sat math formulas pdf

SAT Math Formulas PDF⁚ A Comprehensive Guide

Having the key SAT math formulas at your fingertips can be a huge help on test day. We’ve compiled all 40 formulas from the table into a convenient, printable PDF sheet you can download and keep handy during your studies. Download the Full SAT Math Formula Sheet PDF. The star denotes the top 10 formulas to know for the SAT.

Essential Formulas for SAT Math

One of the most important requirements for mastering SAT Math is having a solid understanding of the key formulas and knowing how to apply them. We’ll show you what math formulas you’ll need to remember, what formulas you’ll be given on the test, and what formulas you can get away with not knowing.

What Formulas Are on the SAT Math Reference Sheet? First and foremost, you see that the SAT reference sheet includes geometry formulas galore! From the circle formulas for area and circumference to the area of a triangle, this sheet is a treasure trove of long-forgotten geometry facts.

Following is a quick formula reference sheet that lists all important SAT Math formulas you MUST know before you sit down for the test. If you learn every formula in this SAT Math Formula Cheat Sheet, you will save yourself valuable time on the test and probably get a few extra questions correct.

Although there are a number of formulas and facts given on the SAT, there are many more that you will need to know in order to answer problems. This worksheet has compiled the other formulas you should know for the SAT Math Section. Official SAT Math Reference Sheet. These equations break down into four categories⁚ Geometry of 2D Shapes (Area, Perimeter, and Circumference) Special Right Triangles; Geometry of 3D Shapes (Volume) Other Reference Info; Let’s take a deeper look at each of these formulas, and walk through when and how you would use them on test day.

Circles

The SAT Math Reference Sheet provides the following formulas for circles⁚

• Area of a Circle⁚ A = πr²
• Circumference of a Circle⁚ C = 2πr

These formulas are essential for solving problems involving circles on the SAT. You should be familiar with them and be able to apply them in different contexts.

Beyond the basic formulas, you may also encounter problems that require knowledge of other circle-related concepts. These include⁚

• Arc Length⁚ The length of a portion of the circle’s circumference. The formula for arc length is⁚ Arc Length = (central angle/360°) * 2πr
• Sector Area⁚ The area of a portion of the circle enclosed by two radii and an arc. The formula for sector area is⁚ Sector Area = (central angle/360°) * πr²
• Equation of a Circle⁚ (x ⎼ h)² + (y ⎼ k)² = r², where (h, k) is the center of the circle and r is the radius.

By understanding these concepts and practicing with various problems, you can improve your ability to solve circle-related questions on the SAT.

Special Right Triangles

The SAT Math Reference Sheet includes information about two special right triangles⁚ the 30-60-90 triangle and the 45-45-90 triangle. These triangles have specific side ratios that can be used to solve problems quickly and efficiently.

30-60-90 Triangle⁚

• The sides of a 30-60-90 triangle are in the ratio of 1⁚√3⁚2.
• The hypotenuse is twice the length of the shorter leg.
• The longer leg is √3 times the length of the shorter leg.

45-45-90 Triangle⁚

• The sides of a 45-45-90 triangle are in the ratio of 1⁚1⁚√2.
• The legs are congruent (equal in length).
• The hypotenuse is √2 times the length of each leg.

Knowing the side ratios of these special right triangles can significantly simplify problems involving right triangles on the SAT. You can use these ratios to find missing side lengths, angles, and even areas.

Practice identifying these triangles within larger figures and applying their side ratios to solve problems effectively.

Area of a Rectangle

The area of a rectangle is the amount of space it occupies within a two-dimensional plane. It is calculated by multiplying the length and width of the rectangle. The formula for the area of a rectangle is⁚

Area = Length × Width

This formula is provided on the SAT Math Reference Sheet, so you don’t need to memorize it. However, it’s essential to understand its application and how to use it to solve problems.

The SAT may present you with problems involving rectangles where you need to find the area, length, or width. You might be given the dimensions of the rectangle directly, or you might need to deduce them from other information provided in the problem.

For example, you might be given the perimeter of a rectangle and asked to find its area. In this case, you would need to use the perimeter formula to find the length and width, and then use those values to calculate the area.

Mastering the area of a rectangle formula and its applications is crucial for tackling geometry problems on the SAT effectively.

Area of a Triangle

The area of a triangle is a fundamental concept in geometry and is frequently encountered on the SAT Math section. Understanding the formula for calculating the area of a triangle and its applications is crucial for success on the exam.

The area of a triangle is defined as half the product of its base and its corresponding height. The base of a triangle is any side of the triangle, and the height is the perpendicular distance from the opposite vertex to the base. The formula for the area of a triangle is⁚

Area = 1/2 × Base × Height

This formula is provided on the SAT Math Reference Sheet, so you don’t need to memorize it. However, it’s essential to understand its application and how to use it to solve problems.

The SAT may present you with problems involving triangles where you need to find the area, base, or height. You might be given the dimensions of the triangle directly, or you might need to deduce them from other information provided in the problem.

For example, you might be given the area of a triangle and one side length and asked to find the height. In this case, you would use the area formula to solve for the height.

Mastering the area of a triangle formula and its applications is crucial for tackling geometry problems on the SAT effectively.

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in geometry that establishes a relationship between the sides of a right triangle. This theorem is a cornerstone of trigonometry and has wide-ranging applications in various fields, including engineering, physics, and architecture. It is also a crucial concept for the SAT Math section, and you should have a solid understanding of it.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, called legs. This can be expressed mathematically as follows⁚

a² + b² = c²

Where ‘a’ and ‘b’ represent the lengths of the legs, and ‘c’ represents the length of the hypotenuse. This theorem allows you to determine the length of any side of a right triangle if you know the lengths of the other two sides.

