📢 GET - 'Critical Thinking & Problem Solving (Business & Finance) ' 😍 #KindleBargain 𝘍𝘰𝘳 𝘢 𝘓𝘪𝘮𝘪𝘵𝘦𝘥 𝘛𝘪𝘮𝘦! ⭐ HERE: https://www.bookzio.com/critical-thinking-problem-solving/ 👈👈👈 🔥 #mustread ⭐ #bookholic ⭐ #readingisfun ⭐ #megabookdeals ⭐ #ebookdeals ⭐

This game is a fun and updated version of connect-the-dots, except that there are many different kinds of dots, and they each have rules about how they can connect. Some have maximum or minimum distances they can connect to/from, and others can only attach from specific directions or a specific numb...

Engaging critical thinking and problem-solving ESL activities, games and worksheets to help your students learn to think independently and make sound decisions.

The Ultimate Guide to Better Thinking, Systematic Problem Solving and Making Impeccable Decisions with Secret Tips to Detect Logical Fallacies

Find the exact real root for the equation $10x^3-12x^2-6x-1=0$. The given cubic cannot be factored easily and beautifully, so the method o...

Prove $\sqrt{2}+\sqrt{3}\gt \pi$. Note that we could use the previously established result from the famous people or even our own finding ...

Solve the equation $x+a^3=\sqrt[3]{a-x}$ where $a$ is real. If one wants to do things in haste and quickly solve the above equation for $x...

For $a\gt b\gt 0$, prove that $\dfrac{a+b}{2}\gt \dfrac{a-b}{\ln a-\ln b}$. There sure is many way to prove this problem, but I am going t...

Prove $\dfrac{22}{7}\gt \pi$. There is a very classic and elegant proof for this inequality involving $\pi$ and its fraction representativ...

Evaluate $\displaystyle\int^{\dfrac{\pi}{4}}_0 \dfrac{x}{(\sin x+\cos x)\cos x}\ dx$. Solving for this problem is a breeze if you're someo...

Solve the system $\dfrac{1}{x}+\dfrac{1}{y+z}=\dfrac{1}{2}$ $\dfrac{1}{y}+\dfrac{1}{x+z}=\dfrac{1}{3}$ $\dfrac{1}{z}+\dfrac{1}{x+y}=\d...

Solve for all 6 complex roots of the equation $x^6+10x^5+70x^4+288x^3+880x^2+1600x+1792=0$. My solution:

Mastering Olympiad Mathematics: Real World Application of Mathematics

Solve the system $\dfrac{1}{x}+\dfrac{1}{y+z}=\dfrac{1}{2}$ $\dfrac{1}{y}+\dfrac{1}{x+z}=\dfrac{1}{3}$ $\dfrac{1}{z}+\dfrac{1}{x+y}=\d...

Express $\dfrac{\cos 1^{\circ}+\cos 2^{\circ}+\cdots+\cos 44^{\circ}}{\sin 1^{\circ}+\sin 2^{\circ}+\cdots+\sin 44^{\circ}}$ in the form $a+...

Show that [MATH]16 < \sum_{k=1}^{80}\dfrac{1}{\sqrt{k}}< 17[/MATH]. It goes without saying that there's more than one way to skin any give...

Find the total number of positive integers ordered pairs of the equation $3^a+3^b+3^c = 7299$. WLOG, let $c>b>a$. Rewrite the RHS of the...

If you're given the two graphs that are plotted in the same Cartesian plane below, what do you notice?

Find [MATH]\sum_{x=0}^{101}\frac{\frac{2x}{101}-1}{\frac{3x^2}{10201}-\frac{3x}{101}+1}[/MATH]. At first glance, this looks like a very ...

Prove $\dfrac{\pi}{4}+\dfrac{1}{6}\gt \arctan\left({\dfrac{6}{5}}\right)$. Do you know if we're pretty familiar with how the graph of a pa...