Irish Numerical Reasoning key terms

An ordered list of numbers or values that follows a rule or pattern, where each item occupies a fixed position in the list.

A single number or value at a particular position within a sequence, often written with a subscript such as a1 for the first term.

A formula that lets you calculate the value of the term at any chosen position n in a sequence without listing all earlier terms.

The consistent operation, such as adding a fixed amount or multiplying by a constant, that generates each successive term of a sequence from the previous one.

The constant amount added to each term to produce the next term in an arithmetic sequence, found by subtracting any term from the one after it.

A sequence in which the gap between consecutive terms is always the same, so the numbers rise or fall by a fixed step.

The constant multiplier linking each term to the next in a geometric sequence, found by dividing a term by the one before it.

A sequence in which each term is obtained by multiplying the previous term by the same fixed factor, producing rapid growth or decay.

A layout listing successive differences between terms, and differences of those differences, to reveal the pattern governing a number series.

The result of subtracting each term in a series from the term that follows it, showing the step-by-step change across the sequence.

The difference between consecutive first differences; a constant second difference signals a quadratic pattern in the original series.

A sequence formed by two or more interleaved patterns, so odd-positioned terms follow one rule while even-positioned terms follow another.

The total obtained by adding together all the terms of a sequence, sometimes required for a stated number of terms.

The result of adding two or more numbers together, often needed as an intermediate step in multi-stage word problems.

The result of subtracting one number from another, expressing how much larger or smaller one quantity is than the other.

The result of multiplying two or more numbers together, frequently used when combining rates, prices or repeated quantities.

The result of dividing one number by another, showing how many times the divisor fits into the dividend.

The amount left over after division when the divisor does not divide the dividend exactly, often needed when grouping items into whole units.

The agreed priority for calculating expressions: work through brackets, then powers, then multiplication and division, then addition and subtraction, left to right.

Grouping symbols that show which parts of an expression must be calculated first, overriding the usual priority of operations.

A single value representing a set of numbers, most commonly the mean, found by adding all values and dividing by how many there are.

The arithmetic average of a data set, calculated as the total of all values divided by the count of values.

The middle value of a data set once the values are arranged in order; with an even count it is the mean of the two middle values.

The value that appears most often in a data set, useful for identifying the most common category or outcome.

A way of expressing a number as a fraction of one hundred, so 25% means 25 parts out of every 100.

The increase or decrease in a value expressed as a percentage of its original amount, calculated by dividing the change by the original and multiplying by 100.

The unit used when comparing two percentages directly, so a move from 20% to 25% is a rise of five percentage points, not five per cent.

A comparison of two or more quantities showing their relative sizes, written with a colon such as 3:2 or as a fraction.

A statement that two ratios are equal, or the share of a whole that a particular quantity represents.

A relationship in which one quantity increases at the same rate as another, so doubling one value doubles the other.

A relationship in which one quantity increases while the other decreases at a matching rate, so their product stays constant.

A technique for ratio and proportion problems that first finds the value of one unit, then multiplies to obtain the required quantity.

A comparison between two quantities measured in different units, such as kilometres per hour or euro per kilogram.

A rate expressed for exactly one unit of the second quantity, for example the cost of a single item or distance covered in one hour.

The distance travelled per unit of time, calculated by dividing the distance covered by the time taken.

The length of the path travelled between two points, found by multiplying speed by the time spent moving.

The duration taken to complete a journey or task, calculated by dividing the distance covered by the speed.

The total distance travelled divided by the total time taken, which is not the same as the average of the individual speeds.

The amount of a task completed per unit of time by a person or machine, often expressed as a fraction of the whole job per hour.

A situation where two or more workers or machines contribute to one task, so their individual work rates are added to find the total rate.

A grid organising data into rows and columns so that values can be located and compared by their row and column headings.

A horizontal line of entries in a table, usually containing all the data for one item or category across the columns.

A vertical line of entries in a table, typically holding one type of measurement or variable for every item listed.

A visual display of data such as a bar chart, line graph or pie chart, used to show patterns, comparisons or trends at a glance.

One of the reference lines on a graph, with the horizontal and vertical axes carrying labelled scales against which data points are read.

The system of numbers and intervals marked along a graph axis, indicating how much each division or gridline represents.

The key beside or within a chart that explains what each colour, line style or symbol represents in the displayed data.

Replacing a number with a nearby simpler value of a stated accuracy, such as the nearest ten, whole number or decimal place.

Producing a quick approximate answer by rounding numbers to convenient values, useful for checking whether a precise answer is reasonable.

A value close to but not exactly equal to the true answer, often accepted when answer options are spaced far apart.

The meaningful digits in a number, counted from the first non-zero digit, used when expressing answers to a stated level of precision.

A position of a digit to the right of the decimal point, used to specify how precisely a number should be rounded.

An average in which each value contributes in proportion to its importance or frequency rather than equally.

The number of times a particular value or category occurs in a data set, often shown in a tally or frequency table.