Maths AI terms: U

U

Unbiased estimate of the population varianceHL only · also s²ₙ₋₁, s_{n-1}^2, Bessel's correction, unbiased estimate of variance, unbiased variance

The value $s_{n-1}^2 = \frac{\sum f_i (x_i - \bar{x})^2}{n - 1} = \frac{n}{n-1}s_n^2$, calculated from a sample of size $n$, whose estimator has expected value equal to the population variance $\sigma^2$.

Introduced in 4.14 Linear transformations of random variables

Unbiased estimatorHL only · also unbiased, unbiased estimate, unbiased estimators

An estimator whose expected value equals the population parameter it estimates, so that over all possible samples it neither overestimates nor underestimates on average.

Introduced in 4.14 Linear transformations of random variables

UndampedHL only · also no damping, undamped oscillation, free oscillation

Describes a system $\ddot{x} + bx = 0$ with $b > 0$ and no damping term, whose auxiliary equation has purely imaginary roots $\pm\sqrt{b}\,\mathrm{i}$

UnderdampedHL only · also under-damped, underdamping, lightly damped, damped oscillation

Describes a damped system $\ddot{x} + a\dot{x} + bx = 0$ whose auxiliary equation has complex roots with negative real part ($a^2 < 4b$

Underestimatealso underestimates, under-estimate, too small an estimate

An approximation that is less than the true value it approximates.

Introduced in 5.8 The trapezoidal rule

Uniform average rateHL only · also constant average rate, constant rate, uniform rate, constant mean rate

The property that the mean number of events per unit of time or space stays the same throughout the period or region being modelled, so that the mean number in any interval is proportional to the interval's size.

Introduced in 4.17 The Poisson distribution

Unionalso A ∪ B, or, unions

The event $A \cup B$ that $A$ occurs or $B$ occurs or both occur; it contains every outcome that is in $A$, in $B$ or in both.

Introduced in 4.6 Combined events

Unique solutionalso unique solutions, exactly one solution, one solution

A single set of values of the unknowns that satisfies every equation in a system, with no other set of values doing so.

Introduced in 1.8 Equations and systems using technology

Unit circleHL only · also unit circles

The circle of radius 1 with its centre at the origin of a coordinate grid.

Introduced in 3.8 The unit circle and trigonometric equations

Unit squareHL only · also unit squares

The square with vertices $(0, 0)$, $(1, 0)$, $(1, 1)$ and $(0, 1)$

Unit vectorHL only · also unit vectors, v̂, v hat

A vector with magnitude 1.

Introduced in 3.10 Vectors

Universal setalso U

The set of everything being considered in a problem, written $U$; in probability it is the sample space, the set of all possible outcomes.

Introduced in 4.6 Combined events

Unstable equilibriumHL only · also unstable, source, repeller, unstable equilibrium point

An equilibrium point from which trajectories starting close to it move away as $t$ increases; for $\dot{\boldsymbol{x}} = M\boldsymbol{x}$ this happens when at least one eigenvalue is positive or the eigenvalues are complex with positive real part.

Introduced in 5.17 Phase portraits

Unstructured questionHL only · also open question, open-ended question, unstructured questions, open questions

A question that the respondent answers freely in their own words, with no answer options given.

Introduced in 4.12 Data collection and reliability

Upper boundalso upper bounds, greatest possible value

The boundary above which a number would no longer round to the recorded value; for a value rounded to the nearest unit $u$, it is the rounded value plus $\frac{u}{2}$, and the true value is strictly less than it.

Introduced in 1.6 Approximation and error

Upper class boundaryalso class boundary, class boundaries, upper boundary, upper class boundaries

The value at the top end of a class interval, which is the boundary it shares with the next class.

Introduced in 4.2 Presenting data

Upper quartilealso Q3, Q₃, third quartile

The value below which three quarters (75%) of the data lie when the data are arranged in order; it is written $Q_3$.

Introduced in 4.2 Presenting data

Use of mathematicsalso criterion E, use of mathematics criterion

Criterion E of the exploration, worth 6 marks, which assesses whether the mathematics is relevant to the aim and at the level of the course, how correct it is, and how much knowledge and understanding of it the student demonstrates; it has separate SL and HL versions.