Digital SAT Math Formula Bible

These flashcards cover the essential formulas and concepts necessary for success on the Digital SAT Math exam.

Slope Formula

To calculate slope given two coordinates: m = (Y2 - Y1) / (X2 - X1).

Slope Intercept Form

The equation of a line in slope-intercept form is: y = mx + b, where m is slope and b is Y-intercept.

Point-Slope Form

The equation in point-slope form is: y - y1 = m(x - x1), where m is slope and (x1, y1) is a point on the line.

Midpoint Formula

The midpoint between two points (x1, y1) and (x2, y2) is: ((x1 + x2)/2, (y1 + y2)/2).

Distance Formula

The distance between two points (x1, y1) and (x2, y2) is: d = √[(x2 - x1)² + (y2 - y1)²].

Arc Length Formula

The length of an arc is given by: (n/360) * (2πr), where n is the central angle and r is the radius.

Area of a Sector Formula

The area of a sector is: (n/360) * (πr²), where n is the central angle and r is the radius.

Quadratic Formula

To find the solutions of a quadratic equation in standard form ax² + bx + c = 0: x = (-b ± √(b² - 4ac)) / (2a).

SOHCAHTOA

A mnemonic for trigonometric ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Probability Formula

Probability is calculated as: P = (Number of Favorable Outcomes)/(Total Number of Outcomes).

Circle Equation

The equation of a circle in the coordinate plane is: (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Exponential Growth Formula

The formula for exponential growth is: y = a(1 + r)ⁿ, where a is the initial value, r is the rate, and n is time.

Vertex of a Parabola

The x-value of the vertex of a quadratic function in standard form y = ax² + bx + c is found using: x = -b/(2a).

Pythagorean Theorem

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse: a² + b² = c².

Special Right Triangles

For a 45-45-90 triangle, legs are equal (x), and the hypotenuse is x√2. For a 30-60-90 triangle, opposite the 30° is x, opposite the 60° is x√3, and hypotenuse is 2x.

Distance = Rate × Time

The formula for distance is: Distance = Rate × Time.

Complementary Angles

Two angles are complementary if their sum is 90 degrees.

Sum of Angles in a Polygon

The sum of the interior angles of a polygon is given by: (n - 2) × 180°, where n is the number of sides.

Rational Function

A rational function is of the form: f(x) = P(x)/Q(x), where P and Q are polynomials.

Triangle Congruence Theorems

Triangles are congruent if: SSS, SAS, ASA, AAS, or HL.

Triangle Similarity Theorems

Triangles are similar if: AA, SAS with proportional sides, or SSS with proportional sides.

Unit Circle

The unit circle helps find the sine and cosine values of angles; sine gives the y-coordinate and cosine gives the x-coordinate.

Exponent Rules

Key exponent rules: multiply bases (add exponents), divide bases (subtract exponents), negative exponents (reciprocal), and zero exponent (equals one).

Absolute Value Equations

To solve |x - c| = d, set up two equations: x - c = d and x - c = -d.

Inequality Rule

When multiplying or dividing both sides of an inequality by a negative number, flip the inequality sign.

Area of an Equilateral Triangle

The area of an equilateral triangle with side s is: Area = (s²√3)/4.