

For x \neq = 5, if \frac{x - 5}{2} = 6, what is the value of \frac{12}{x - 5} ?

ExplanationFrom , multiply both sides by to get . ThenSo the correct answer is .Concept summaryUse the given rational equation to find the repeated expression in the denominator, then substitute that value into the new fraction.

Question 3 of 5

Which expression is equivalent to \frac{x ^{2} - 9}{x + 3} for all values of x such that the expression is defined?

Explanation Factor the numerator: x^{2} - 9 = (x - 3) (x + 3) . Then \frac{( x - 3 ) ( x + 3 )}{x + 3} = x - 3, as long as x \neq = - 3 . So the equivalent expression is x - 3 for all values where the original expression is defined. Concept summary To rewrite a rational expression in an equivalent form, factor the numerator or denominator and then cancel any common factors, keeping domain restrictions in mind.

Question 4 of 5

The graph of the function y = \frac{4}{x} passes through the point (k, 2) . What is the value of k ?

Explanation Since the point (k, 2) is on the graph of y = \frac{4}{x}, substitute x = k and y = 2 into the equation: 2 = \frac{4}{k} . Solving gives k = 2 . So the correct answer is 2 . Concept summary For a point on the graph of a rational function, substitute the point's coordinates into the equation and solve for the unknown coordinate.

Question 5 of 5

For real numbers x and y, suppose \frac{1}{x} = 3 and \frac{1}{y} = 5. What is the value of \frac{x + y}{x y} ?

Explanation Use the identity \frac{x + y}{x y} = \frac{x}{x y} + \frac{y}{x y} = \frac{1}{y} + \frac{1}{x} . Since \frac{1}{x} = 3 and \frac{1}{y} = 5, the value is 3 + 5 = 8. Concept summary A rational expression can often be rewritten before substituting. Here, \frac{x + y}{x y} = \frac{1}{x} + \frac{1}{y} .

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.

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Your results

4of 5 correct

Estimated SAT Math band

700+

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

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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. A car rental company charges a one-time fee of \ 24 pl u s \ 0.20 per mile driven. If the total cost of a rental is represented by C = 24 + 0.20 m , where m is the number of miles driven, which expression represents the number of miles driven in terms of the total cost C ?

Q2. For x  = 5 , if 2 x − 5  = 6 , what is the value of x − 5 12  ?

Q3. Which expression is equivalent to x + 3 x 2 − 9  for all values of x such that the expression is defined?

Q4. The graph of the function y = x 4  passes through the point ( k , 2 ) . What is the value of k ?

Q5. For real numbers x and y , suppose x 1  = 3 and y 1  = 5. What is the value of x y x + y  ?