Like any other first introduction, this can be awkward, but we’re here to help break the ice. In this post, we’re going to cover what formulas are on the SAT Reference Sheet and how they can be used to solve problems on the test. There are a few other formulas that you should <\/em>memorize, but don’t panic, we’ll cover those in this article as well.<\/p>\n\n\n\n The math section of the SAT makes up half of your total SAT score. Math is split into two sections. One section allows you to use a calculator, but another section prohibits calculator use. You’ll have a raw score from each section, and these two raw scores will be combined and converted into a number on a scale between 200 and 800. <\/p>\n\n\n\n There are 58 math questions in total – 38 on the calculator-optional section, and 20 on the no-calculator section. Most of these questions are multiple-choice; however, there will be 13 “grid-in” questions. On grid-in questions, you’ll be asked to provide your own numeric answer rather than selecting from a list of possible choices. <\/p>\n\n\n\n Questions come from one of these four categories:<\/p>\n\n\n\n Most of the formulas on the SAT reference sheet have to do with geometry, so they may be most helpful on the “Additional Topics in Math” section. However, there may be times when it’s helpful to use the reference sheet on other types of questions as well. <\/p>\n\n\n\n There are eight formulas and five rules or laws on the SAT reference sheet. We’ll cover each one in detail below. <\/p>\n\n\n\n What’s the formula? <\/em>A=\u03c0r2<\/sup><\/p>\n\n\n\n What do the variables represent?<\/em> A <\/em>represents the area of a circle. r <\/em>represents the radius of a circle, or the distance of a straight line between the center and the edge of a circle.<\/p>\n\n\n\n How can I use it?<\/em> You can use this formula to solve for the area of a circle if given the radius or diameter (divide the diameter by two to find the radius), or to determine the radius of a circle when given the area. For example, let’s say you know the radius of a circle is three centimeters. To solve for area, you can plug it into the formula A=\u03c0(3)2<\/sup>. When solved, you will discover that the area is 28.27 cm2<\/sup>. <\/p>\n\n\n\n *NOTE: We won’t say this for each formula or example in this post, but you should know that the SAT often leaves \u03c0 in its answer choices. So, the answer here could be 9\u03c0 cm2<\/sup> rather than 28.27 cm2<\/sup>.<\/em><\/p>\n\n\n\n What’s the formula? <\/em>C=2\u03c0r <\/p>\n\n\n\n What do the variables represent?<\/em> C represents the circumference of a circle. r <\/em>represents the radius of a circle, or the distance of a straight line between the center and the edge of a circle. This equation can also be written as C=\u03c0d, where d <\/em>represents the diameter of the circle.<\/p>\n\n\n\n How can I use it?<\/em><\/em> If the test asks you to determine the radius of a circle with a circumference of 27 centimeters. You can plug 27 into the formula for circumference (27=2\u03c0r) and solve for r. <\/em>You’ll come up with an answer of 4.3 centimeters for the radius. Or, say you are asked to determine the circumference of a circle with a radius that is 4 cm long. You can plug 4 into this equation (C=2\u03c0(4)) to determine that the circumference is 8\u03c0 cm. <\/p>\n\n\n\n What’s the formula? <\/em>A=lw<\/p>\n\n\n\n What do the variables represent?<\/em> A <\/em>is the area of a rectangle. l <\/em>is the length, and w <\/em>is the width. If you’re working with a square, the equation can also be written as A=s2<\/sup>, where A <\/em>represents area and s <\/em>represents the length of one side.<\/p>\n\n\n\n How can I use it?<\/em> <\/em> If you have two out of the three variables available, you can solve for the missing variable. For example, if you know that the area A <\/em>of a rectangle is 36 cm, and the length l<\/em> of one side is 9 cm, you can plug these numbers into the equation 36=9<\/em>w to determine that the width equals 4 cm.<\/p>\n\n\n\n What’s the formula? <\/em>A=1<\/sup>\/2<\/sub><\/sup>bh <\/p>\n\n\n\n What do the variables represent?<\/em> A <\/em>represents the area of a triangle. b <\/em>represents the length of the base of the triangle, and h <\/em>represents the height of the triangle from the base up to the highest point.<\/p>\n\n\n\n How can I use it?<\/em> <\/em> As with the area of a rectangle, if you’re only missing one variable, it’s easy to plug in the numbers you know to solve for whatever’s missing. If a triangle has a base of 8cm and a height of 6 cm, you can plug the variables into the equation A=1<\/sup>\/2<\/sub><\/sup>(6)(8) to learn that A=24cm. <\/p>\n\n\n\n What’s the formula? <\/em>a2<\/sup>+b2<\/sup>=c2<\/sup><\/p>\n\n\n\n What do the variables represent?<\/em> In a right triangle, c <\/em>represents the length of the hypotenuse, which is the longest side of the triangle. Then a <\/em>and b <\/em>each represent one of the shorter legs of the triangle. It doesn’t matter which leg is a <\/em>and which is b<\/em>, as long as the hypotenuse is c.<\/em><\/p>\n\n\n\n How can I use it?<\/em> <\/em>Suppose you have a right triangle. One side is 4 cm long, and one is six cm long. Using the Pythagorean Theorem, you plug the numbers into the equation (42<\/sup>+62<\/sup>=c2<\/sup>) to determine that c<\/em>=7.21 cm.