Master the SAT Math Formulas with this Comprehensive Review

Table of Contents

1. Introduction
2. The Importance of Knowing Formulas
3. Percent Change Formula
4. X-Intercepts, Roots, and Zeros
5. Sum and Product of the Roots
6. Vertex Formula
7. Vertex Form and Standard Form
8. Discriminants
9. Sokatoa
10. Complementary Rule
11. Circles
12. Equation of the Circle on the Coordinate Plane
13. Distance Formula
14. Area and Volume Formulas
15. Speed Training for Memorizing Formulas
16. Conclusion

Introduction

When it comes to scoring high on the math section of the SAT, it all boils down to having the right concepts, formulas, and rules memorized. In this article, we will provide You with a comprehensive list of the 12 formulas you need to know before your next SAT. Whether you are a first-time SAT test taker or looking to refresh your memory, we've got you covered. We will go over each formula, explain how to use it, and provide you with insights to ensure your success on the test.

The Importance of Knowing Formulas

Before we dive into the specific formulas, it's essential to recognize the significance of knowing these formulas. Many students underestimate the importance of memorizing formulas on the SAT. However, the ability to recall these formulas quickly can make a significant difference in your performance. By having these formulas at the tip of your fingers, you save valuable time and eliminate the need to constantly refer back to a formula sheet. Remember, speed and accuracy are crucial on the SAT, and knowing these formulas will give you a competitive edge.

Percent Change Formula

The percent change formula is used to calculate the percent increase or decrease from one number to another. The formula is as follows: final minus initial, divided by initial, times 100. This formula will help you determine the percent change between two quantities, whether it's a positive increase or negative decrease. For example, if you had 27 cookies and now have 13, you can use the percent change formula to calculate the percentage decrease. Substituting the values into the formula, you would get (13 - 27) / 27 * 100 = -50%, indicating a 50% decrease in the number of cookies.

Insight: Understanding how to use the equation method is crucial alongside the percent change formula. The SAT often includes equation-Based questions, so it's essential to familiarize yourself with both the formula and equation methods.

X-Intercepts, Roots, and Zeros

In quadratic functions, the x-intercepts, also known as roots or zeros, play a significant role on the SAT. There are two methods to find the x-intercepts for a parabola. The first method is factoring, which is used when the numbers are clean and easy to work with. By factoring the quadratic equation, you can determine the x-intercepts straightforwardly. However, if the numbers are complex or the equation is not factorable, you can use the quadratic formula.

The quadratic formula is as follows: x = (-B ± √(B^2 - 4AC)) / 2A, where A, B, and C are the coefficients of the quadratic equation. By substituting the values into the formula, you can find the x-intercepts or roots of the parabola. It's crucial to remember that when a quadratic equation shows radicals in the answer choices, it indicates that the equation is not factorable and should be solved using the quadratic formula.

Insight: Ensure you understand the concept of sum and product of the roots. Sometimes, the SAT will ask for the sum or product of the roots individually or together. The sum of the roots can be found using the formula -B / A, and the product of the roots can be found using the formula C / A.

Vertex Formula

The vertex of a parabola is another important concept tested on the SAT. There are two methods to find the vertex: the B/2A method and the midpoint method. If the question provides you with the equation of the parabola, you can use the B/2A method, which is -(B/2A). This method allows you to determine the x-coordinate of the vertex. However, if the question does not provide the equation and asks you to find the vertex, you can use the midpoint method. The vertex is always located halfway between the two x-intercepts. Using the midpoint formula, you can find the x-coordinate, and then substitute it into the equation to determine the y-coordinate of the vertex.

Insight: Understand the distinction between the vertex form and standard form of a quadratic function. The vertex form, represented as (x - h)^2 + k, shows the location of the vertex as constants. The h and k values indicate the x and y coordinates of the vertex, respectively.

Discriminants

Discriminants are frequently tested on the SAT and serve two purposes. First, discriminants can be used to find the number of roots or x-intercepts of a parabola. By calculating the discriminant of a quadratic equation (B^2 - 4AC), you can determine whether it has zero, one, or two roots. The discriminant formula provides valuable information about the nature of the parabola. Secondly, discriminants can also be used to find the number of intersections between a line and a parabola. By combining the equations, substituting values into the discriminant formula, and analyzing the results, you can determine the number of intersections.

