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The Ultimate CLT Math Formula Cheat Sheet.



Preparing for the Classical Learning Test (CLT)?


One of the biggest questions students have is: What formulas do I need to know for the exam?


The good news is that the CLT provides you with a formula sheet during the Quantitative Reasoning section, so you won’t be expected to memorize every conversion and equation. But—there’s a catch. The official formula sheet is pretty limited. To maximize your score, you’ll want to go in with a broader set of formulas in your toolkit.


That’s where this CLT Math Formula Cheat Sheet comes in. Below, we’ve pulled together both:

The official formulas you’ll see on test day


The extra formulas that aren’t given to you but are very likely to show up in questions.


The Exact CLT Math Formula Sheet—Explained


If your student is preparing for the Classical Learning Test (CLT), good news: the Quantitative Reasoning section includes a formula sheet. Below is precisely what appears on that sheet.


Geometry

  • Area of a circle: A = πr² (r = radius)

  • Circumference of a circle: C = 2πr

  • Degrees in a circle: 360°

  • Radians in a circle: 2π

  • Volume of a sphere: V = (4/3)πr³

  • Surface area of a sphere: S = 4πr²

  • Area of a rectangle: A = length × width

  • Area of a triangle: A = ½(base × height)

  • Sum of interior angles in a triangle: 180°

  • Pythagorean Theorem: a² + b² = c² (for right triangles)


Trigonometry

  • sin θ = opposite ÷ hypotenuse

  • cos θ = adjacent ÷ hypotenuse

  • tan θ = opposite ÷ adjacent

  • csc θ = 1 ÷ sin θ

  • sec θ = 1 ÷ cos θ

  • cot θ = 1 ÷ tan θ

  • Identity: sin²θ + cos²θ = 1

  • Identity: tan θ = sin θ ÷ cos θ


Special Right Triangles

  • 30°–60°–90° Triangle: side ratio = 1 : √3 : 2

  • 45°–45°–90° Triangle: side ratio = 1 : 1 : √2


Test-Day Tips

  • The CLT provides these formulas so you don’t need to memorize every one, but practice using them until they feel automatic.

  • For trigonometry, always label the triangle’s sides (opposite, adjacent, hypotenuse) before plugging into formulas.

  • For geometry word problems, draw the figure, then substitute values into the formulas last to reduce mistakes.



Final Thoughts

This formula sheet is a valuable tool—but the real key is knowing when to use each formula. Practice applying them to different problem types so they become second nature by test day.


At Niceville Tutoring, we help students master not just formulas but also the strategies that make math less intimidating.



 
 
 

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