To truly master Digital SAT Math, it's essential to familiarize yourself with numerous formulas that won't be provided on test day. Here, we've compiled a list of 20 such formulas to kickstart your preparation.
But why stop there? With our SAT preparation course, you'll not only gain access to over 50 math formulas but also learn how to effectively apply them to official DSAT practice problems. Don't miss out—enroll today and elevate your SAT performance to new heights.
Algebra 1. Slope-Intercept Form of a Line
The slope-intercept form of a linear equation is a way to represent a straight line on a graph.
y is the dependent variable
x is the independent variable
m is the slope
b is the y-intercept.
2. Slope Formula
The slope formula calculates the rate of change of a line.
m is the slope of the line.
(x₁, y₁) and (x₂, y₂) are two points on the line.
3. Slopes of Perpendicular Lines
The slopes of perpendicular lines are negative reciprocals of each other.
m1 is the slope of one line.
m2 is the slope of the perpendicular line.
Problem-Solving & Data Analysis
4. Percentage Formula
The percentage formula calculates a portion or rate as a percentage of a whole.
"Part" refers to the portion or the part of the whole that you're interested in.
"Whole" refers to the total or the entire quantity.
The result is multiplied by 100 to express it as a percentage.
5. Percentage Change
The percentage change formula calculates the relative change between two values as a percentage.
"New Value" refers to the updated or current value.
"Old Value" refers to the initial or previous value.
The result is multiplied by 100 to express it as a percentage.
6. Simple Probability
"Number of favorable outcomes" refers to the number of outcomes that satisfy the condition you're interested in.
"Total number of outcomes" refers to the total number of possible outcomes in the sample space.
7. Distance-Rate-Time Formula
The distance-rate-time formula is a fundamental equation used to solve problems involving distance, rate (or speed), and time.
"Distance" is the total distance traveled.
"Rate" (or "Speed") represents the speed at which the object is moving.
"Time" represents the duration of travel.
Advanced Math
8. Quadratic Formula
The quadratic formula is a fundamental tool in algebra for solving quadratic equations. The quadratic formula provides the solutions for x (the values of x) that satisfy this equation.
9. Standard Form of a Quadratic
The standard form of a quadratic equation is a way of writing quadratic equations that simplifies their representation.
a determines the direction and width of the parabola. (If a>0 the parabola opens upwards. If a<0, the parabola opens downwards.)
b determines the horizontal shift (if any) of the parabola.
c determines the vertical shift (if any) of the parabola. (Graphically, c is the y-intercept.)
10. Vertex Form of a Quadratic
The vertex form of a quadratic equation is an alternative way to represent a quadratic function.
a is a non-zero constant that determines the direction and width of the parabola (positive a opens upwards, negative a opens downwards).
(h,k) represents the coordinates of the vertex of the parabola. The vertex is the highest or lowest point on the graph of the quadratic function, depending on the value of a.
h is the x-coordinate of the vertex.
k is the y-coordinate of the vertex.
11. Factored Form of a Quadratic
The factored form of a quadratic equation is a way of expressing a quadratic equation as a product of linear factors.
12. Exponential Function
These are the values of x that make the quadratic equation equal to zero.
a is the initial value or y-intercept.
b is the growth or decay rate (decimal).
If b>1, it signifies exponential growth.
If 0<b<1, it indicates exponential decay.
13. Exponential Growth and Decay
Exponential growth and decay refer to the rapid increase or decrease of a quantity over time, following an exponential pattern.
a is the initial amount or value at time .
r is the growth or decay rate (decimal).
x is time.
14. Discriminant
The discriminant is a value calculated from the coefficients of a quadratic equation and its value determines the nature of the roots of the quadratic equation.
If D > 0, there are two distinct real solutions.
If D = 0, there is one real solution (a repeated root).
If D < 0, there are no real solutions, but two complex conjugate solutions.
Geometry & Trigonometry
15. Pythagorean Theorem
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
c is the hypotenuse (longest side across from the 90 degree angle).
a and b are the other two sides.
16. The Equation of a Circle
The equation of a circle is a mathematical representation that describes all the points in a two-dimensional plane that are equidistant from a fixed point called the center.
(x, y) is any point on the circle.
(h, k) is the coordinates of the center of the circle.
r is the radius of the circle.
17. Arc Length
Arc length refers to the length of a portion of the circumference of a circle or a curve. It is the distance along the curved line between two points on the arc.
r is the radius of the circle.
θ is the angle (in radians) subtended by the arc at the center.
18. Area of a Sector
The area of a sector is the region enclosed by an arc and the two radii originating from the center of a circle. It is a portion of the circle's total area.
r is the radius of the circle.
θ is the central angle of the sector (in radians).
19. Converting between Radians and Degrees
Converting between radians and degrees is a common operation in trigonometry and geometry.
20. Complementary Angle Relationship of Sine and Cosine
The complementary angle relationship of sine and cosine refers to the relationship between the sine and cosine functions of two angles that sum up to 90 degrees (or π/2 radians).
Specifically, if θ and ϕ are complementary angles, meaning θ + ϕ = 90, then the sine of one angle is equal to the cosine of the other angle, and vice versa.