The SAT may present you with problems involving right triangles where you need to apply the Pythagorean Theorem to find the length of a missing side. You might be given the lengths of two sides and asked to find the length of the third side, or you might be given the length of one side and the relationship between the other two sides and asked to solve for their lengths.

Understanding the Pythagorean Theorem and its applications is essential for success on the SAT Math section. It is a powerful tool for solving various geometric problems and can help you navigate challenging questions involving right triangles.

Slope

Slope is a fundamental concept in algebra and geometry that represents the steepness of a line. It describes how much a line rises or falls for every unit of horizontal change. The slope of a line is a crucial element in understanding linear equations and their graphs. It plays a significant role in various mathematical applications, including determining the rate of change, predicting trends, and analyzing data.

On the SAT Math section, you’ll encounter problems that require you to calculate the slope of a line, interpret its meaning, or use it to solve for other variables. The slope of a line is represented by the letter ‘m’ and can be calculated using the following formula⁚

m = (y2 ⎼ y1) / (x2 ⎯ x1)

Where (x1, y1) and (x2, y2) are any two distinct points on the line. This formula calculates the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between the two points, which gives you the slope of the line.

The slope of a line can be positive, negative, zero, or undefined. A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. A zero slope signifies a horizontal line, and an undefined slope signifies a vertical line.

Mastering the concept of slope is essential for success on the SAT Math section. It enables you to understand linear relationships, analyze graphs, and solve problems involving lines and their equations.

Slope-Intercept Form

The slope-intercept form of a linear equation is a widely used representation that provides a clear and concise way to express the relationship between the slope and y-intercept of a line. This form is particularly helpful for graphing lines, determining the equation of a line given its slope and y-intercept, and solving various problems involving linear equations.

The slope-intercept form is written as⁚ y = mx + b, where⁚

• y represents the dependent variable (usually on the vertical axis)
• x represents the independent variable (usually on the horizontal axis)
• m represents the slope of the line, indicating its steepness and direction
• b represents the y-intercept, which is the point where the line crosses the y-axis

This form makes it easy to identify the slope and y-intercept of a line simply by looking at the equation. For instance, if the equation is y = 2x + 3, we know that the slope (m) is 2 and the y-intercept (b) is 3. This information allows us to quickly graph the line by plotting the y-intercept and using the slope to find additional points.

The slope-intercept form is a versatile tool for understanding and manipulating linear equations; It is frequently used in various mathematical applications, including solving systems of equations, finding the equation of a line given two points, and analyzing linear relationships in data.

On the SAT Math section, you may be asked to identify the slope and y-intercept of a line given its equation in slope-intercept form, or you may need to convert an equation from another form into slope-intercept form. Understanding this form is crucial for success in solving linear equations and interpreting their graphs.

Point-Slope Form

The point-slope form of a linear equation is a powerful tool for expressing the relationship between a line and a specific point on that line. This form is particularly useful when you know the slope of the line and a point that lies on it, as it allows you to directly write the equation without needing to find the y-intercept.

The point-slope form is represented as⁚ y ⎯ y1 = m(x ⎼ x1), where⁚

• y represents the dependent variable (usually on the vertical axis)
• x represents the independent variable (usually on the horizontal axis)
• m represents the slope of the line, indicating its steepness and direction
• (x1, y1) represents the coordinates of the given point on the line

To use the point-slope form, simply substitute the values of the slope (m) and the coordinates of the given point (x1, y1) into the equation. For instance, if the slope is 3 and the point is (2, 1), the equation in point-slope form would be⁚ y ⎼ 1 = 3(x ⎯ 2). From here, you can easily rearrange the equation into other forms, such as slope-intercept form, if needed.

The point-slope form is particularly useful for deriving the equation of a line when you are given its slope and a point on the line. It is also valuable for solving problems involving linear equations when you need to find the equation of a line that passes through a given point and has a specific slope.

On the SAT Math section, you may be asked to find the equation of a line given its slope and a point, or you may need to convert an equation from another form into point-slope form. Mastering this form is essential for success in working with linear equations and understanding their relationships to points and slopes.

Quadratic Equations

Quadratic equations are fundamental to algebra and are frequently encountered on the SAT Math section. They are polynomial equations with a highest power of 2, generally represented by the standard form⁚ ax² + bx + c = 0, where a, b, and c are coefficients, and a ≠ 0. Understanding quadratic equations is crucial for solving various problems involving parabolas, projectile motion, and optimization.

One common method for solving quadratic equations is factoring. This involves finding two binomials that multiply to give the original quadratic expression. Factoring allows you to identify the values of x that make the equation equal to zero, known as the roots or solutions. For example, x² + 5x + 6 = 0 can be factored as (x + 2)(x + 3) = 0, leading to solutions x = -2 and x = -3.

Another method, the quadratic formula, is a more general approach that can be used to solve any quadratic equation. It provides the solutions directly, even when factoring is challenging. The quadratic formula is given by⁚ x = (-b ± √(b² ⎯ 4ac)) / 2a. This formula requires substituting the values of a, b, and c from the quadratic equation and then simplifying the expression to obtain the solutions.

Understanding the relationship between the quadratic formula and the graph of a parabola (which is represented by a quadratic equation) is essential. The discriminant (b² ⎯ 4ac) within the quadratic formula reveals information about the nature of the roots. If the discriminant is positive, the equation has two distinct real roots, indicating two x-intercepts on the parabola. If the discriminant is zero, there is one real root, signifying that the parabola touches the x-axis at its vertex. If the discriminant is negative, there are no real roots, implying that the parabola does not intersect the x-axis.

The SAT Math section often includes questions that require solving quadratic equations, interpreting their graphs, or applying them to real-world scenarios. Familiarity with these concepts and their applications is crucial for success on the exam.

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