Algebra 1 Formulas Flashcards

Quadratic Equation

• The Quadratic Formula is used to find the roots of quadratic equations.
• The formula is expressed as x = [-b ± √(b² - 4ac)] / 2a, where a, b, and c are coefficients from the equation ax² + bx + c = 0.

Algebraic Identities

• Difference of Two Squares states that a² - b² can be factored into (a + b)(a - b).
• This identity is useful for simplifying expressions and solving equations.
• A Perfect Square Trinomial follows the form a² + 2ab + b², which factors to (a + b)² or (a - b)².

Combinatorics

• Permutations (P(n,r)) calculate the number of ways to arrange r items from n distinct items, using the formula P(n, r) = n! / (n - r)!, where order matters.
• Combinations (C(n,r)) calculate the number of ways to select r items from n distinct items, given by C(n, r) = n! / [(n - r)!r!], where order does not matter.

Statistics

• Standard Deviation is a measure of how much individual data points differ from the mean.
• The formula is δ = √[(X₁ - x)² + (X₂ - x)² + ... + (X₇ - x)²] / n, where x is the mean and n is the number of data points.

Geometry

• Pythagorean Theorem relates the sides of a right triangle, expressed as a² + b² = c², where c is the hypotenuse.
• The Law of Sines states that the ratios of the sides of a triangle to the sine of their opposite angles are equal: sinA/a = sinB/b = sinC/c.
• The Law of Cosines generalizes the Pythagorean theorem for any triangle: a² = b² + c² - 2bcCosA.

Circular Geometry

• Arc Length is a portion of the circumference of a circle, calculated with the formula l = (n/360) x 2Πr, where n is the central angle in degrees and r is the radius.

Linear Functions

• Slope (m) measures the steepness of a line and is calculated as m = (y₂ - y₁) / (x₂ - x₁).
• Slope-Intercept Form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.
• Point-Slope Form of a line is expressed as y - y₁ = m(x - x₁), useful for writing the equation of a line given a point and slope.

Circle Equation

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