CMA Foundation Paper 3 key terms

Interest computed only on the original principal for the whole period, using the formula I = P × r × t, where r is the annual rate as a decimal and t is time in years.

Interest added to the principal at each conversion period so that later interest is earned on earlier interest; the amount grows as P(1 + i)^n where i is the rate per period.

The equivalent annual rate that produces the same year-end growth as a nominal rate compounded more than once a year; it exceeds the nominal rate whenever compounding occurs more than annually.

A series of equal payments made at regular intervals, such as monthly deposits or loan instalments; the future value and present value of the stream are found using standard annuity factors.

The amount that must be invested today at a given rate to produce a specified future sum; it is the future amount discounted back over the relevant number of periods.

A comparison of two quantities of the same kind expressed as a quotient, showing how many times one contains the other; ratios are often simplified to lowest whole numbers.

A statement that two ratios are equal, such as a : b = c : d; in a true proportion the product of the extremes equals the product of the means.

A fraction or ratio expressed with denominator 100, denoted by the symbol %; converting between percentages, decimals and fractions is a basic skill in commercial arithmetic.

A sequence in which each term after the first is obtained by adding a fixed constant called the common difference; the nth term is a + (n − 1)d.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed constant called the common ratio; the nth term is a × r^(n−1).

The total of the first n terms of an arithmetic progression, given by n/2 × [2a + (n − 1)d] or equivalently n/2 × (first term + last term).

The total of the first n terms of a geometric progression, a(1 − r^n)/(1 − r) for r ≠ 1; when |r| < 1 the infinite sum equals a/(1 − r).

An equation of the form ax² + bx + c = 0 with a ≠ 0; its two roots are found by factorisation or by the quadratic formula, and the discriminant b² − 4ac reveals their nature.

The quantity b² − 4ac in a quadratic equation; if positive the roots are real and distinct, if zero they are equal, and if negative they are complex conjugates.

The values of the unknown variable that make an equation true; for a quadratic, the roots are the values at which the corresponding parabola crosses the horizontal axis.

A set of two or more equations in the same unknowns that must be satisfied at the same time; they are solved by elimination, substitution or matrix methods.

A single number computed from the elements of a square matrix; for a 2 × 2 matrix it is ad − bc, and a non-zero value shows the associated simultaneous equations have a unique solution.

A rectangular arrangement of numbers in rows and columns, used to store data and to solve systems of linear equations through operations such as addition, multiplication and inversion.

The exponent to which a fixed base must be raised to produce a given number; if y = b^x then x = log_b y, and logarithms turn multiplication into addition.

A function of the form f(x) = a^x with a positive base other than 1; it models growth and decay, and its inverse is the logarithm with the same base.

The value a function approaches as the input approaches a chosen point; a derivative is defined only when this approach settles on a single finite value.

A property of a function whose graph has no breaks or jumps near a point: the limit there exists, the function is defined there, and the two are equal.

The instantaneous rate at which a function changes with respect to its variable, found as the limit of the difference quotient; geometrically it is the slope of the tangent line.

The largest and smallest values of a function, found by setting the first derivative to zero and testing the sign of the second derivative to classify each turning point.

The additional cost of producing one more unit, approximated by the derivative of the total cost function with respect to output; it is a standard application of calculus in business.

The responsiveness of quantity demanded to a change in price, measured as the percentage change in quantity divided by the percentage change in price; demand is elastic when this magnitude exceeds one.

The reverse process of differentiation, used to recover a total from a marginal function; the definite integral also measures the area under a curve between two limits.

The arithmetic average, obtained by adding all observations and dividing by their number; it uses every value but is strongly affected by extreme observations.

The middle value of a data set arranged in order; for an even number of observations it is the average of the two central values, and it is resistant to outliers.

The value or category that occurs most frequently in a data set; a distribution may have one mode, several modes, or no mode at all.

A measure of spread equal to the positive square root of the variance; it expresses dispersion in the same units as the original data.

The average of the squared deviations of observations from their mean; its square root gives the standard deviation, and it is always non-negative.

The standard deviation expressed as a percentage of the mean; because it is unit-free, it is used to compare the relative variability of two or more data sets.

One of three values that divide ordered data into four equal parts; the second quartile equals the median and the first and third support the interquartile range.

A measure of the asymmetry of a distribution; when the mean exceeds the median the distribution is right-skewed, and when the mean is smaller it is left-skewed.

A number between −1 and +1 that measures the strength and direction of the linear relationship between two variables, without implying that either variable causes the other.

The straight line fitted to paired data by least squares, used to predict one variable from another; its slope shows the average change in the dependent variable per unit change in the independent variable.

The square of the correlation coefficient, showing the proportion of the variation in the dependent variable that is explained by the fitted regression relationship.

A number from 0 to 1 expressing how likely an event is; for equally likely outcomes it is the count of favourable outcomes divided by the count of all possible outcomes.

Events that cannot occur together in the same trial; for such events the probability that either occurs is the sum of their separate probabilities.

Events whose occurrences do not influence each other; for such events the probability that both occur is the product of their individual probabilities.

The long-run average outcome of a random variable, computed as the sum of each value multiplied by its probability; it need not equal any value the variable can actually take.

The probability distribution of the number of successes in a fixed number of independent trials, each with the same two possible outcomes and the same success probability.

A graph plotting one variable on the horizontal axis and another on the vertical axis, used to inspect visually whether a linear or other relationship exists between them.