ЦТ Mathematics key terms

The nonnegative distance of a real number from zero on the number line. It strips away any minus sign, so the absolute value of −7 is 7 and of 7 is 7.

A real number that can be written as a fraction a/b where a and b are integers and b is not zero; its decimal form either ends or repeats.

A real number that cannot be expressed as a ratio of two integers. Its decimal expansion never ends and never repeats, as with √2 and π.

A way of expressing a part per hundred. One percent equals 1/100, so 35 percent means 35 out of 100, or the decimal 0.35.

A relationship in which one quantity changes by the same factor as another, so their ratio stays constant; doubling one quantity doubles the other.

An equation in one variable whose highest power is two, usually written ax² + bx + c = 0 with a not equal to zero.

For a quadratic equation ax² + bx + c = 0, the quantity b² − 4ac. Its sign tells how many real roots the equation has.

An equation that is true for every value of its variables within the allowed domain, such as (x + 1)² = x² + 2x + 1.

Two or more equations that must be satisfied at the same time by the same values of the variables; a solution makes every equation true.

An inequality in which each variable appears only to the first power, such as 2x − 3 < 7; its solutions form an interval on the number line.

The collection of all values of the variable that make an equation or inequality true. For an inequality it is often shown as an interval on the number line.

The set of all input values for which the function is defined and produces a real output. It excludes values causing division by zero or a negative square root.

The set of all output values a function can actually produce as its input varies over the domain; it need not include every real number.

A function that either never decreases or never increases on an interval. If it always moves one way, it is strictly monotonic there.

A function that reverses another function: if f maps a to b, then its inverse maps b back to a, provided the original function is one-to-one.

For an acute angle in a right triangle, the ratio of the side opposite the angle to the hypotenuse; extended to all angles by the unit circle.

An equation involving trigonometric functions that holds for every angle for which both sides are defined, such as sin²x + cos²x = 1.

A sequence in which each term after the first is obtained by adding a fixed number, the common difference, to the previous term.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed nonzero number called the common ratio.

Triangles whose corresponding angles are equal and whose corresponding side lengths are in the same ratio; their areas compare as the square of that ratio.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².

A quantity with both magnitude and direction, often represented by an arrow; in the plane it can be written as an ordered pair of components.

A three-dimensional solid bounded by flat polygonal faces, with straight edges and vertices; examples include prisms, pyramids, and cubes.

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

The total area of all the outer faces or curved surfaces of a three-dimensional solid, measured in square units. It is often split into lateral area plus base area.

The product of all positive integers from 1 up to a given nonnegative integer n, written n!; by convention 0! equals 1.

A number between 0 and 1 expressing how likely an event is, calculated in simple cases as favorable outcomes divided by all equally likely outcomes.

The sum of a set of numbers divided by how many numbers there are; it is the ordinary average and is sensitive to extreme values.

A ratio comparing two quantities with different units, such as kilometres per hour or work completed per day; it often links distance, time, and speed.

The amount of a substance in a mixture divided by the total amount of mixture, often expressed as a percentage or fraction. It is used in problems about solutions, alloys, and dilution.

A condition that limits the possible values in an optimization or modelling problem, such as a maximum budget or a minimum required quantity.

Total distance travelled divided by total time taken, not the average of separate speeds unless equal times are spent at each speed.