ASTB Math FREE Sample Practice Questions
7- C
\(|9 – (12 ÷ | 2 – 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5\)
8- D
METHOD ONE
\(log_{2}x = 5\)
Apply logarithm rule: \(a = log_b(b^a)\)
\(5 = log_2(2^5) = log_2(32)\)
\(log_2x = log_2(32)\)
When the logs have the same base: \(log_b(f(x)) = log_b(g(x))⇒ f(x) = g(x)\)
then: \(x = 32\)
METHOD TWO
We know that:
\(log_ab=c⇒b=a^c \)
\(log_2x=5⇒x=2^5=32\)
9- D
\(\frac{x^3}{16}\)
\(⇒\) reciprocal is: \(\frac{16}{x^3}\)
10- A
\(f(x) = ln (2x + 1)\)
\(y = ln (2x + 1)\)
Change variables \(x\) and \(y: x = ln (2y + 1)\)
solve: \(x = ln (2y + 1)\)
\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\)
The Best Books to Ace the ASTB Math Test
ASTB Math Practice Workbook 2026 The Most Comprehensive Review for the Math Section of the ASTB Test
Need more ASTB Math practice?
Use the free ASTB Math Worksheet Creator to make a fresh one-skill worksheet with answers and step-by-step explanations. It is a good next step after a lesson, a formula review, or a missed practice-test question.
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For a complete study path: pair this printable practice with ASTB Math for Beginners and ASTB Math Practice Workbook.
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