30 Important Sat Formula Sheets: Have you ever been stumped by a math question on an exam, only to discover upon study that it was a simple one? Many students who take the SAT without the SAT Formula sheet 2023 have exactly this experience.
Beginning in elementary school and extending through senior year of high school, the SAT assesses a wide range of arithmetic courses. Despite the fact that you have likely mastered these formulas in the past, you may not have used them in quite some time. This is one of the reasons why the SAT is so challenging: it incorporates so many distinct forms of mathematics.
You must abandon your high school math mentality (where you just remember what you’ve learnt in the last month or two in order to ace the test) and review the math you have learned over the years. Certain helpful calculations and concepts will be more difficult to recall if you do not study for the SAT.
The ability to retain these math facts will allow you to answer questions more swiftly and prevent casual errors, despite the fact that there are always multiple valid solutions.
To assist you in focusing on your preparation, we have categorized these formulas and offered a brief explanation of each idea. Do you want to discover, depending on your SAT score, how likely you are to gain admission to the institutions to which you have applied? The SAT math test is unlike any other test you’ve ever taken.
It is intended to take common principles and challenge you to apply them in fresh (and often weird) ways. It is challenging, but you can increase your score by paying close attention to detail and comprehending the fundamental principles and concepts covered on the examination.
So, what formulae must you learn for the SAT math part prior to the test? On the exam, you are provided with twelve formulas and three geometric laws. Memorizing the following formulas can save you time and effort, but it is ultimately useless because they are provided on every SAT math area.
Due to the fact that you are only provided with geometry formulae, you should memorize your algebra and trigonometry formulas prior to test day (we will cover these in the next section). In any event, you should focus your study efforts on algebra because geometry has been deemphasized on the new SAT, accounting for only 10 percent (or fewer) of problems on each test.
Nevertheless, you must comprehend the meaning of the geometry formulas provided. In this detailed tutorial, I will cover every formula that you MUST know before sitting the exam. If you need a refresher on how a formula works, I will also explain that to them. If you are familiar with each formula on this list, you will save time on the exam and perhaps answer a few more questions correctly.
List of the Important Sat Formula Sheets
The following is a list of the Important Sat Formula Sheets:
A) Algebra and Arithmetic
1. Line in slope-intercept form
The denotes the equation’s slope, whereas the represents the y-value of the y-intercept. In the equation y=2x+4, for instance, the slope is 2 and the y-intercept is 4. (0,4). This is one of the most Important Sat Formula Sheets and should be included on your SAT math cheat sheet.
2. Form of a Parabola/Quadratic Vertex
y= a(x-h)² +k
You may be better familiar with quadratics in their factored or y=ax2+bx+c forms. On the SAT, you must be able to recognize vertex form and convert quadratics to it. The values of h and k provide the coordinates of the vertex (h,k). This is one of the most Important Sat Formula Sheets and should be on your SAT cheat sheet.
3. Distance Formula
d=√[(x₂ – x₁)² + (y₂ – y₁)²]
The distance formula, which is derived from the Pythagorean Theorem (discussed later in this post), is useful for quickly computing the distance between two places. To calculate the distance, plug the coordinate values into this formula, being sure to utilize squares and square roots at the relevant points. This is a required SAT formula and should be included on your 2022 SAT formula sheet.
4. Quadratic Equation
x = (-b ± √(b2 − 4ac))/ (2a)
If you are unable to quickly factor a quadratic equation (parabola), you can use the quadratic formula to locate its roots. The quadratic must have the form y = ax2 + bx + c, and then the coefficients and constants are simply inserted into the formula. Because the numerator has both plus and negative signs, you will receive two answers. This is one of the most Important Sat Formula and equations to memorize.
5. Exponent Rule (Multiplication)
am × a = am+n
The ability to use exponents in a variety of ways will be of tremendous assistance on the SAT, especially on the segment that does not require a calculator. In this example, the exponents can be combined together if the same base number is raised to separate powers and multiplied together. This is one of the Important Sat Formula and equations you should remember.
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6. Exponent Rule (Division)
am ÷ a = am-n
Similar to the multiplication rule, exponents can be subtracted when the same base number raised to different powers is divided. Additionally, you can rewrite the expression on the right to match the one on the left. This is a required and Important Sat Formula and should be included on your 2022 SAT formula sheet.
7. Exponent Rule (Power Raised to a Power)
(am)n = am*n
In accordance with the principles for exponents, raising a power to a higher power is comparable to multiplying the exponents together. This list of techniques to modify exponents is not exhaustive, so if you find yourself forgetting any of them, review! This is one of the most significant SAT math formulae and should be on your SAT cheat sheet.
