TSI Math FREE Sample Practice Questions

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

$16.99

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 \(log_2⁡x = 5\), 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 TSI Math Prep Resource for 2022

$29.99

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:
\(log_a⁡b-log_a⁡c=log_a\frac{b}{c}⁡\space and \space log_a⁡b=c⇒b=a^c\)
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\( \space f(x) = g(x)\), 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
\(log_2⁡x = 5\)
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: \(x = ln (2y + 1)\)
\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\)

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

The Best Books to Ace the TSI Math Test

$14.99

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

$15.99
$13.99
$14.99

Have any questions about the TSI Test?

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

Related to "TSI Math FREE Sample Practice Questions"

Top 10 Free Websites for TSI Math Preparation
TSI Math-Test Day Tips
Top 10 Tips You MUST Know to Retake the TSI Math
Top 10 Tips to Create a TSI Math Study Plan
Top 10 Tips to Overcome TSI Math Anxiety
What does TSI Test Stand for?
Overview of the TSI Mathematics Test
What Kind of Math Is on the TSI Test?
Top 10 TSI Math Prep Books (Our 2022 Favorite Picks)
Top 10 TSI Math Test-taking Tips

What people say about "TSI Math FREE Sample Practice Questions"?

No one replied yet.

Leave a Reply