Formula

A formula is a mathematical expression that represents a relationship or a rule between different variables. Formulas are used in various areas of mathematics, science, engineering, and economics to calculate or solve for unknown quantities. They often involve symbols, letters, and numbers to represent the variables and constants in the equation.

Types of Formulas

There are different types of formulas used in mathematics:

Geometric Formulas: These formulas are used to calculate the area, perimeter, volume, and other properties of geometric shapes such as circles, triangles, rectangles, and spheres.
Algebraic Formulas: Algebraic formulas involve equations that represent relationships between variables, such as the quadratic formula, distance formula, and the formula for the sum of an arithmetic series.
Scientific Formulas: These formulas are used in science and engineering to represent physical laws and principles, such as the formulas for force, energy, velocity, and acceleration.

Application of Formulas

Formulas are applied in various real-world scenarios, such as calculating the cost of a mortgage, determining the amount of medication to administer based on a patient's weight, or solving problems related to distance, time, and speed. They are also used in creating mathematical models for scientific experiments, financial analysis, and engineering designs.

Using Formulas

When using a formula, it's important to understand the meaning of each variable and constant in the equation. Substituting the known values into the formula allows you to solve for the unknown quantity. It's also important to use the correct formula for the specific problem or situation being addressed.

Overall, formulas play a crucial role in mathematics and its applications, providing a systematic and efficient way to represent mathematical relationships and make calculations.

◂Math Worksheets and Study Guides Eighth Grade. Functions

The resources above cover the following skills:

Grade 8 Curriculum Focal Points (NCTM)

Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations

Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Connections to the Grade 8 Focal Points (NCTM)

Algebra: Students encounter some nonlinear functions (such as the inverse proportions that they studied in grade 7 as well as basic quadratic and exponential functions) whose rates of change contrast with the constant rate of change of linear functions. They view arithmetic sequences, including those arising from patterns or problems, as linear functions whose inputs are counting numbers. They apply ideas about linear functions to solve problems involving rates such as motion at a constant speed.