Math Formula Sheet

The CLT gives you a short formula sheet for the Quantitative Reasoning section, and it does not allow a calculator. So the formulas it gives are only part of what you need: everything else has to be in your head on test day. This page sets up the math chapters that follow with that split in mind.

What the CLT gives you on test day

The CLT’s own formula sheet, which you can consult throughout the Quantitative Reasoning section, lists:

• Area of a circle: $\pi r^2$; circumference of a circle: $2\pi r$
• There are $360°$, or $2\pi$ radians, in a circle
• Volume of a sphere: $\frac{4}{3}\pi r^3$; surface area of a sphere: $4\pi r^2$
• Area of a rectangle: length × width
• Area of a triangle: $\frac{1}{2}$(base × height); the interior angles of a triangle sum to $180°$
• The Pythagorean theorem: $a^2+b^2=c^2$, where $c$ is the hypotenuse
• The trigonometric ratios: $\sin \theta =\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos \theta =\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan \theta =\frac{\text{opposite}}{\text{adjacent}}$
• Their reciprocals: $\csc \theta =\frac{1}{\sin \theta }$, $\sec \theta =\frac{1}{\cos \theta }$, $\cot \theta =\frac{1}{\tan \theta }$
• Two identities: $\tan \theta =\frac{\sin \theta }{\cos \theta }$ and ${\sin }^2\theta +{\cos }^2\theta =1$
• The special right triangles: a $30°$-$60°$-$90°$ triangle has sides in the ratio $1:\sqrt{3}:2$, and a $45°$-$45°$-$90°$ triangle has sides in the ratio $1:1:\sqrt{2}$

Know even these by heart: looking one up costs time you won’t have to spare.

What you need to memorize

With no calculator, everything not on that list is yours to bring: the slope and line formulas, the quadratic formula, the exponent rules, the percent and average formulas, and the geometry the CLT leaves off its sheet, such as the equation of a circle, arc length, and the volume of a cylinder or a cone. Arithmetic has to be quick, too: know your times tables to $15\times 15$ and the perfect squares to $20^2$.

You don’t need to learn these from a list. Each chapter ahead teaches its formulas where they come up, and the geometry and trigonometry lessons say which ones the CLT provides and which it doesn’t.

The dump sheets

When you want them all in one place, the CLT dump sheets on this course’s Resources page pull them together: one sheet each for math reasoning, geometry, and trigonometry, and two for algebra. Each one marks what the CLT gives you on test day and what you must memorize. There are sheets for the test itself, Verbal Reasoning, and Grammar/Writing as well.

If flashcards help you, make them for the formulas that don’t stick; your review quizzes already bring back what you’re due to practice.