Maths AA terms: R

R

Radianalso rad, radians

The angle at the centre of a circle subtended by an arc whose length equals the radius. A full turn is $2\pi$ radians, so $\pi \text{ radians} = 180°$.

Introduced in 3.4 Radians, arcs and sectors

Range (of a function)

The set of all output values that a function actually takes when $x$ runs through the whole domain.

Introduced in 2.2 Functions, domain, range and inverse

Range (of data)

The difference between the largest and smallest values in a data set.

Introduced in 4.3 Measures of central tendency and dispersion

Rate of changealso rates of change

How fast one quantity changes compared with another, measured in units of the first quantity per unit of the second (for example metres per second). On a graph it is a gradient.

Introduced in 5.1 Limits and the derivative

Rational exponentalso fractional exponent, fractional index

An exponent that is a fraction $\frac{m}{n}$. It means a root followed by a power: $a^{m/n} = \left(\sqrt[n]{a}\right)^m = \sqrt[n]{a^m}$

Rational function

A function that can be written as a quotient of two polynomials, $f(x) = \frac{p(x)}{q(x)}$, where $q(x)$

Real partHL only · also Re(z)

For $z = a + b\mathrm{i}$ with $a, b \in \mathbb{R}$, the real number $a$, written $\mathrm{Re}(z)$

Real valuealso real terms, purchasing power

The value of an amount of money measured by what it can buy, after allowing for inflation, rather than by the number written on it.

Introduced in 1.4 Financial applications of geometric sequences

Reciprocal functionalso f(x) = 1/x

The function $f(x) = \frac{1}{x}$, $x \neq 0$

Reciprocal trigonometric functionsHL only · also sec, cosec, cot, secant, cosecant, cotangent

The functions $\sec\theta = \frac{1}{\cos\theta}$, $\operatorname{cosec}\theta = \frac{1}{\sin\theta}$

Recurring decimalalso repeating decimal

A decimal in which a digit or block of digits repeats forever, such as $0.\dot{3} = 0.333\ldots$ or $0.\dot{1}\dot{2} = 0.1212\ldots$

Recursive formulaalso recurrence relation, term-to-term rule

A rule that gives each term of a sequence from the term before it, such as $u_{n+1} = u_n + 3$, together with a starting value such as $u_1 = 2$

Reflectionalso reflections

A transformation that flips a graph in a mirror line. $y = -f(x)$ is the reflection of $y = f(x)$ in the $x$-axis, and $y = f(-x)$

Regression linealso line of best fit, least squares regression line, regression line of y on x

The least squares line $y = ax + b$ that makes the sum of the squares of the vertical distances from the data points to the line as small as possible. It passes through the mean point $(\bar{x}, \bar{y})$

Regression line of x on yalso x on y line

The least squares line $x = cy + d$ that minimises the sum of the squares of the horizontal distances from the data points to the line. It is used to predict $x$ from a given value of $y$.

Introduced in 4.10 Regression of x on y

Related anglealso reference angle, related acute angle

The acute angle between the radius to a point on the unit circle and the $x$-axis. Angles with the same related angle have trigonometric ratios equal in size, differing at most in sign.

Introduced in 3.5 The unit circle

Related rates of changeHL only · also related rates, connected rates of change

Rates of change of two or more quantities that are linked by an equation, usually all with respect to time $t$. One rate is found from another with the chain rule, for example $\frac{dV}{dt} = \frac{dV}{dr} \times \frac{dr}{dt}$

Relative frequencyalso experimental probability

The number of times an event occurs divided by the number of trials. It is used as an estimate of the probability of the event.

Introduced in 4.5 Concepts of probability

Remainder theoremHL only

When a polynomial $P(x)$ is divided by $(x - a)$, the remainder is $P(a)$. When it is divided by $(ax - b)$

Repeated rootalso equal roots, double root

A root that occurs twice, as in $a(x - h)^2 = 0$, which happens exactly when $\Delta = 0$. The graph touches the $x$

Residualalso residuals

The difference between an observed value and the value predicted by a regression line, $y - \hat{y}$ for the line of $y$ on $x$; on a scatter diagram it is the vertical distance from a point to the line.

Introduced in 4.4 Linear correlation and regression

Restricted domainHL only

A domain chosen as part of the largest possible one, usually so that a many-to-one function becomes one-to-one and has an inverse, for example $f(x) = x^2$, $x \ge 0$.

Introduced in 2.14 Odd, even and self-inverse functions

Riemann sumalso sum of rectangles, lower sum, upper sum

A sum of areas of thin rectangles, $\sum f(x_i)\,\delta x$, that approximates the area under a curve. As the rectangles become narrower, the sum tends to the definite integral.

Introduced in 5.5 Introduction to integration

Right conealso cone, slant height

A cone whose apex lies directly above the centre of its circular base. Its slant height $l$, from the apex to the rim, satisfies $l^2 = r^2 + h^2$

Right pyramid

A pyramid whose apex lies directly above the centre of its base, so the line from the apex to that centre is perpendicular to the base. Its volume is $V = \frac{1}{3}Ah$.

Introduced in 3.1 Distance, midpoint, volume and surface area

Right-hand ruleHL only

A way to find the direction of $\boldsymbol{v} \times \boldsymbol{w}$: with the fingers of the right hand curling from $\boldsymbol{v}$ towards $\boldsymbol{w}$, the thumb points along $\boldsymbol{v} \times \boldsymbol{w}$

Roots of unityHL only · also nth roots of unity

The $n$ solutions of $z^n = 1$, given by $z = \mathrm{e}^{2k\pi\mathrm{i}/n}$

Row reductionHL only · also Gaussian elimination, elimination, row operations

Solving a system of linear equations by swapping equations, multiplying an equation by a non-zero constant and adding a multiple of one equation to another, until the unknowns can be found one at a time.

Introduced in 1.16 Systems of linear equations