30 Important SAT Formula Sheet 2023
Have you ever been stumped by a math test question only to realize how simple it was after reviewing your test? That is exactly what many students who take the SAT without SAT Formula sheet 2023 experience. The SAT covers a wide range of math topics, beginning in elementary school and continuing through the senior year of high school. While you have probably learned these formulas at some point, you may have not used them in a while. This is part of what makes the SAT difficult: because it draws on so many different types of math.
You must break out of the high school math mindset (where you only remember what you have learned in the last month or so to ace the test) and go over the math you have learned over the years. If you don’t study for the SAT, it will take you longer to remember certain useful formulas and concepts. While there is always more than one way to arrive at the correct answer, being able to recall these math facts quickly will allow you to answer questions more efficiently and avoid careless mistakes.
We have organized these formulas into categories to help you focus on your preparation, and we have provided a quick overview of each concept. Do you want to know your chances of admission to the schools you’re applying to based on your SAT score? The SAT math exam is unlike any other math exam you have ever taken. It’s intended to take familiar concepts and force you to apply them in novel (and often bizarre) ways. It’s difficult, but you can improve your score by paying attention to detail and understanding the basic formulas and concepts covered by the test.
So, what formulas do you need to memorize for the SAT math section before the exam? On the test, you are given 12 formulas and three geometry laws. Memorizing the given formulas can help you save time and effort, but it is ultimately unnecessary because they are provided in every SAT math section. Because you are only given geometry formulas, memorize your algebra and trigonometry formulas before test day (we will cover these in the next section). In any case, you should focus your study efforts on algebra because geometry has been de-emphasized on the new SAT, accounting for only 10% (or less) of the questions on each test.
You must, however, understand what the given geometry formulas mean. In this comprehensive guide, I will go over every critical formula you MUST know before taking the test. I will also explain to them in case you need a refresher on how a formula works. You will save time on the test and most likely answer a few more questions correctly if you know every formula on this list.
A) Algebra and Arithmetic
1. Slope-Intercept Form of a Line
The represents the slope of the equation, and the represents the y-value of the y-intercept in the equation. For instance, if we have the equation y=2x+4, the slope is 2 and the y-intercept is (0,4). This is one of the most important SAT formulas to know and should be included in your SAT math cheat sheet.
2. Vertex Form of a Parabola/Quadratic
y= a(x-h)² +k
You may be more familiar with quadratics in their factored form or the form y=ax²+bx+c. You should be able to recognize vertex form and convert quadratics to it for the SAT. The values of h and k give you the vertex coordinates (h,k). This is one of the most important math formulas for SAT and should be included in your SAT cheat sheet.
3. Distance Formula
d=√[(x₂ – x₁)² + (y₂ – y₁)²]
The distance formula is derived from the Pythagorean Theorem (covered later in this post), and it is useful for calculating the distance between two points quickly. Plug the coordinate values into this formula to find the distance, making sure to use squares and square roots at the appropriate steps. This is one of the formulas to know for SAT and should be included in your SAT formula sheet 2022.
4. Quadratic Equation
x = (-b ± √(b2 − 4ac))/(2a)
If you can’t easily factor a quadratic equation (parabola), the quadratic formula can help you find its roots. The quadratic must be in the form y= ax²+ bx +c, the coefficients and constants are then simply entered into the formula. Because there are plus and minus signs in the numerator, you will get two answers. This is one of the useful SAT math formulas and equation to remember for SAT.
5. Exponent Rule (Multiplication)
am × an = am+n
Knowing how to manipulate exponents in a variety of ways will greatly benefit you on the SAT, particularly the no-calculator section. In this case, if the same base number is raised to different powers and multiplied together, the exponents can be added together. This is one of the useful SAT math formulas and equations to remember for SAT.
6. Exponent Rule (Division)
am ÷ an = am-n
Similar to the multiplication rule, if the same base number raised to different powers is being divided, the exponents can be subtracted. You can also rewrite the expression on the right so that it matches the one on the left. This is one of the formulas to know for SAT and should be included in your SAT formula sheet 2022.
7. Exponent Rule (Power Raised to a Power)
(am)n = am*n
Continuing with the exponent rules, raising a power to another power is equivalent to multiplying the exponents together. This is not an exhaustive list of ways to manipulate exponents, so if you find yourself forgetting any of them, brush up! This is one of the most important math formulas for SAT and should be included in your SAT cheat sheet.
8. Binomial Product 1—Square Difference
(x-y)(x+y) = x²- y²
The no-calculator section is the best place to recognize the binomial products and quickly factor them in. You don’t need to FOIL or use any other method; you can convert from the factor to the expanded form on the fly. The difference of squares is frequently used by SAT developers in a variety of contexts. This is one of the most important SAT formulas to know and should be included in your SAT math cheat sheet.
9. Binomial Product 2—Trinomial of Perfect Squares (Positive)
(x+y)² = x²+ 2xy +y²
Students sometimes forget about the perfect squares trinomial after they leave algebra class, but it is also important to remember. It saves time because it allows you to quickly convert from one form to another, but it is a little more difficult to catch than the expanded difference of squares. Looking at the first and last values is a good way to tell if you’re dealing with one —are they the perfect squares?. This is one of the useful SAT math formulas and equations to remember for SAT.
