OST Algebra I key terms

Any number that can be placed on a number line, including whole numbers, fractions, decimals, and irrational values such as the square root of two. It excludes imaginary numbers.

A number that can be written as a fraction of two integers with a nonzero denominator. Its decimal form either stops or repeats a block of digits forever.

A real number that cannot be written as a fraction of two integers. Its decimal form never stops and never repeats, as with pi or the square root of two.

A whole number together with its negative counterpart and zero: for example, negative three, zero, and seven. No fractional or decimal part is allowed.

The distance of a number from zero on the number line, always zero or positive. Written with vertical bars, so the absolute value of negative six is six.

A horizontal line with evenly spaced marks used to picture numbers by position. Distance to the right means greater value, and distance to the left means lesser value.

A small raised number showing how many times a base is used as a factor. In three to the fourth power, four is the exponent and the value is eighty-one.

The number being repeatedly multiplied in an exponential expression. In two to the fifth power, two is the base and it appears as a factor five times.

A number that produces a given value when multiplied by itself. The square root of forty-nine is seven, and negative seven also squares to forty-nine.

A symbol or expression indicating a root of a quantity. Simplifying a radical means rewriting it with the smallest possible number under the root sign.

A way of writing very large or very small numbers as a factor between one and ten multiplied by a power of ten, such as three point two times ten to the sixth.

A rough comparison of size based on powers of ten. Two quantities differ by one order of magnitude when one is about ten times as large as the other.

Changing a measurement from one unit to another by multiplying by a ratio equal to one, such as sixty minutes over one hour, so value is preserved.

A letter or symbol standing for an unknown or changing quantity in an expression or equation. Its value may be found by solving or may vary freely.

A mathematical phrase built from numbers, variables, and operations, with no equals sign. Examples include three x plus five and the product of two binomials.

A statement that two expressions have equal value, written with an equals sign. Solving it means finding every value of the variable that makes the statement true.

A statement comparing two expressions that are not necessarily equal, using symbols for less than, greater than, or their or-equal versions. Solutions form a range of values.

An equation in which every variable appears to the first power and no variables are multiplied together. Its graph is a straight line and it usually has one solution.

A measure of steepness equal to vertical change divided by horizontal change between two points on a line. It is often called rise over run.

The point where a graph crosses the vertical axis, occurring where the input value is zero. In a linear model it often represents a starting amount.

Two or more equations considered together, whose solution is the set of values satisfying all of them at once. Graphically it is where the lines or curves intersect.

The collection of all values that make an equation or inequality true. A single-variable equation may have one value, many values, or no values at all.

An expression formed by adding or subtracting terms made of a number times a whole-number power of a variable. Example: four x cubed minus two x plus nine.

To rewrite an expression as a product of simpler expressions, or one of those multiplied pieces. Factoring x squared minus nine gives x minus three times x plus three.

If a product of factors equals zero, then at least one factor must equal zero. This principle is the main tool for solving equations written in factored form.

A function whose rule can be written with the variable squared as its highest power. Its graph is a parabola opening upward or downward.

The turning point of a parabola, where it reaches its maximum or minimum output. For an upward-opening parabola it is the lowest point on the graph.

The vertical line through a parabola's vertex that divides the graph into mirror-image halves. Reflecting any point across it gives another point on the curve.

A rule assigning exactly one output to each allowed input. Passing the vertical line test on a graph confirms that no input has two outputs.

The complete set of input values for which a function is defined. It may be restricted by division by zero or by taking square roots of negatives.

The complete set of output values a function actually produces. For a quadratic opening upward with vertex at zero, the range is all nonnegative numbers.

How much the output of a function changes per unit change in the input, computed as change in output divided by change in input over an interval.

A function in which the variable appears in the exponent, producing repeated multiplication by a constant factor. It grows or decays at a constant percent rate.

A function whose graph is a straight line, showing a constant rate of change. Its rule has the form output equals slope times input plus starting value.

A graph plotting paired data as points on two axes, used to look for a relationship between two measured quantities. Patterns suggest association, not necessarily cause.

A straight line drawn through a scatter plot that comes closest to the plotted points overall. It is used to summarize trend and make predictions within the data range.

A measure of how strongly two variables move together in a linear pattern, described as positive, negative, or near zero. It does not by itself prove causation.

The difference between an observed value and the value predicted by a model for the same input. A positive residual means the data point lies above the prediction line.

A table that counts data classified by two categories at once, with row and column totals. It supports statements about joint, marginal, and conditional frequencies.

The chance of an event given that another event is known to have occurred. It is computed as the joint frequency divided by the total for the known condition.