Maths AA terms: B

B

Back substitutionHL only

Solving a system in triangular form by finding the unknown in the last equation first, then substituting it into the equations above it in turn.

Introduced in 1.16 Systems of linear equations

Base (of a power)also base

The number that is raised to an exponent. In $a^n$ the base is $a$; in $\log_a b$ the base $a$ is the number being raised to a power, with $a > 0$ and $a \neq 1$.

Introduced in 1.5 Exponents and introduction to logarithms

Base caseHL only · also basis step

The first step of a proof by induction: a direct check that the statement $P(n)$ is true for the smallest value of $n$ it claims, usually $n = 1$.

Introduced in 1.15 Proof by induction, contradiction and counterexample

Base vectorsHL only · also i j k, standard basis vectors

The unit vectors $\boldsymbol{i}$, $\boldsymbol{j}$ and $\boldsymbol{k}$ in the positive directions of the $x$-, $y$- and $z$

Bayes' theoremHL only · also Bayes' rule

A formula that reverses a conditional probability: $P(B \mid A) = \frac{P(B)P(A \mid B)}{P(B)P(A \mid B) + P(B')P(A \mid B')}$

Bearingalso three-figure bearing

The direction of one point from another, given as an angle measured clockwise from north and written with three digits, such as $045°$ or $210°$.

Introduced in 3.3 Applications of trigonometry

Bernoulli trialalso success, failure

A single random trial with exactly two possible outcomes, called success (with probability $p$) and failure (with probability $1 - p$).

Introduced in 4.8 The binomial distribution

Biasalso sampling bias

A systematic tendency for a sample or a method of collecting data to give results that differ from the true values for the population in the same direction.

Introduced in 4.1 Populations, samples and sampling

Binomialalso binomial expression

An algebraic expression with exactly two terms, such as $a + b$, $2x - 3$ or $x^2 + \frac{1}{x}$

Binomial coefficientalso nCr, n choose r

The number $\binom{n}{r} = {}^nC_r = \frac{n!}{r!(n-r)!}$

Binomial distributionalso B(n, p)

The distribution of the number of successes $X$ in $n$ independent trials, each with the same probability of success $p$. Written $X \sim B(n, p)$, with $P(X = r) = \binom{n}{r}p^r(1 - p)^{n - r}$

Binomial theoremalso binomial expansion

The result $(a+b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r$

Bivariate data

Data in which two variables are measured or recorded for each individual or item, giving pairs of values $(x, y)$ that can be plotted and compared.

Introduced in 4.4 Linear correlation and regression

Boundary condition

A known value of a function, such as a point on its graph, used to find the constant of integration and so pick out one antiderivative from the family $F(x) + C$.

Introduced in 5.5 Introduction to integration

Box-and-whisker diagramalso box plot

A diagram of a data set drawn on a scale: a box from $Q_1$ to $Q_3$ with a line at the median, and whiskers to the smallest and largest values that are not outliers.

Introduced in 4.2 Presenting data