TASC General Mathematics Level 3 key terms

A letter or symbol that stands for a number which can change or is not yet known. In an equation such as 3x + 2 = 11, the letter x is the variable.

The number multiplied by a variable in an algebraic expression. In 7y the coefficient is 7; in -4ab the coefficient is -4.

Terms that have exactly the same variable parts and can therefore be combined by adding or subtracting their coefficients. For example, 5x and -2x are like terms.

To rewrite an expression in a shorter equivalent form by combining like terms, removing brackets, or cancelling common factors, without changing its value.

The rule that multiplying a sum by a number gives the same result as multiplying each addend separately: a(b + c) = ab + ac. It is used to expand brackets.

A mathematical statement saying two expressions are equal, joined by an equals sign. Solving it means finding the value of the variable that makes the statement true.

A value of the variable that makes an equation true. Substituting it back into the original equation should produce a correct numerical statement.

Replacing a variable with a given number and calculating the result. For example, substituting x = 4 into 2x + 1 gives 9.

An equation in which every variable appears to the first power only, so its graph is a straight line. An example is 2x - 5 = 11.

Two or more equations that must be satisfied by the same values of the variables at once. Their solution is the point where their graphs intersect.

A statement comparing two expressions that are not necessarily equal, using symbols such as <, >, ≤ or ≥. Solving one gives a range of possible values.

Rewriting an expression as a product of factors. For example, 6x + 9 factorises to 3(2x + 3) because 3 is common to both terms.

A rule that assigns exactly one output value to each input value. A function can be described by a formula, a table, a graph or a mapping.

The value put into a function, often called the independent variable and usually denoted x. Each input produces exactly one output.

The result a function produces from a given input, often called the dependent variable and usually denoted y or f(x).

The set of all input values for which a function is defined. For example, a function with a denominator cannot accept inputs that make the denominator zero.

The set of all output values a function actually produces from its domain. It may be found from a graph by reading the vertical spread of the curve.

A function whose graph is a straight line, written in the form y = mx + c, where m is the gradient and c is the y-intercept.

A measure of how steep a line is, calculated as the change in y divided by the change in x between two points on the line.

The point where a graph crosses the vertical y-axis, occurring where x equals zero. In y = mx + c the value c is the y-intercept.

How much one quantity changes for each unit change in another. On a graph it equals the gradient of the line or curve over the interval considered.

The variable that is deliberately changed or chosen in a relationship, usually plotted on the horizontal axis. Its value does not depend on the other variable.

The variable whose value responds to changes in another variable, usually plotted on the vertical axis. Its value depends on the independent variable.

A grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin. Points are located on it using ordered pairs (x, y).

Two numbers written in the order (x, y) that locate a point on the coordinate plane, giving its horizontal position first and vertical position second.

The point (0, 0) where the x-axis and y-axis meet on the coordinate plane. It is the starting reference point for locating all other points.

A point where two graphs cross, so both relationships hold there at once. Its coordinates solve the pair of equations represented by the graphs.

A graph plotting paired data as individual points on a coordinate plane, used to show whether two variables are related and to spot trends or outliers.

A straight line drawn through a scatterplot to summarise the overall trend of the data and allow predictions to be estimated.

The average found by adding all the values in a data set and dividing the total by the number of values. It is affected by extreme values.

The middle value when the data are arranged in order. With an even number of values, it is the mean of the two middle values.

The value that appears most often in a data set. A set may have one mode, several modes, or no mode if all values occur equally often.

The difference between the largest and smallest values in a data set. It is a simple measure of how spread out the data are.

A value that is unusually far from the rest of the data. Outliers can strongly affect the mean but have little effect on the median.

The number of times a particular value or category occurs in a data set. Frequencies are often shown in tables, tallies or bar charts.

A number between 0 and 1 describing how likely an event is, where 0 means impossible and 1 means certain. It may be written as a fraction, decimal or percentage.

A single outcome or collection of outcomes from an experiment or trial, such as rolling an even number on a die.

All outcomes in the sample space that are not part of a given event. The probability of an event plus the probability of its complement equals 1.

Interest calculated on both the original amount and on interest already added, so the balance grows faster than with simple interest. Formula: A = P(1 + r)^n.

Interest calculated only on the original amount invested or borrowed, not on interest already earned. Formula: I = P × r × t.

The original amount of money invested or borrowed, before any interest is added or charged.