8. Binomial Product 1 – Difference Squared
(x-y)(x+y) = x²- y²
The no-calculator part is ideal for recognizing and quickly factoring in binomial products. You can convert from the factor to the expanded form without using FOIL or any other method. SAT developers typically employ the difference of squares in a variety of settings. This is one of the most essential SAT formulas and should be included on your SAT math cheat sheet.
9. Binomial Product 2 – Trinomial of Perfect Squares (Positive)
(x+y)² = x²+ 2xy +y²
After leaving algebra class, students sometimes forget about the perfect squares trinomial, although it is vital to remember. It saves time because you can quickly convert from one form to another, but it is a bit trickier to grasp than the enlarged difference of squares. Examining the first and last values is an useful approach to determine whether you are dealing with perfect squares. This is one of the SAT math formulae and equations you should remember.
10. Binomial Product 2 – Perfect Squares Trinomial (Negative)
(x-y)² = x²- 2xy +y²
This trinomial is similar to the preceding one, with the exception that the quantity involves subtraction as opposed to addition. In contrast to the factored version, binomial products on the SAT typically contain coefficients. By placing coefficients in front of and constants for on the left-hand side of the equation, you can practice detecting these patterns.
The equation is then multiplied to determine how the pattern reacts with various permutations. With a SAT calculator, you can determine how your SAT math score influences your admissions prospects. This is a required SAT formula that should be included on your Sat Formula Sheets 2023.
11. Complex Conjugate
(a+bi) (a-bi) = a² +b²
At least one question on the majority of SAT math exams will include the manipulation of imaginary numbers. The complex conjugate eliminates the imaginary portion of a complex number, leaving a real number (note how it mimics the difference of squares!). The conjugate of a complex number of the type a+bi is a-bi. This is one of the most significant SAT math formulae and should be on your Sat Formula Sheets.
12. Exponential Growth and Decay
y = a(1 ± r)x
This is technically two separate equations, one containing a plus sign and the other a negative sign. Knowing the overall style of exponential equations will aid you in answering a range of SAT questions requiring interpretation or manipulation of these equations.
The value is the beginning point, growth rate (when positive), and decay rate (when negative). This is one of the most essential SAT formulas and should be included on your Sat Formula Sheets.
B) Numbers, Ratios, and Proportions
13. Simple interest
This one comes less frequently on the SAT than compound interest, but it is still beneficial to know. indicates the principal amount, the decimal interest rate, and the time, which is often stated in years. This is a required SAT formula and should be included on your 2022 Sat Formula Sheets.
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14. Compound interest
A = P(1 + r/n)nt
The good news is that P, r, and t have the same meaning as in simple interest in this equation. The number of times interest is compounded during 1t is represented by n. For example, n = 4 if interest is compounded quarterly over a year.
This is one of the most important Sat Formula Sheets and equations to memorize.
Mean = Sum of the terms divided by the number of unique terms
In mathematics, average and mean refer to the same quantity: the result of dividing the sum of a set by the number of items in the set. It might alternatively be thought of as the sum divided by the count. You must have the ability to compute and comprehend averages. Make certain you grasp the difference between the mean and the median. This is one of the necessary Sat Formula Sheets and should be included on your 2023 SAT formula sheet.
16. Random Sampling
Although this is not a formula, a significant number of SAT statistics questions prioritize comprehending concepts in context over completing mathematical operations. Sampling at random is the technique of selecting study participants at random from a population.
This guarantees that your research is representative of the population as a whole. This is one of the most essential SAT formulas and should be included on your Sat Formula Sheets.
17. Random assignment
Random assignment is when participants in a study are randomly assigned to a therapy or trial. It decreases bias in your study and enables you to attribute treatment causation. On the SAT, you will frequently be asked how to reduce bias or how broadly you can generalize results.
In these situations, random sampling and random assignment must be distinguished. This is one of the necessary SAT formulae and should be included on your 2023 Sat Formula Sheets.
18. Standard Deviation
You are not required to calculate standard deviation on the SAT, but you will be assessed on it theoretically, along with random sampling and random assignments. The standard deviation measures the dispersion of a set of data.
A greater standard deviation suggests a wider range, whereas a smaller standard deviation indicates a narrower range. You must comprehend how alterations to the data set might increase or decrease the standard deviation. This is one of the necessary SAT formulae and should be included on your 2023 Sat Formula Sheets.
C) Trigonometric and Geometric Calculations
19. Area of an Equilateral Triangle
x= [−b±√(b2−4ac)] / 2a
On the SAT reference sheet is the formula for the regular area of a triangle, but you must also know the height of a triangle. You may not always be provided the height and must calculate it, but you may rapidly compute the area of an equilateral triangle by inserting one of its sides into the following formula. It is unnecessary to calculate the height! This is a required SAT formula and should be included on your 2023 Sat Formula Sheets.
