ICAP QAT key terms

A fraction expressed with denominator 100; used to compare quantities and to compute increases, decreases, discounts, and markups in everyday commercial problems.

The difference between a new value and an original value, divided by the original value and multiplied by 100; the base is always the earlier or reference figure.

Two or more percentage changes applied one after another; the combined effect equals the product of the individual multipliers minus one, never the simple sum of the percentages.

A single factor representing a percentage change, such as 1.15 for a 15 percent increase or 0.85 for a 15 percent decrease, used to chain changes quickly.

A comparison of two or more quantities of the same kind, written with a colon or as a fraction, showing how many times one amount contains another.

A statement that two ratios are equal; in a proportion a/b = c/d, the cross products ad and bc are equal, allowing an unknown term to be solved.

A technique that first finds the value of one unit by division, then multiplies by the required number of units to answer the question.

The sum of a set of values divided by how many values there are; it acts as a balance point and is the basis for many weighted and combined-group problems.

An average in which each value is multiplied by its frequency or weight before dividing by the total weight, so larger groups influence the result more strongly.

A method for combining two ingredients of different prices or concentrations to find the ratio in which they must be mixed to obtain a target value.

Interest calculated only on the original principal for the whole period, computed as principal times rate times time divided by 100.

Interest calculated on the principal plus previously accumulated interest, so the amount grows by a fixed multiplier each period rather than by a fixed addition.

How often interest is added to the balance within a year, such as yearly, half-yearly, or quarterly; more frequent compounding raises the effective annual rate.

The true annual growth rate after accounting for compounding within the year; it exceeds the nominal rate whenever compounding occurs more than once a year.

The original sum of money borrowed, lent, or invested, on which interest is calculated and to which accumulated interest is added.

The gain or shortfall when an item is sold, measured against its cost price; profit occurs when selling price exceeds cost price and loss when it falls below.

The amount paid to acquire or produce an item, including overheads where stated; it is the base against which profit or loss percentage is measured.

The amount for which an item is sold to the buyer, from which profit or loss is determined by comparison with the cost price.

The listed or labelled price before any discount is allowed; the selling price equals the marked price reduced by the discount given.

A reduction from the marked price, usually stated as a percentage of that marked price rather than of the cost price.

The relationship that distance equals speed multiplied by time; used to find any one of the three when the other two are known, with consistent units.

The rate at which two moving objects approach or separate; for motion in opposite directions the speeds add, and for the same direction the difference is used.

Total distance travelled divided by total time taken, which is not the simple mean of the individual speeds unless equal distances are covered at each speed.

Problems relating the rate at which workers or machines complete a task; rates add when working together, and time is the reciprocal of the combined rate.

The fraction of a job completed in one unit of time by a person or machine; combining rates by addition gives the rate for the group working simultaneously.

A variation of time-and-work problems in which inlet pipes fill a tank and outlet pipes empty it; filling rates are positive and emptying rates negative.

An arrangement of items in which order matters; the number of arrangements of r items chosen from n distinct items is n factorial divided by (n minus r) factorial.

A selection of items in which order does not matter; the count of ways to choose r items from n is n factorial divided by r factorial times (n minus r) factorial.

The product of all positive integers up to a given number, written with an exclamation mark; by convention zero factorial equals one.

A number between zero and one expressing how likely an event is, found by dividing the number of favourable outcomes by the total number of equally likely outcomes.

Events that cannot occur at the same time; for such events the probability that either happens is the sum of their individual probabilities.

Events whose outcomes do not affect one another; the probability that both occur equals the product of their separate probabilities.

A sequence in which each term differs from the previous one by a fixed constant; its nth term and sum can be found from the first term and common difference.

A sequence in which each term is obtained by multiplying the previous term by a fixed ratio; it grows or shrinks by a constant factor.

The sum of the terms of a sequence; common exam forms include sums of natural numbers, squares, and cubes, each with a standard closed formula.

The middle value of a data set arranged in order; with an even count it is the mean of the two central values and is unaffected by extreme outliers.

The value that appears most frequently in a data set; a set may have one mode, several modes, or none if all values occur equally often.

The classification of numbers into natural, whole, integer, rational, irrational, and real types, together with rules for divisibility, factors, and multiples.

The highest common factor is the largest number dividing two or more numbers exactly; the lowest common multiple is the smallest number they all divide.

A quick test for whether one number divides another without remainder, such as checking digit sums for divisibility by three or nine.