NCEA L1 Maths key terms

A whole number with no fractional or decimal part, such as -3, 0, 7 or 250. It can be positive, negative or zero, but never a fraction.

Any number that can be written as one integer divided by another non-zero integer, so fractions and terminating or repeating decimals qualify, while values like pi do not.

A whole number that divides another number exactly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.

The result of multiplying a given whole number by any integer. Multiples of 5 include 5, 10, 15 and 20, and they continue without end.

A whole number greater than 1 whose only positive factors are 1 and itself. Examples are 2, 3, 5, 7 and 11; 1 is not prime.

The largest number that divides two or more given numbers exactly. For 18 and 24 the common factors are 1, 2, 3 and 6, so the highest common factor is 6.

The smallest number that is a multiple of each of two or more given numbers. For 4 and 6 the multiples meet first at 12, so 12 is the lowest common multiple.

A way of expressing part of a whole as one number over another, such as three quarters. The bottom number shows how many equal parts the whole is split into.

The top number of a fraction, which counts how many equal parts are being taken. In the fraction three quarters, the numerator is 3.

The bottom number of a fraction, which states how many equal parts the whole has been divided into. It cannot be zero because division by zero is undefined.

A fraction or proportion expressed out of 100, written with a percent sign. For example, 40% means 40 parts in every 100, which equals 0.4 as a decimal.

A number written using place value after a decimal point, where each position represents tenths, hundredths and so on. For instance, 0.75 means seven tenths plus five hundredths.

A comparison of two or more quantities showing their relative sizes, often written with a colon. A ratio of 2:3 means the second amount is one and a half times the first.

A statement that two ratios are equal, or a way of scaling quantities so their relative sizes stay the same. If 3 pens cost 6 dollars, 5 pens cost 10 dollars by proportion.

A ratio that compares quantities with different units, such as kilometres per hour or dollars per kilogram. It describes how much of one thing corresponds to one unit of another.

The change when a quantity grows, expressed as a percent of the original amount. The increase is divided by the starting value and multiplied by 100.

The change when a quantity shrinks, expressed as a percent of the original amount. The decrease is divided by the starting value and multiplied by 100.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 4.5 times 10 to the power 6.

Replacing a number with a nearby value that has fewer significant figures or decimal places, choosing the nearest suitable value. For example, 4.67 rounds to 4.7 to one decimal place.

The digits in a number that carry meaningful information about its precision, ignoring leading zeros. For instance, 0.00450 has three significant figures: 4, 5 and 0.

A short way of writing repeated multiplication of the same number, shown by a base and an exponent. For example, 2 to the power 4 means 2 x 2 x 2 x 2, which equals 16.

A number that, when multiplied by itself, gives the original value. The square root of 49 is 7 because 7 times 7 equals 49.

A combination of numbers, variables and operations with no equals sign, such as 3x plus 5. It represents a value that changes as the variable changes.

A letter or symbol standing for a number that may be unknown or may change. In the expression 2n plus 1, the letter n is the variable.

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

An equation in which the variable appears only to the first power, so its graph is a straight line. An example is 4x minus 3 equals 9.

An equation containing a variable raised to the power 2 as its highest term, such as x squared minus 5x plus 6 equals 0. It usually has up to two solutions.

Rewriting an expression as a product of simpler expressions that multiply back to the original. For example, x squared minus 9 factorises to (x minus 3)(x plus 3).

A measure of how steep a line is, found by dividing the vertical change by the horizontal change between two points on it. A horizontal line has gradient zero.

The point where a graph crosses the vertical y-axis, occurring where x equals zero. In the equation y equals 2x plus 5, the y-intercept is 5.

A rule for right-angled triangles stating that the square of the longest side equals the sum of the squares of the other two sides, written as a squared plus b squared equals c squared.

The branch of mathematics linking the angles and side lengths of triangles through ratios called sine, cosine and tangent. It is used to find unknown sides or angles in right-angled triangles.

A direction measured clockwise from north, always given as a three-digit angle between 000 and 360 degrees. A bearing of 090 degrees means due east.

The amount of turn between two lines or rays that meet at a point, measured in degrees or radians. A full turn is 360 degrees and a right angle is 90 degrees.

The amount of flat surface enclosed by a two-dimensional shape, measured in square units such as square centimetres. A rectangle's area is its length multiplied by its width.

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

The total distance around the outside edge of a two-dimensional shape, measured in ordinary length units. For a rectangle it is twice the length plus twice the width.

A measure of centre found by adding all the values in a data set and dividing by how many values there are. It is often called the average.

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

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

A simple measure of spread found by subtracting the smallest value in a data set from the largest. It shows the total width of the data but ignores values in between.

The spread of the middle half of a data set, found by subtracting the lower quartile from the upper quartile. It is less affected by extreme values than the range.

One of three values that split an ordered data set into four equal parts: the lower quartile, the median and the upper quartile. Each part holds about a quarter of the data.

A measure of how far values in a data set typically sit from the mean. A large value means the data is widely spread; a small value means it is tightly clustered.

A table that lists each value or category in a data set alongside how many times it occurs. It makes large data sets easier to summarise and analyse.

The number of times a particular value or category appears in a data set. In a frequency table, the frequencies usually add up to the total number of observations.

The frequency of a value divided by the total number of observations, giving a proportion or percentage. It estimates how likely that value is to occur.

A chart for numerical data in which bars touch to show how many values fall in each interval or class. The width of each bar represents the size of the interval.

A chart using separate bars of equal width whose heights show the frequency of each category. The bars do not touch because the categories are distinct.

A diagram showing a data set's smallest value, lower quartile, median, upper quartile and largest value. It gives a quick picture of centre and spread.

A graph plotting one variable against another as points, used to look for a relationship between them. A pattern of points rising to the right suggests positive correlation.

A measure of how strongly two variables are related, described as positive, negative or none. Correlation does not by itself prove that one variable causes the other.

A straight line drawn through a scatter plot to summarise the overall trend of the points. It can be used to estimate values not shown in the data.

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

The complete set of all possible outcomes of a probability experiment. For one roll of an ordinary die, the sample space is 1, 2, 3, 4, 5 and 6.

A single outcome or a collection of outcomes from a probability experiment, such as rolling an even number. Its probability is the number of favourable outcomes divided by all outcomes.

A branching diagram showing the possible outcomes of two or more stages of an experiment. Multiplying along a branch gives the probability of that combination of outcomes.

A group selected from a population in which every member has an equal chance of being chosen. It is used to gather data that fairly represents the whole population.

The entire group of people, objects or values that a study is interested in. A sample is taken from it when measuring every member is impractical.

A systematic error that makes a sample or survey result unrepresentative of the population. It can come from the way participants are chosen or from how questions are worded.