<\/p>\n\n\n\n What’s the formula? <\/em> This isn’t a special formula. Rather, these are special rules for 30\/60\/90 or 45\/45\/90 right triangles.<\/p>\n\n\n\n What do the variables represent?<\/em> You’ll want to look at the SAT Formulas Sheet for proper context, but in a 30\/60\/90 triangle, x <\/em>represents the length of the shortest side. In a 45\/45\/90 triangle, s represents the length of either one of the shorter legs.<\/p>\n\n\n\n How can I use it?<\/em> <\/em>The benefit of these rules is that if you have a 30\/60\/90 or 45\/45\/90 triangle, you only need to know the length of one side to solve for the other two. For example, if you have a 30\/60\/90 triangle, and you know the hypotenuse is 12 millimeters long, you can also determine that the shortest leg is 6 mm, and the longer leg is 10.39 mm.<\/p>\n\n\n\n What’s the formula? <\/em>V=lwh<\/p>\n\n\n\n What do the variables represent?<\/em> V <\/em>represents volume, l <\/em>represents length, w <\/em>represents width, and h <\/em>represents height.<\/p>\n\n\n\n How can I use it?<\/em> <\/em>For this formula, and for each of the volume formulas on the SAT reference sheet, you’ll take the variables provided and plug them into the equation to solve for the missing variable. For example, if you have a rectangle with a volume of 60 cm3<\/sup>, and you know that the length equals 4cm and the width equals 3cm, you can plug each number into the equation 60=(4)(3)h to determine that h=5. <\/p>\n\n\n\n What’s the formula? <\/em>V=\u03c0r2<\/sup>h<\/p>\n\n\n\n What do the variables represent?<\/em> V represents volume, r <\/em>represents the radius of the circular side, and h <\/em>represents the height from the bottom circular side to the top circular side.<\/p>\n\n\n\n How can I use it?<\/em> <\/em>Like the formula just above, all you need to do is plug each variable provided into the equation and solve for the missing variable. <\/p>\n\n\n\n What’s the formula? <\/em>V=4<\/sup>\/3<\/sub>\u03c0r3<\/sup> <\/p>\n\n\n\n What do the variables represent?<\/em> V<\/em> represents volume <\/em>and r <\/em>represents the radius from any point on the surface of the sphere to the middle.<\/p>\n\n\n\n How can I use it?<\/em> <\/em>Once again, we have a volume formula that can be used to find – you guessed it – volume. But only if it’s just one variable that you need. <\/p>\n\n\n\n What’s the formula? <\/em>V=1<\/sup>\/3<\/sub>\u03c0r2<\/sup>h<\/p>\n\n\n\n What do the variables represent?<\/em> V <\/em>represents volume (shocker), r <\/em>represents the radius of the circular side, and h <\/em>represents the height from the circular side to the point of the cone. <\/p>\n\n\n\n How can I use it?<\/em> <\/em>This formula won’t help you find the volume of a sphere or a pyramid, but if it’s the volume of a cone you need….prepare to be amazed.<\/p>\n\n\n\n What’s the formula? <\/em>V=1<\/sup>\/3<\/sub>lwh<\/p>\n\n\n\n What do the variables represent?<\/em> V <\/em>represents volume, l <\/em>represents length, w <\/em>represents width, and h <\/em>represents height.<\/p>\n\n\n\n How can I use it?<\/em> <\/em>If you need to know the volume of the space where King Tut is buried, or perhaps the volume of the Memphis Bass Pro Shop, this formula will come in handy.<\/p>\n\n\n\n What does this mean?<\/em> Any time you have multiple sectors in a circle, the angles represented by each sector will always add up to 360. <\/p>\n\n\n\n How is this helpful?<\/em> Let’s say you have a circle divided into three sectors. The angle of one sector is 136\u00b0 and the angle of another is 85\u00b0. You’re asked to solve for x, <\/em>which represents the angle of the missing sector. You can simply subtract 136 and 85 from 360 to determine that the third angle is 139\u00b0. <\/p>\n\n\n\n What does this mean?<\/em> A radian is an arc with a length equal to the length of the radius of the circle. Every circle has exactly 2\u03c0 radians.<\/p>\n\n\n\n![\"\"](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2022\/03\/sat-reference-sheet-1.png\")
About SAT Math<\/h2>\n\n\n\n
![\"\"](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2022\/03\/sat-reference-sheet-2-1024x593.png\")
<\/figure>\n\n\n\nWhat formulas are on the SAT reference sheet?<\/h2>\n\n\n\n
Area of a Circle<\/h4>\n\n\n\n
Circumference of a Circle<\/h4>\n\n\n\n
Area of a Rectangle <\/h4>\n\n\n\n
Area of a Triangle<\/h4>\n\n\n\n
The Pythagorean Theorem<\/h4>\n\n\n\n
![\"Sheldon](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2022\/03\/sat-reference-sheet-3-1024x568.png\")
Properties of Special Right Triangles<\/h4>\n\n\n\n
Volume of a Rectangular Solid<\/h4>\n\n\n\n
Volume of a Cylinder<\/h4>\n\n\n\n
Volume of a Sphere<\/h4>\n\n\n\n
Volume of a Cone<\/h4>\n\n\n\n
Volume of a Pyramid<\/h4>\n\n\n\n
![\"\"](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2022\/03\/sat-reference-sheet-4-1024x441.png\")
Laws Provided on the SAT Reference Sheet<\/h4>\n\n\n\n
“The number of degrees of arc in a circle is 360.”<\/h6>\n\n\n\n
“The number of radians of arc in a circle is 2\u03c0.”<\/h6>\n\n\n\n
![\"\"](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2022\/03\/sat-reference-sheet-5-6-1024x643.png\")
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