Insight: Remember to pay Attention to the discriminant's values when solving quadratic equations. A positive discriminant indicates two distinct roots, a discriminant of zero indicates one repeated root, and a negative discriminant indicates no real roots.

Sokatoa

Sokatoa, derived from the trigonometric ratios sine, opposite/hypotenuse; Cosine, adjacent/hypotenuse; and tangent, opposite/adjacent, is essential knowledge for the SAT. Understanding and utilizing Sokatoa enables you to solve trigonometry problems efficiently. To store this information effectively, ensure you set up the angle, the side lengths, and the correct ratios. Remember that on the SAT, the information given for the sine, cosine, and tangent ratios is generally in the form of Simplified ratios, not the exact side lengths.

Insight: Be alert to the complementary rule, especially when sine and cosine are set equal to each other. This implies that their angles add up to 90 degrees. Recognizing this rule can simplify problem-solving and prevent confusion.

Circles

Understanding the formulas for sector area and arc length of a circle is crucial for success on the SAT. The sector area formula is calculated by multiplying the proportion of the circle by the total area. Similarly, the arc length formula is determined by multiplying the proportion of the circle by the circumference. Utilizing these formulas allows you to find the area and length of a specific section of a circle. Remember that the angle over 360 represents the fraction or proportion of the circle represented by the arc or sector.

Insight: Pay attention to the question's requirements regarding the fraction or proportion of the circle being referenced. You can either find the area of the sector and the total area, or Apply the given proportion to calculate the desired value.

Equation of the Circle on the Coordinate Plane

The equation of a circle on the coordinate plane is another concept frequently tested on the SAT. This equation is used to represent the location of a circle on a graph. Understanding how to complete the square is essential to solve these types of problems effectively. Additionally, familiarize yourself with the concept of points inside the circle, outside the circle, and on the circle. By mastering this concept, you can accurately determine a point's position in relation to the circle based on its coordinates.

Insight: The distance formula is a valuable tool when solving problems involving the equation of a circle. It provides a straightforward method to find the distance between two coordinates, saving time and effort.

Area and Volume Formulas

Memorizing the essential area and volume formulas tested on the SAT is essential for problem-solving efficiency. By having these formulas at your disposal, you can quickly calculate the area or volume of various shapes without wasting time referring back to a formula sheet. Some key formulas to remember include the area of a parallelogram and the area of a hexagon, as they have proven to be helpful in SAT math questions.

Insight: Speed training can significantly improve your ability to memorize and recall formulas quickly. By dedicating time to practice and repetition, you can train your brain to retrieve formulas within a matter of seconds, enhancing your performance on the SAT math section.

Conclusion

In conclusion, mastering the necessary formulas, concepts, and rules is vital for achieving success on the SAT math section. By understanding and memorizing these formulas, you save valuable time and increase your problem-solving efficiency. Additionally, being familiar with various concepts, such as Sokatoa, discriminants, and vertex formulas, allows for a deeper understanding of mathematical principles. Remember to practice regularly and dedicate time to speed training to ensure these formulas become Second nature. With the knowledge and confidence gained from mastering these formulas, you will be well-prepared to tackle any math question the SAT throws your way.

Highlights

• Memorizing formulas is crucial for achieving high scores on the SAT math section.
• Understanding and applying formulas quickly can save valuable time during the test.
• Key formulas include the percent change formula, x-intercepts and roots, vertex formula, and discriminant.
• Other important concepts covered in this article include Sokatoa, complementary rule, equation of the circle, and area and volume formulas.
• Regular practice and speed training are essential for memorizing and recalling formulas efficiently.

FAQ

Q: Why is it important to memorize formulas for the SAT math section? A: Memorizing formulas allows you to quickly and accurately solve math problems, saving valuable time during the test and increasing your chances of achieving a high score.

Q: Are all of these formulas necessary to know for the SAT? A: While not all of the formulas may be tested, being familiar with these formulas will ensure you are well-prepared for any math question that may appear on the SAT.

Q: How can I effectively memorize and recall these formulas during the test? A: Regular practice, repetition, and speed training exercises can help train your brain to quickly retrieve these formulas, improving your problem-solving efficiency during the SAT.

Q: Can I refer to a formula sheet during the SAT? A: No, the SAT does not provide a formula sheet. It is essential to memorize the necessary formulas to save time and ensure accuracy during the test.