10. Binomial Product 2—Perfect Squares Trinomial (Negative)
(x-y)² = x²- 2xy +y²
This trinomial is similar to the previous one, except that the quantity involves subtraction rather than addition. While the factored form lacks coefficients, the binomial products on the SAT frequently do. Practice recognizing these patterns by entering coefficients in front of and constants for on the left-hand side of the equation. Then multiply the expression to see how the pattern behaves with various combinations. With an SAT calculator, you can see how your SAT math score affects your chances of admission. This is one of the formulas to know for SAT and should be included in your SAT formula sheet 20223
11. Complex Conjugate
(a+bi) (a-bi) = a² +b²
Most SAT math tests will include at least one question involving the manipulation of imaginary numbers. The complex conjugate removes the imaginary part of a complex number, leaving you with a real number (notice how it resembles the difference of squares!). When given a complex number in the form a+bi, the conjugate is a-bi. This is one of the most important math formulas for SAT and should be included in your SAT cheat sheet.
12. Exponential Growth and Decay
y = a(1 ± r)x
This is technically two different equations, one with a plus and one with a minus in it. Knowing the general format of exponential equations will help you with a variety of SAT questions in which you may need to interpret or manipulate these equations. The value is the starting point, the rate of growth when positive, and the rate of decay when negative. This is one of the most important SAT formulas to know and should be included in your SAT math cheat sheet.
B) Statistics, Ratios, and Percentages
13. Simple interest
This one appears less frequently than compound interest on the SAT, but it is still useful to know. represents the principal amount, the interest rate expressed as a decimal, and the time, which is usually expressed in years. This is one of the formulas to know for SAT and should be included in your SAT formula sheet 2022.
14. Compound interest
A = P(1 + r/n)nt
The good news is that P, r and t have the same meaning in this equation as they do in simple interest. The n represents the number of times the interest is compounded during 1t. For instance, if interest is compounded quarterly over a year, then n =4.
This is one of the useful SAT math formulas and equation to remember for SAT.
Mean = Sum of the terms/Number of different terms
In mathematics, the terms average and mean refer to the same thing: the number obtained by dividing the sum of a set by the number of values in the set. It’s also possible to think of it as the sum divided by the count. You should be able to calculate and interpret averages. Make sure you understand the distinction between mean and median. This is one of the formulas to know for SAT and should be included in your SAT formula sheet for 2023.
16. Random Sampling
Although this isn’t a formula, many of the SAT statistics-based problems emphasize interpreting concepts in context rather than performing mathematical operations. Random sampling is the process of selecting participants for a study at random from a population. This ensures that your research is representative of the general population. This is one of the most important SAT formulas to know and should be included in your SAT math cheat sheet.
17. Random Assignment
When participants in a study are randomly assigned to a treatment or trial, this is known as random assignment. It reduces bias in your study and allows you to attribute causation to the treatment. On the SAT, you will frequently be asked what will reduce bias or how much you can generalize results to the rest of the population. In these cases, you must distinguish between random sampling and random assignment. This is one of the formulas to know for SAT and should be included in your SAT formula sheet for 2023.
18. Standard Deviation
The SAT does not require you to calculate standard deviation, but you will be tested on it conceptually, as with random sampling and random assignments. The standard deviation is a measure of the spread of the data set. A higher standard deviation indicates a wider spread, while a lower standard deviation indicates a narrower spread. You will need to understand how changes in the data set can cause the standard deviation to increase or decrease. This is one of the formulas to know for SAT and should be included in your SAT formula sheet for 2023.
C) Trigonometry and Geometry
19. Area of an Equilateral Triangle
x= [−b±√(b2−4ac)] / 2a
The regular area of a triangle formula is included on the SAT reference sheet, but you must also know the height of a triangle. You may not always be given the height and must calculate it, but you can quickly find the area of an equilateral triangle by plugging the length of one of its sides into the formula above. There is no need to calculate the height! This is one of the formulas to know for SAT and should be included in your SAT formula sheet 2022.
20. Equation of a Circle
(x-h)² + (y-k)² = r²
Typically, there is only one question involving the equation of a circle. In this equation, and are the coordinates for the circle’s centre and radius, respectively. This is one of the most important math formulas for SAT and should be included in your SAT cheat sheet.
21. Sine Ratio
Some students are concerned when they learn that trig will be on the SAT, but it is usually in the form of trig ratios. Remember that the value of sine for a given angle in a right triangle is the length of the opposite side divided by the length of the hypotenuse or opposite/hypotenuse. This is one of the most important math formulas for SAT and should be included in your SAT cheat sheet.
22. Cosine Ratio
Remember what the cosine ratio is, just like the sine ratio: the length of the adjacent side divided by the length of the hypotenuse, or adjacent/hypotenuse. This is one of the most important SAT formulas to know and should be included in your SAT math cheat sheet.
