SAT Math key terms

An equation whose graph is a straight line. Its variables appear only to the first power, and with two variables it can be written in the form ax + by = c.

A number measuring how steep a line is: the vertical change between two points divided by the horizontal change between those same points. It is the same everywhere on a straight line.

The point where a graph meets the vertical axis, found by setting the input equal to zero. In the form y = mx + b, it is the constant b.

How much one quantity changes for each one-unit change in another. For a linear relationship it equals the slope and stays the same at every point.

Two or more equations that must all be true at the same time. Its solution is the set of variable values satisfying every equation in the group simultaneously.

A way to solve a system by adding or subtracting multiples of the equations so that one variable cancels out, leaving a single equation in one variable.

A comparison stating that one expression is less than, greater than, or possibly equal to another. Its solution is a range of values, and multiplying or dividing by a negative number reverses the sign.

Two expressions that produce the same result for every value substituted into them, even though they may look different after expanding, factoring, or combining like terms.

A condition that a solution must satisfy, such as a quantity that cannot be negative or a cost that cannot exceed a budget. It limits which values count as valid answers.

A function that can be written as f(x) = ax squared plus bx plus c, where a is not zero. Its graph is a U-shaped curve that opens upward when a is positive.

The turning point of a quadratic graph, where the function reaches its lowest value if the curve opens upward or its highest value if the curve opens downward.

A quadratic written as f(x) = a(x minus h) squared plus k. This arrangement displays the turning point (h, k) directly and shows whether the graph opens up or down.

The formula x = (negative b plus or minus the square root of b squared minus 4ac) divided by 2a, which gives every solution of ax squared plus bx plus c = 0, including cases that cannot be factored.

The portion of the quadratic formula under the square root, b squared minus 4ac. Its sign reveals whether the equation has two, one, or no real solutions.

An input value for which the function's output equals zero. On a graph, zeros are the places where the curve crosses or touches the horizontal axis.

A function in which the input appears in the exponent, typically f(x) = a times b to the x power. A base above 1 gives growth; a base between 0 and 1 gives decay.

A way of naming a function and its output, as in f(x) = 3x + 1. Writing f(5) means the output produced when the input is 5.

The set of all input values for which a function is defined. Division by zero and even roots of negative numbers are the usual reasons a value is excluded.

The set of all output values a function actually produces as its input runs through every value in the domain.

In a right triangle, the square of the longest side equals the sum of the squares of the two shorter sides: a squared plus b squared equals c squared.

A triangle containing one 90-degree angle. The side opposite that angle is the longest side and is called the hypotenuse.

Triangles whose corresponding angles are equal and whose corresponding side lengths are all in the same ratio. That ratio lets you find unknown lengths.

For an acute angle in a right triangle, the length of the side opposite that angle divided by the length of the hypotenuse.

For an acute angle in a right triangle, the length of the side next to that angle (but not the hypotenuse) divided by the length of the hypotenuse.

For an acute angle in a right triangle, the length of the opposite side divided by the length of the adjacent side.

An angle measure defined as arc length divided by radius. One full turn is 2 pi radians, so pi radians equals 180 degrees.

The distance along the curved edge of a circle between two points. It equals the radius multiplied by the central angle measured in radians.

An equation of the form (x minus h) squared plus (y minus k) squared equals r squared, which describes every point a distance r from the center (h, k).

The amount of three-dimensional space an object occupies, measured in cubic units and usually computed from a base area and a height or from a standard formula.

A comparison of two quantities by division, often written as a to b or as a fraction. It describes relative size rather than an absolute count.

An equation stating that two ratios are equal. It is used to scale quantities up or down and is solved by cross-multiplying.

A rate stated per single unit of one quantity, such as miles per hour or cost per ounce, found by dividing one quantity by the other.

The amount of increase or decrease divided by the original amount, expressed as a percent. The starting value is always used as the denominator.

A graph of paired data points, one point for each individual or trial, used to see whether two variables are associated and roughly how.

A straight line drawn through a scatterplot that stays as close as possible to the plotted points, used to predict one variable from the other.

The arithmetic average of a data set: add all the values and divide by the number of values. Extreme values pull the mean toward them.

The middle value when a data set is ordered from least to greatest; with an even number of values, the average of the two middle ones. It is not strongly affected by outliers.

A summary number for how far data values typically sit from their mean. A larger value means the data are more spread out.

A subset of a population chosen so that every member has an equal chance of being selected. Only samples drawn this way support conclusions about the whole population.

A table that organizes data by two categorical variables, placing counts for each combination in cells so that row and column percentages can be compared.