NSSCO Mathematics (6131) key terms

A counting number from 1 upwards: 1, 2, 3, and so on. It has no fractional or decimal part and does not include zero or negative values.

A whole number that may be positive, negative, or zero, such as -4, 0, or 17. It never has a fractional or decimal part.

A number that can be written as one integer divided by another non-zero integer, such as 3/4 or -0.25. Its decimal form either stops or repeats a pattern.

A real number that cannot be written as a fraction of two integers. Its decimal form continues forever without repeating, as with pi or the square root of 2.

A whole number greater than 1 whose only positive divisors are 1 and itself, such as 2, 3, 7, or 13. The number 1 is not prime.

A whole number that divides another exactly, leaving no remainder. For example, 3 and 4 are factors of 12.

The result of multiplying a given whole number by any integer. The multiples of 5 are 5, 10, 15, 20, and so on.

The largest whole number that divides two or more given numbers exactly. For 18 and 24 the highest common factor is 6.

The smallest positive number that is a multiple of two or more given numbers. For 4 and 6 the lowest common multiple is 12.

A way of writing numbers as a value between 1 and 10 multiplied by a power of ten, such as 4.7 x 10^5. It suits very large or very small quantities.

The digits of a number that carry meaning for its accuracy, starting from the first non-zero digit. Rounding 0.004567 to two significant figures gives 0.0046.

A fraction or ratio expressed out of one hundred, using the symbol %. For instance, 45% means 45 parts in every 100.

A comparison of two or more quantities of the same kind, written with a colon such as 3:5. It shows how many parts of each quantity are present.

A statement that two ratios are equal, or a relationship where quantities change at the same relative rate. If 2 pens cost 6 dollars, 5 pens cost 15 dollars in direct proportion.

A combination of numbers, variables, and operations without an equals sign, such as 3x + 7 or 2(a - b). It can be simplified or evaluated but not solved.

The number that multiplies a variable in an algebraic term. In 7x the coefficient is 7, and in -3ab it is -3.

Terms that contain exactly the same variables raised to the same powers, so they can be combined. For example, 4x and -9x are like terms and add to -5x.

Rewriting an expression as a product of simpler expressions. For instance, 6x + 9 factorises to 3(2x + 3), and x^2 - 5x + 6 to (x - 2)(x - 3).

Removing brackets by multiplying each term inside by the factor outside. For example, 3(2x - 5) expands to 6x - 15.

An equation in which the variable appears only to the first power, so its graph is a straight line. An example is 4x - 7 = 13.

An equation whose highest power of the variable is two, usually written ax^2 + bx + c = 0 with a not zero. It can have two, one, or no real solutions.

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

A statement comparing two expressions that are not necessarily equal, using symbols such as <, >, or the versions with a line beneath. For example, 2x + 1 < 9.

The total distance around the outside edge of a flat shape. For a rectangle it equals twice the length plus twice the width.

The amount of flat surface enclosed by a shape, measured in square units such as cm squared. A rectangle's area is length multiplied by width.

The amount of space a solid occupies, measured in cubic units such as cm cubed. For a cuboid it is length times width times height.

The total area of all the outer faces of a solid. For a cube with edge length s it equals 6 times s squared.

A rule about angles, chords, and tangents in a circle, such as the angle in a semicircle being 90 degrees. These rules allow unknown angles to be found.

In a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides. It is used to find a missing side length.

The longest side of a right-angled triangle, lying opposite the right angle. It is the side squared alone on one side of Pythagoras' equation.

A ratio of two sides of a right-angled triangle linked to an acute angle, namely sine, cosine, or tangent. These ratios let sides and angles be calculated.

A rule stating that each side of a triangle divided by the sine of its opposite angle is constant. It is used for non-right-angled triangles when a matching pair is known.

A rule relating the three sides of a triangle to one angle: a squared equals b squared plus c squared minus 2bc cos A. It works for triangles without a right angle.

A direction measured clockwise from north, written as a three-figure angle such as 045 degrees. It describes the direction of one point from another.

The average found by adding all values and dividing by how many there are. For 2, 4, and 9 the mean is 5.

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

The value that occurs most often in a set of data. A data set may have one mode, several modes, or none at all.

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 number from 0 to 1 describing how likely an event is, where 0 means impossible and 1 means certain. It can be found from equally likely outcomes or from experiment.