Maths AA terms: M

M

Maclaurin polynomialHL only · also Taylor polynomial, truncated series

The polynomial formed by the terms of a Maclaurin series up to a chosen power of $x$. It has the same value and the same first few derivatives as the function at $x = 0$, so it approximates the function near $0$.

Introduced in 5.19 Maclaurin series

Maclaurin seriesHL only · also power series, Taylor series

The infinite series $f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + \frac{x^3}{3!}f'''(0) + \ldots$, which writes a function as a power series in $x$ built from its derivatives at $x = 0$.

Introduced in 5.19 Maclaurin series

Magnitude (of a vector)HL only · also length of a vector, modulus of a vector

The length of a vector, written $|\boldsymbol{v}|$. For $\boldsymbol{v} = v_1\boldsymbol{i} + v_2\boldsymbol{j} + v_3\boldsymbol{k}$

Many-to-one function

A function in which at least one output comes from two or more different inputs, such as $f(x) = x^2$, where $f(-3) = f(3) = 9$. It has no inverse function on that domain.

Mathematical modelalso model, modelling

A function or equation that describes a real situation, with variables standing for real quantities. Its domain is limited to values that make sense in the context.

Introduced in 2.2 Functions, domain, range and inverse

Meanalso average, arithmetic mean

The sum of the data values divided by the number of values; for a frequency table, $\bar{x} = \frac{\sum f x}{n}$.

Introduced in 4.3 Measures of central tendency and dispersion

Mean pointalso (x̄, ȳ)

The point $(\bar{x}, \bar{y})$ whose coordinates are the means of the two variables in a set of bivariate data. Every regression line and every good line of best fit passes through it.

Introduced in 4.4 Linear correlation and regression

Measure of central tendencyalso measure of location

A single value that represents the centre or typical value of a data set: the mean, the median or the mode.

Introduced in 4.3 Measures of central tendency and dispersion

Measure of dispersionalso spread, measure of spread

A single value describing how spread out a data set is: the range, the interquartile range, the variance or the standard deviation.

Introduced in 4.3 Measures of central tendency and dispersion

Median

The middle value of a data set arranged in order; for an even number of values, the mean of the two middle values.

Introduced in 4.3 Measures of central tendency and dispersion

Median of a continuous random variableHL only

The value $m$ that splits the area under the probability density function into two halves, so that $\int_{-\infty}^{m} f(x)\,dx = 0.5$.

Introduced in 4.14 Continuous random variables

Mid-interval valuealso class midpoint, mid-point of a class

The value halfway between the lower and upper boundaries of a class interval, used to represent every value in that class.

Introduced in 4.2 Presenting data

Midpoint

The point exactly halfway along a line segment. Its coordinates are the means of the endpoints' coordinates: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)$

Modal class

The class interval with the highest frequency in grouped data (with equal class widths).

Introduced in 4.3 Measures of central tendency and dispersion

Mode

The value that occurs most often in a data set. A data set can have more than one mode, or none.

Introduced in 4.3 Measures of central tendency and dispersion

Mode of a continuous random variableHL only

The value of $x$ at which the probability density function $f(x)$ takes its greatest value on the domain.

Introduced in 4.14 Continuous random variables

Modulus (of a complex number)HL only · also absolute value of z

The distance $|z| = \sqrt{a^2 + b^2}$

Multiplicity (of a root)HL only

The number of times a factor $(x - a)$ appears in the fully factorised form of a polynomial. A root of odd multiplicity is a point where the graph crosses the $x$-axis; a root of even multiplicity is a point where it touches the axis and turns.

Introduced in 2.12 Polynomial functions

Mutually exclusive eventsalso disjoint events

Events that cannot occur together, so $P(A \cap B) = 0$ and $P(A \cup B) = P(A) + P(B)$