ADF JOA Numerical key terms

An ordered list of numbers generated by a rule, such as adding a fixed amount or multiplying by a constant. Candidates identify the rule to predict the next or missing term.

The constant amount added (or subtracted) between consecutive terms in an arithmetic sequence. Found by subtracting any term from the one that follows it.

The constant factor by which each term in a geometric sequence is multiplied to produce the next term. Found by dividing a term by the one before it.

A sequence in which each term after the first equals the previous term plus a fixed number. The gap between neighbouring terms never changes.

A sequence in which each term is obtained by multiplying the previous term by a fixed non-zero number. Terms grow or shrink by a constant factor.

A table listing first differences, then differences of those differences, and so on, used to expose the pattern behind a series, especially one following a quadratic or higher rule.

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

A sequence that switches between two separate rules or directions, such as odd-positioned terms following one pattern and even-positioned terms following another.

A series in which each term equals the sum of the two preceding terms, possibly after a small adjustment. Recognised by checking whether adding earlier terms reproduces later ones.

Any of the basic processes of addition, subtraction, multiplication, or division performed on numbers. Order of operations governs which is carried out first.

The agreed sequence for evaluating expressions: brackets first, then powers, then multiplication and division, then addition and subtraction, working left to right within each level.

A memory aid for order of operations: Brackets, Orders (powers and roots), Division and Multiplication, Addition and Subtraction. Division and multiplication rank equally, as do addition and subtraction.

The value a digit carries because of its position in a number, such as the 3 in 3,400 meaning three thousand. Essential for accurate column arithmetic.

Borrowing from or carrying to the next column when adding or subtracting, so each column holds a single digit. Also called borrowing and carrying.

Approximating a value by rounding numbers to convenient figures before computing. Useful for checking whether an exact answer is reasonable.

Replacing a number with a nearby value of a chosen precision, decided by the digit after the target place. A digit of 5 or more rounds up.

Estimating by working with the leading digits of numbers first and adjusting with the remaining digits. Gives a quick rough total without full calculation.

A fraction expressed out of one hundred, so 45% means 45 parts per 100. Used to compare parts of a whole on a common scale.

The difference between an old and new value, divided by the old value, then multiplied by 100. Shows increase or decrease relative to the starting amount.

The plain arithmetic difference between two percentages, such as 12% rising to 15% being a 3 percentage point rise. Differs from a percentage change of the percentages themselves.

A comparison of two or more quantities by division, written with a colon or as a fraction. States how many parts of one thing exist per part of another.

An equation stating that two ratios are equal. Used to scale a known ratio up or down to match a new total.

A technique of first finding the value of one unit by dividing, then multiplying to find the value of the required number of units.

A ratio comparing one share with the entire total rather than with another share. Converting it to a fraction of the total aids percentage and share calculations.

A relationship in which one quantity increases at the same rate as another, so their ratio stays constant. Doubling one doubles the other.

A relationship in which one quantity rises while the other falls so that their product stays constant. Doubling one halves the other.

A grid presenting values in rows and columns, with headings naming each category. Reading the correct row and column intersection is the core skill.

The sum of all entries across one horizontal line of a table. Often used to compute shares or percentages within that category.

The sum of all entries down one vertical line of a table. Helps verify figures and calculate overall percentages.

A graph using rectangular bars whose lengths represent quantities. Comparing bar lengths gives quick relative magnitudes across categories.

A graph plotting points joined by lines, typically showing how a value changes over time. The slope of the line indicates the rate of change.

The marked intervals along a graph axis that assign numerical meaning to distance. Misreading the scale is a common source of error.

A comparison of two quantities with different units, such as kilometres per hour or cost per item. Expressed as one quantity per single unit of another.

The distance travelled per unit of time, calculated by dividing distance by time. Rearranging the relationship gives distance or time when the other two are known.

Total distance divided by total time for a whole journey, not the simple mean of the separate speeds. Required when speeds differ across legs of a trip.

The sum of a set of values divided by how many values there are, also called the mean. Balances the values as if each were equal.

A mean in which each value contributes in proportion to its assigned weight rather than equally. Used when groups of different sizes are combined.

Changing a measurement from one unit to another using a known equivalence, such as 1 kilometre equals 1,000 metres, while preserving the actual quantity.

A word or symbol placed before a base unit to scale it, such as kilo for one thousand or milli for one thousandth. Each step between prefixes moves the decimal three places.

Checking that units in a calculation combine correctly, for example that distance divided by time yields a speed. Catches many setup errors before computing.