Question 1 of 5
Which expression is equivalent to for all positive values of ?
Explanation
Since , we can write
because is positive, so .
Concept summary
To simplify a radical, factor out perfect squares and use when .
Advanced Math · Exponential And Radical Equations
SAT Exponential And Radical Equations Practice Questions (Free + Explanations) | Quiz 3
Question 12345 of 5
Question 2 of 5
The graph of is shown in the -plane. Which point lies on the graph?
Explanation
A point lies on the graph of if its coordinates satisfy the equation. For , substituting gives , so this point is on the graph.
Concept summary
To tell whether a point is on the graph of an exponential function, substitute the point's -value into the equation and see whether the resulting -value matches.
Question 3 of 5
For real numbers and , the system
and
is satisfied. What is the value of ?
Explanation
Since both equations are true at the same time, substitute into . This gives . Squaring both sides gives , so .
Concept summary
In a system, both equations must be true at once. If one equation gives a value for a variable, substitute it into the other equation and solve.
Question 4 of 5
A table shows values of the function .
What value should replace the question mark?
Explanation
Use the rule . When , substitute to get . So the missing value is .
Concept summary
For a radical function like , substitute the given -value, simplify inside the radical first, and then take the square root.
Question 5 of 5
Given that is a positive number and , which of the following must be true about and ?
Explanation
Since , square both sides to get . Then compute . So the statement that must be true is and .
Concept summary
If and is positive, then . After finding , substitute it into any linked quantity.
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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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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More SAT Math practiceYour 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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More SAT Math practiceYour 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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More SAT Math practiceYour 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 practiceYour 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