# TSI Math FREE Sample Practice Questions

Preparing for the TSI Math test? To do your best on the TSI Math test, you need to review and practice real TSI Math questions. There’s nothing like working on TSI Math sample questions to hone your math skills and put you more at ease when taking the TSI 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 TSI Math test.

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

Start preparing for the 2022 TSI 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 TSI Math Test**

**10 Sample TSI 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 \(log_2x = 5\), 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 TSI Math Prep Resource for 2022**

## Answers:

1- **C**

METHOD ONE

\(log_4(x+2) – log_4(x-2) = 1\)

Add\(\space log_4(x-2)\)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:

\(a = log_b(b^a) ⇒ 1 = log_4(4^1) = log_4(4)\)

\(then: log_4(x+2) = log_4(4) + log_4(x-2)\)

\(Logarithm \space rule: log_c(a) + log_c(b) = log_c(ab)\)

\(then: log_4(4) + log_4(x-2) = log_4(4(x-2))\)

\(log_4(x+2) = log_4(4(x-2))\)

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:

\(log_ab-log_ac=log_a\frac{b}{c}\space and \space log_ab=c⇒b=a^c\)

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\( \space f(x) = g(x)\), then \(\space ln(f(x)) = ln(g(x))\)

\(ln(e^{(5x + 1 )})= ln(10)\)

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

\(log_2x = 5\)

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: \(x = ln (2y + 1)\)

\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\)

**Looking for the best resource to help you succeed on the TSI Math test?**

**The Best Books to Ace the TSI Math Test**

## More from Effortless Math for TSI Test …

### Are you looking for prep books that will guarantee you a high score on the TSI math test?

Top 10 TSI Math Prep Books (Our 2021 Favorite Picks) helps you find the best book for you

### Worried about TSI exam day?

TSI Math-Test Day Tips briefly provides you with important tips for the exam day.

### Do you know the formulas for the TSI math test?

If you have not thought about this yet, do not worry! We provide you with a complete list of formulas: TSI Math Formulas.

**The Perfect Prep Books for the TSI Math Test**

## Have any questions about the TSI Test?

Write your questions about the TSI or any other topics below and we’ll reply!

## Related to This Article

### More math articles

- How to Solve Word Problems of Volume of Cubes and Rectangular Prisms
- How to Use Box Multiplication Method
- How to Solve Point-Slope Form of Equations?
- 8th Grade NYSE Math Worksheets: FREE & Printable
- The Ultimate 7th Grade OAA Math Course (+FREE Worksheets)
- The Ultimate 6th Grade MAP Math Course (+FREE Worksheets)
- The Enchanted Forest of How to Compare Ratios – A Tale of Mathematical Adventure
- 10 Most Common 3rd Grade ACT Aspire Math Questions
- How to Identify Errors Involving the Order of Operations?
- Full-Length TABE 11 & 12 Math Practice Test

## What people say about "TSI Math FREE Sample Practice Questions - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.