PERT Math key terms

An equation in which every variable is raised to the first power and no variable is multiplied by another. Its graph is a straight line and it usually has exactly one solution.

A number describing how steep a line is, found by dividing the vertical change between two points by the horizontal change. A positive slope rises left to right; a negative slope falls.

The point where a line crosses the vertical axis, written as (0, b). It gives the value of y when x equals zero.

The equation y = mx + b, where m is the slope and b is the y-intercept. It lets you graph a line quickly from just two numbers.

A statement comparing two expressions with <, >, <=, or >= instead of an equals sign. Its solution is a range of values rather than a single number.

The collection of all values that make an equation or inequality true. For a linear inequality it is usually an interval shown as a shaded region on a number line.

Two lines in the same plane that never meet. They have the same slope but different y-intercepts, so they form a system with no solution.

A letter or symbol that stands for an unknown or changing number in an expression or equation, such as x in 3x + 5.

The number multiplied by a variable in an algebraic term, such as the 3 in 3x. A coefficient of 1 is usually left unwritten.

Terms that have exactly the same variable parts, such as 4x and -7x. Only like terms can be combined by adding or subtracting their coefficients.

The rule a(b + c) = ab + ac, which says multiplication applies to every term inside parentheses. It is the main tool for removing parentheses when simplifying.

A combination of numbers, variables, and operations with no equals sign. It can be simplified or evaluated for given values, but it is not solved.

The agreed sequence for computing an expression: parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

A raised number showing how many times the base is used as a factor, as in 2^4 = 222*2. It does not mean multiplying the base by the exponent.

An expression built from terms with whole-number exponents on the variables, combined by addition or subtraction, such as 3x^2 - 5x + 2.

A rule that assigns exactly one output value to each allowed input value. The input is usually x and the output is written f(x).

The set of all input values for which a function is defined. In a fraction, any value that makes the denominator zero must be excluded.

The set of all output values a function actually produces. On a graph it is read from the vertical axis.

A check of whether a graph represents a function: if any vertical line crosses the graph more than once, one input has two outputs, so it is not a function.

Two or more equations that must be true for the same values of the variables at the same time. The solution is the point or points their graphs share.

A way to solve a system by solving one equation for a variable, then replacing that variable in the other equation so only one variable remains.

A way to solve a system by adding or subtracting the equations, sometimes after multiplying one by a constant, so that one variable cancels out.

An equation that can be written as ax^2 + bx + c = 0 with a not equal to zero. It usually has two solutions, which may be equal or may not be real.

The U-shaped curve that is the graph of a quadratic function. It opens upward when a is positive and downward when a is negative.

The highest or lowest point of a parabola, where the curve turns around. It lies on the axis of symmetry and gives the maximum or minimum value.

The vertical line x = -b/(2a) that splits a parabola into two mirror-image halves. It passes through the vertex of the parabola.

The formula x = (-b plus or minus the square root of b^2 - 4ac) divided by 2a, which gives the solutions of any quadratic equation written in standard form.

The expression b^2 - 4ac found under the square root in the quadratic formula. Its sign tells how many real solutions a quadratic equation has.

Rewriting an expression as a product of simpler expressions. Setting each factor of a quadratic equal to zero gives the equation's solutions.

An input value that makes the function equal zero; on a graph, where the curve crosses the horizontal axis. For a quadratic these zeros are its solutions.

The rule a^2 + b^2 = c^2 for right triangles, where c is the hypotenuse and a and b are the legs. It is used to find a missing side length.

Triangles with the same shape whose matching angles are equal and whose side lengths are in the same ratio. Their corresponding sides form a proportion.

An equation stating that two ratios are equal, such as a/b = c/d. Cross-multiplying turns it into a linear equation you can solve.

The amount of surface a flat shape covers, measured in square units. The formula depends on the shape, such as length times width for a rectangle.

The amount of space a three-dimensional solid fills, measured in cubic units. For a rectangular box it is length times width times height.

The total distance around the outside of a flat shape, measured in linear units. For a rectangle it is twice the sum of its length and width.

Changing a measurement from one unit to another by multiplying by a ratio equal to one, such as 12 inches per foot.

The average of a data set, found by adding all the values and dividing by how many there are. It is pulled toward unusually large or small values.

The middle value of a data set listed in order; with an even count it is the average of the two middle values. It is not strongly affected by outliers.