20. Equation of a Circle
(x-h)² + (y-k) (y-k)
² = r²
Typically, there is a single question involving the circle equation. In this equation, and represent the center and radius of the circle, respectively. This is one of the most significant SAT math formulae and should be on your Sat Formula Sheets.
21. Sine Ratio
Some students are apprehensive when they find out that trigonometry will be on the SAT, however it is often presented as trig ratios. Remember that the value of sine for a given angle in a right triangle is the opposite side divided by the hypotenuse or opposite/hypotenuse. This is one of the most significant SAT math formulae and should be on your Sat Formula Sheets.
22. Cosine Ratio
Cosine ratio is the length of the adjacent side divided by the length of the hypotenuse, or adjacent/hypotenuse. This is one of the most essential SAT formulas and should be included on your SAT math cheat sheet.
23. Tangent Ratio
The tangent ratio, commonly known as opposite/adjacent, is the length of the opposing side divided by the length of the adjacent side. Some students employ the mnemonic SOH CAH TOA to recall trig ratios. This is one of the SAT math formulae and equations you should remember.
24. Degrees to Radians
While ratios are the most common sort of trigonometry, you may also encounter the unit circle or more sophisticated mathematics. Multiply the degrees by /180 to convert them into radians. Multiply the radians by 180/ if you need to convert them to degrees. This is one of the Sat Formula Sheets and equations you should remember.
25. The Pythagorean Theorem
a² +b² =c²
The Pythagorean Theorem, which applies to right triangles, permits the determination of one of the side lengths given the length of any other side. The legs of the triangle are and the hypotenuse is. This is one of the most essential SAT formulas and should be included on your Sat Formula Sheets.
26. Regular Polygon Interior Angle
(n − 2) × 180/n
There will likely be one question on the SAT using a regular polygon that is neither a triangle nor a square. Understanding the distinct and consistent features of regular polygons dependent on the number of sides will aid you in solving these challenges. This equation determines the degree measurement at each angle based on the number of sides. This is one of the most significant SAT math formulae and should be on your Sat Formula Sheets
27. 3-4-5 triangle
You may have noticed the 30-60-90 and 45-45-90 right triangles on the SAT’s reference sheet. In contrast, the 3-4-5 is a particular right triangle whose sides are simple integers. This triangle appears frequently on the SAT, especially in the no-calculator section, so keep an eye out for it. It can prevent the use of the Pythagorean theorem. This is one of the SAT math formulae and equations you should remember.
28. 5-12-13 triangle
Another unique right triangle with whole-number sides, the 5-12-13 triangle is less well-known and appears less frequently than the 3-4-5 triangle. Nonetheless, it is advantageous to be able to quickly answer the remaining sides without employing the Pythagorean theorem, therefore look for these numbers or their multiples in triangle puzzles. This is one of the most significant SAT math formulae and should be on your Sat Formula Sheets.
29. Arc Length in a Circle
Arc Length = (/180) r, where is measured in degrees.
Although geometry questions do not make up a significant component of the SAT, you may be asked about arcs or sectors in a circle. An arc is the distance between two locations on a circle and is often determined by extending two radii from the circle’s center and generating an angle between them. To get the length of an arc, multiply the degree measurement as a fraction by the circumference calculation. This is a required SAT formula and should be included on your 2023 Sat Formula Sheets.
30. Sector Area in a Circle
Comparable to an arc, the sector is the region between two radii extending from the circle, much like a slice of pie. To determine the sector’s area, multiply the degree measure as a fraction by the formula for the area of a circle. This is a required SAT formula and should be included on your 2023 Sat Formula Sheets.
FAQs On Sat Formula Sheets
Is there a formula sheet for the SAT?
The SAT provides a reference sheet of math formulas in the SAT math section – but it's short. You'll use more formulas on test day than you see on the sheet.
What is the format of SAT?
The SAT is a 3 hour 50 minute exam (including an optional essay which takes 50 minutes), consisting of five sections: Reading, Writing, Math (with calculator), and Math (no calculator). The SAT is a paper-based test administered at schools and sites around the country on select dates throughout the year.
Is the SAT exam hardest?
Research indicates that it is not. In addition, college students might prefer the ACT because more colleges use it in admissions decisions. Other key factors that may make one test harder than another include time limit and complexity.
Is SAT Writing hard?
Getting to an 800 SAT Writing score isn't easy. It'll require near perfection and a mastery of both grammar rules and essay writing.