ASTB Math FREE Sample Practice Questions

ASTB Math FREE Sample Practice Questions

Preparing for the ASTB Math test? To succeed on the ASTB Math test, you need to practice as many real ASTB Math questions as possible.  There’s nothing like working on ASTB Math sample questions to measure your exam readiness and put you more at ease when taking the ASTB Math test. The sample math questions you’ll find here are brief samples designed to give you the insights you need to be as prepared as possible for your ASTB Math test.

Check out our sample ASTB Math practice questions to find out what areas you need to practice more before taking the ASTB Math test!

Start preparing for the 2020 ASTB Math test with our free sample practice questions. Also, make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

The Absolute Best Book to Ace the ASTB Math Test

10 Sample ASTB Math Practice Questions

1- Solve the equation: \(log_{4⁡}(x+2) – log_4⁡(x-2) = 1\)

☐A. 10

☐B. \(\frac{3}{10}\)

☐C. \(\frac{10}{3}\)

☐D. 3

2- Solve: \(e^{(5x + 1 )}= 10 \)

☐A. \(\frac{ln⁡(10) + 1}{5}\)

☐B. \(\frac{ln⁡(10) – 1}{5}\)

☐C. \(5ln (10) + 2\)

☐D. \(5ln (10) – 2\)

3- If \(f(x) = x – \frac{5}{3}\) and \(f ^{–1}\) is the inverse of \(f(x)\), what is the value of \(f ^{–1(5)\)?

☐A. \(\frac{10}{3}\)

☐B. \(\frac{3}{20}\)

☐C. \(\frac{20}{3}\)

☐D. \(\frac{3}{10}\)

4- What is cos \(30^{\circ}\)?

☐A. \(\frac{1}{2}\)

☐B. \(\frac{{\sqrt{2}}}{2}\)

☐C. \(\frac{{\sqrt{3}}}{2}\)

☐D. \(\sqrt{3}\)

5- If \(\theta\) is an acute angle and sin \(\theta = \frac{3}{5}\), then cos \(\theta\) =?

☐A. \(-1\)

☐B. 0

☐C. \(\frac{4}{5}\)

☐D. \(\frac{5}{4}\)

6- What is the solution of the following system of equations?
\(-2x- y = -9 \)
\(5x-2y= 18\)

☐A. \((–1, 2)\)

☐B. \((4, 1)\)

☐C. \((1, 4)\)

☐D. \((4, -2)\)

7- Solve.
\(|9 – (12 ÷ | 2 – 5 |)| = \)?

☐A. 9

☐B. \(-6\)

☐C. 5

☐D. \(-5\)

8- If \(log_{2⁡}x = 5\), then \(x = \)?

☐A. \(2^{10}\)

☐B. \(\frac{5}{2}\)

☐C. \(2^{6}\)

☐D. 32

9- What’s the reciprocal of \(\frac{x^3}{16}\)?

☐A. \(\frac{16}{x^3}-1\)

☐B. \(\frac{48}{x^3}\)

☐C. \(\frac{16}{x^3}+1\)

☐D. \(\frac{16}{x^3}\)

10- Find the inverse function for \(ln (2x + 1)\)?

☐A. \(\frac{1}{2}(e^{x }– 1)\)

☐B. \((e^{x }+ 1)\)

☐C. \(\frac{1}{2}(e^{x }+ 1)\)

☐D. \((e^{x }– 1)\)

Best ASTB Math Prep Resource for 2020

Answers:

1- C
METHOD ONE
\(log_4⁡(x+2) – log_4⁡(x-2) = 1\)
Add \(log_4⁡(x-2)\) to both sides
\(log_4⁡(x+2) – log_4⁡(x-2)+ log_4⁡(x-2)= 1 + log_4⁡(x-2)\)
\(log_4⁡(x+2) = 1 + log_4⁡(x-2)\)
Apply logarithm rule:
\(a = log_b⁡(b^a) ⇒ 1 = log_4⁡(4^1) = log_4⁡(4)\)
then: \(log_4⁡(x+2) = log_4⁡(4) + log_4⁡(x-2)\)
Logarithm rule: \(log_c⁡(a) + log_c⁡(b) = log_c⁡(ab)\)
then: \(log_4⁡(4) + log_4⁡(x-2) = log_4⁡(4(x-2))\)
\(log_4⁡(x+2) = log_4⁡(4(x-2))\)
When the logs have the same base:
\(log_b⁡(f(x)) = log_b⁡(g(x)) ⇒ f(x) = g(x)
(x+2) = 4(x-2)\)
\(x = \frac{10}{3}\)

METHOD TWO
We know that:
\(log_a⁡b-log_a⁡c=log_a\frac{b}{c}⁡\space and \space log_a⁡b=c⇒b=a^c\)
Then: \(log_4⁡(x+2)- log_4⁡(x-2)=log_4\frac{(x + 2)}{(x – 2)}⁡=1⇒\frac{(x + 2)}{(x – 2)}=4^1=4⇒x+2=4(x-2)
⇒x+2=4x-8⇒4x-x=8+2→3x=10⇒x=\frac{10}{3}\)

2- B
\(e^{(5x + 1 )}= 10\)
If \( f(x) = g(x)\), then \(ln(f(x)) = ln(g(x))\)
\(ln⁡(e^{(5x + 1 )})= ln(10)\)
Apply logarithm rule:
\(log_a⁡(x^b) = b log_a⁡(x)\)
\(ln⁡(e^{(5x + 1 )})= (5x + 1)ln(e)\)
\((5x + 1)ln(e) = ln(10)\)
\((5x + 1)ln(e) = (5x + 1)\)
\((5x + 1) = ln(10) \)
\( ⇒x = \frac{ln⁡(10) – 1}{5}\)

3- C
\(f(x) = x –\frac{5}{3}⇒ y = x – \frac{5}{3}⇒ y+ \frac{5}{3}=x\)
\(f^{-1 }= x+ \frac{5}{3}\)
\(f ^{–1}(5) = 5 +\frac{5}{3}=\frac{20}{3}\)

4- C
cos \(30^{\circ} = \frac{\sqrt 3}{2}\)

5- C
sin\(θ=\frac{3}{5}⇒\) we have following triangle, then:
\(c=\sqrt {(5^2-3^2 )}=\sqrt{(25-9)}=\sqrt 16=4\)
cos\(θ=\frac{4}{5}\)

6- B
\(-2x- y = -9\)
\(5x-2y= 18\)
\(⇒\) Multiplication \((–2)\) in first equation
\(4x +2y =18\)
\(5x-2y= 18\)
Add two equations together \(⇒ 9x =36 ⇒ x= 4\) then: \(y = 1\)

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: \(a = log_b⁡(b^a)\)
\(5 = log_2⁡(2^5) = log_2⁡(32)\)
\(log_2⁡x = log_2⁡(32)\)
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

Related to "ASTB Math FREE Sample Practice Questions"

Top 10 ASTB Math Practice Questions
Top 10 ASTB Math Practice Questions
ASTB Math Practice Test Questions
ASTB Math Practice Test Questions
ASTB Math Formulas
ASTB Math Formulas
How to prepare for the ASTB Math Test
How to prepare for the ASTB Math Test
ASTB Math Worksheets
ASTB Math Worksheets
The Ultimate ASTB Math Course
The Ultimate ASTB Math Course

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…