ASTB Math FREE Sample Practice Questions

ASTB Math FREE Sample Practice Questions: work through realistic questions in the same format and difficulty as the real test, then check every answer against a full step-by-step solution so you can see where you lost marks and what to review next.

7- C
(|9, (12 ÷ | 2 to 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5)

8- D
METHOD ONE
\(log_{2}⁡x = 5\)
Apply logarithm rule: \(a = log_b⁡(b^a)\)
\(5 = log_2⁡(2^5) = log_2⁡(32)\)
\(log_2⁡x = log_2⁡(32)\)
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:
\(log_a⁡b=c⇒b=a^c \)
\(log_2⁡x=5⇒x=2^5=32\)

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

Download

$29.99 Original price was: $29.99.$19.99Current price is: $19.99.

Rated 4.25 out of 5 based on 76 customer ratings

Satisfied 61 Students

The Ultimate Middle School Math Bundle Grades 6-8

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.