Table of Contents

**Critical SAT Math Formulas**

#### The SAT math test is unlike any math test you’ve taken before. It’s designed to take concepts you’re used to and make you apply them in new (and often strange) ways. It’s tricky, but with attention to detail and knowledge of the basic formulas and concepts covered by the test, you can improve your score.

**So what formulas do you need to have memorized for the SAT math section before the day of the test?** In this complete guide, I’ll cover every critical formula you MUST know before you sit down for the test. I’ll also explain them in case you need to jog your memory about how a formula works. If you understand every formula in this list, you’ll save yourself valuable time on the test and probably get a few extra questions correct.

**Formulas Given on the SAT, Explained**

*This is exactly what you’ll see at the beginning of both math sections (the calculator and no calculator section). It can be easy to look right past it, so familiarize yourself with the formulas now to avoid wasting time on test day.*

#### You are given 12 formulas on the test itself and three geometry laws. It can be helpful and save you time and effort to memorize the given formulas, but **it is ultimately unnecessary,** as they are given on every SAT math section.

**You are only given geometry formulas, so prioritize memorizing your algebra and trigonometry formulas before the test day (we’ll cover these in the next section). **You should focus most of your study effort on algebra anyways because geometry has been de-emphasized on the new SAT and now makes up just 10% (or less) of the questions on each test.

#### Nonetheless, you do need to know what the given geometry formulas mean. The explanations of those formulas are as follows:

**Area of a Circle**

**A=πr**^{2}

^{2}

#### > π is a constant that can, for the purposes of the SAT, be written as 3.14 (or 3.14159)

*> r* is the radius of the circle (any line drawn from the center point straight to the edge of the circle)

**Circumference of a Circle**

**C=2πr (or C=πd)**

**>** d is the diameter of the circle. It is a line that bisects the circle through the midpoint and touches two ends of the circle on opposite sides. It is twice the radius.

**Area of a Rectangle**

*A=lw*

*A=lw*

#### > l is the length of the rectangle

#### > w is the width of the rectangle

**Area of a Triangle**

**>** b is the length of the base of the triangle (the edge of one side)

**>** h is the height of the triangle

**i.** In a right triangle, the height is the same as a side of the 90-degree angle. For non-right triangles, the height will drop down through the interior of the triangle, as shown above.

**The Pythagorean Theorem**

**a**^{2}+b^{2}+c^{2}

^{2}+b

^{2}+c

^{2}

**>** In a right triangle, the two smaller sides (*a* and *b*) are each square. Their sum is equal to the square of the hypotenuse (c, the longest side of the triangle).

**Properties of Special Right Triangle: Isosceles Triangle**

#### > An isosceles triangle has two sides that are equal in length and two equal angles opposite those sides.

#### > An isosceles right triangle always has a 90-degree angle and two 45 degree angles.

#### > The side lengths are determined by the formula: x, x, x√2, with the hypotenuse (the side opposite 90 degrees) having a length of one of the smaller sides *√2.

#### i. E.g., An isosceles right triangle may have side lengths of 12, 12, and 12√2.

**Properties of Special Right Triangle: 30, 60, 90 Degree Triangle**

#### > A 30, 60, 90 triangle describes the degree measures of the triangle’s three angles.

#### > The side lengths are determined by the formula: x, x√3, and 2x

#### i. The side opposite 30 degrees is the smallest, with a measurement of x.

#### ii. The side opposite 60 degrees is the middle length, with a measurement of x√3.

#### iii. The side opposite 90 degree is the hypotenuse (longest side), with a length of 2x.

#### iv. For example, a 30-60-90 triangle may have side lengths of 5, 5√3, and 10.

**Volume of a Rectangular Solid**

*V=lwh*

*V=lwh*

**>** l is the length of one of the sides.

**>** h is the height of the figure.

**>** w is the width of one of the sides.

**Volume of a Cylinder**

**V=πr**^{2}h

^{2}h

**>** r is the radius of the circular side of the cylinder.

**>** h is the height of the cylinder.

**Volume of a Sphere**

**>** r is the radius of the sphere.