TASC Mathematics Methods – Foundation Level 3 key terms

A rule that assigns exactly one output value to each input value from a specified set, often written as f(x).

The complete set of input values for which a function or relation is defined and produces a valid output.

The set of all output values a function actually produces when every value in its domain is used.

A function whose graph is a straight line, written in the form f(x) = mx + b where m is slope and b is the y-intercept.

A measure of how steeply a line rises or falls, calculated as the change in vertical value divided by the change in horizontal value between two points.

A function of the form f(x) = ax squared plus bx plus c, where a is nonzero, whose graph is a parabola.

The U-shaped curve produced by graphing a quadratic function; it opens upward when the leading coefficient is positive and downward when negative.

The highest or lowest point on a parabola, located at the turning point of the quadratic curve.

The values of the variable that make a function equal zero, also called zeros or x-intercepts of the graph.

Rewriting an algebraic expression as a product of simpler expressions, such as turning a quadratic into two linear factors.

Multiplying out brackets to remove them and write an expression as a sum of terms without grouping symbols.

Two or more equations that must be satisfied by the same values of the variables at the same time.

Replacing a variable with a given value or expression, often used to solve simultaneous equations or evaluate a function.

Solving simultaneous equations by adding or subtracting them, or multiples of them, to remove one variable.

A statement comparing two expressions that are not necessarily equal, using symbols such as less than, greater than, or not equal to.

A function formed by applying one function to the output of another, written as f of g of x.

A function that reverses the effect of another function, so that applying both in turn returns the original input.

A function in which the variable appears in the exponent, such as f(x) = a times b to the power x, producing rapid growth or decay.

The instantaneous rate at which a function changes with respect to its input, equal to the slope of the tangent line at a point.

The process of finding a derivative, using rules such as the power rule, product rule, and chain rule.

A differentiation rule stating that the derivative of x to the power n is n times x to the power n minus one.

A straight line that touches a curve at a single point and has the same slope as the curve at that point.

The slope of a curve or line at a particular point, describing how steeply it rises or falls there.

How quickly one quantity changes relative to another, such as distance per unit time or cost per unit produced.

The total change in a quantity divided by the total change in another over an interval, equal to the slope between two points.

A point on a curve where the derivative equals zero, marking a local maximum, local minimum, or point of inflection.

The greatest value a function reaches, either across its whole domain or within a local neighbourhood of a point.

The smallest value a function reaches, either across its whole domain or within a local neighbourhood of a point.

A number between zero and one describing how likely an event is, where zero means impossible and one means certain.

The set of all possible outcomes of a random experiment or trial.

A subset of the sample space, consisting of one or more outcomes that share a defined characteristic.

The event consisting of all outcomes in the sample space that are not part of a given event.

The probability that an event occurs given that another event is already known to have occurred.

A relationship between two events where the occurrence of one does not change the probability of the other occurring.

The arithmetic average of a data set, found by adding all values and dividing by the number of values.

The middle value of a data set when the values are arranged in order, or the average of the two middle values.

A measure of how spread out data values are around the mean, equal to the square root of the variance.

The average of the squared differences between each data value and the mean, describing how spread out the data is.

A value that divides an ordered data set into four equal parts, with the median as the second quartile.

The difference between the upper quartile and the lower quartile, showing the spread of the middle half of the data.

A simplified mathematical description of a real situation, used to analyse behaviour and make predictions about the real world.

A condition accepted as true when building a model, which simplifies the situation but may limit how accurately the model reflects reality.

A quantity in a model that can change or take different values, often represented by a letter such as x or t.

A fixed but adjustable quantity in a model that shapes the relationship between variables, such as a growth constant.

A way in which a model falls short of reality, such as ignored factors, simplified assumptions, or a restricted range of validity.