23. Tangent Ratio
Finally, the tangent ratio is the length of the opposite side divided by the length of the adjacent side, also known as opposite/adjacent. To remember trig ratios, some students use the mnemonic SOH CAH TOA. This is one of the useful SAT math formulas and equations to remember for SAT.
24. Degrees to Radians
While basic ratios are the most common type of trig, you may come across the unit circle or more advanced math. When converting degrees to radians, multiply the degrees by π/180. If you need to convert radians to degrees, multiply the radians by 180/π. This is one of the useful SAT math formulas and equations to remember for SAT.
25. Pythagorean Theorem
a² +b² =c²
The Pythagorean Theorem, which applies to right triangles, allows you to solve for one of the side lengths given any other side length. and are the triangle’s legs, and is the hypotenuse. This is one of the most important SAT formulas to know and should be included in your SAT math cheat sheet.
26. Regular Polygon Interior Angle
(n − 2) × 180/n
The SAT will most likely include one question involving a regular polygon that isn’t a triangle or square. Regular polygons have distinct and consistent properties based on the number of sides, and understanding these properties can assist you in solving these problems. Based on the number of sides, this equation tells you what the degree measure is at each angle. This is one of the most important math formulas for SAT and should be included in your SAT cheat sheet.
27. 3-4-5 triangle
The SAT includes two special right triangles that you may have seen on your reference sheet: the 30-60-90 and 45-45-90 triangles. The 3-4-5, on the other hand, is a special right triangle with sides that are simple integers. This triangle is frequently used in SAT problems, particularly in the no-calculator section, so keep an eye out for it! It can help you avoid using the Pythagorean theorem. This is one of the useful SAT math formulas and equations to remember for SAT.
28. 5-12-13 triangle
The 5-12-13 triangle, another special right triangle with whole-number sides, is less well-known and appears less frequently than the 3-4-5 triangle. Still, knowing how to quickly solve the remaining sides without using the Pythagorean theorem is useful, so look for these numbers or their multiples in triangle problems. This is one of the most important math formulas for SAT and should be included in your SAT cheat sheet.
29. Length of Arc in a Circle
Length of an Arc = θ × (π/180) × r, where θ is in degree
Although geometry questions do not account for a large portion of the SAT, you may encounter a question about arcs or sectors in a circle. An arc is a length between two points on a circle, which is usually measured by extending two radii from the circle’s centre and forming an angle between them. To find the length of an arc, use the degree measure as a fraction and multiply it by the circumference equation. This is one of the formulas to know for SAT and should be included in your SAT formula sheet 2022.
30. Area of Sector in a Circle
The sector, like an arc, is the area between two radii extending from the circle, similar to a slice of pie. To find the area of the sector, multiply the degree measure as a fraction and multiply it by the equation for the area of a circle. This is one of the formulas to know for SAT and should be included in your SAT formula sheet 2023.
Though this list includes all of the formulas you will need (both those you will be given and those you will need to memorize), it doesn’t cover every aspect of SAT Math. You will also need to know how to factor equations, manipulate and solve for absolute values, and manipulate and use exponents, among other things. All of these topics are covered in this section. Another thing to remember is that, while memorizing the formulas in this article that aren’t on the test is important.
Knowing this list of formulas doesn’t mean you’re ready for the SAT Math test. You should also practice using these formulas to answer questions so that you know when to use them. Before you leave, here’s a bonus tip: memorize the perfect squares and perfect cubes. This can help you with quadratic equations, which frequently involve squares, and cubes are frequently used in exponent problems. Memorizing these will reduce the need for you to do the math on scratch paper or with a calculator.
Practicing formulas is the best way to remember them. Unlike a high school math exam, where you know what topics will be covered, the SAT will simply ask you a question and leave it up to you to figure out which formulas apply. You will be able to quickly identify which formula to use if you practice using formulas with a variety of problems.
Frequently Asked Questions on SAT Exams 2023
Candidates are permitted to retake the SAT exam as many times as they wish. The SAT is administered five times per year (March, May, August, October, and December) However, it is also dependent on the program/college to which you are applying. If the college requires you to submit your highest SAT scores, you can take the test as many times as you want and send your highest scores to them; they will not accept any other SAT scores. If the college requires you to send all of your score reports, it is recommended that you do so no more than three times.
Candidates are graded in two sections: Evidence-Based Reading and Writing and Math. Each one is graded on a scale of 200 to 800. Both of these scores add up to the total SAT score. The total score can range between 400 and 1600. Furthermore, the optional Essay score is reported separately.
As a result, the College Board does not specify any prerequisites for taking the SAT 2023. Furthermore, there is no age limit set by the SAT administrative authority. Students in their junior or senior years of high school are most likely to take the exam. Students who want to enroll in undergraduate programs in the United States and other countries take the SAT exam. It can also be used to request financial assistance.
A significant difference between the two exams is that the ACT includes a whole section on Science that the SAT does not. Students with a science background can take the ACT to demonstrate their knowledge of science subjects. There is a significant structural difference between the two exams. For example, during the ACT exam, applicants may use a calculator, whereas, during the SAT exam, applicants are not permitted to use a calculator due to a brief ‘no calculator subsection.’
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