Maths AA terms: T

T

Tangent (to a curve)also tangent line

The straight line that touches a curve at a point and has the same gradient as the curve there. It is the limit of chords through that point as the second point moves towards it.

Introduced in 5.1 Limits and the derivative

Telescoping seriesHL only · also method of differences

A series whose terms can be written as differences, so that most of them cancel when added and only a few terms at the start and end remain.

Introduced in 1.11 Partial fractions

Term (of a sequence)also nth term, terms

One number in a sequence. The term in position $n$ is written $u_n$, so $u_1$ is the first term; a formula for $u_n$ in terms of $n$ is called the general term.

Introduced in 1.2 Arithmetic sequences and series

Theorem

A mathematical statement that has been proved to be true, such as Pythagoras' theorem or the binomial theorem.

Introduced in 1.6 Simple deductive proof

Theoretical probability

A probability found by reasoning about the outcomes rather than by experiment, for example $P(A) = \frac{n(A)}{n(U)}$ when all outcomes are equally likely.

Introduced in 4.5 Concepts of probability

Total distance travelledalso distance travelled

The total length of path covered by a particle, counting motion in both directions as positive: $\int_{t_1}^{t_2} |v|\,dt$

Transformation (of a graph)also transformations

A change that moves, flips or resizes a graph by applying a rule to every point on it, such as a translation, a reflection or a stretch.

Introduced in 2.11 Transformations of graphs

Translationalso shift

A transformation that slides every point of a graph the same distance in the same direction, without changing its shape. A translation by the vector $\binom{a}{b}$ maps $y = f(x)$ to $y = f(x - a) + b$

Tree diagramalso probability tree

A diagram of branches showing the outcomes of successive trials and their probabilities. Probabilities are multiplied along a path and added between paths.

Introduced in 4.6 Venn diagrams, tree diagrams and combined events

Trialalso experiment

A single performance of an experiment whose result is uncertain, such as one roll of a die or one toss of a coin.

Introduced in 4.5 Concepts of probability

Triangular formHL only · also row echelon form, echelon form

The form of a system after row reduction in which each equation has fewer unknowns than the one before, for example the last equation contains only $z$, so the system can be solved by back substitution.

Introduced in 1.16 Systems of linear equations

Triangulation

Finding a distance or position that cannot be measured directly by measuring angles from the two ends of a baseline of known length and solving the triangle formed.

Introduced in 3.3 Applications of trigonometry

Trigonometric equationalso trig equation

An equation involving circular functions of an unknown angle, such as $2\sin x = 1$. It usually has infinitely many solutions, so it is solved on a stated interval.

Introduced in 3.8 Solving trigonometric equations

Trigonometric ratioalso sine, cosine, tangent ratio, SOH CAH TOA

For an acute angle $\theta$ in a right-angled triangle, one of $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

Trigonometric substitutionHL only

A substitution such as $x = a\sin\theta$ or $x = a\tan\theta$ that turns $\sqrt{a^2 - x^2}$

Two-way tablealso contingency table

A table of frequencies classified by two categories at once, with row and column totals, used to find probabilities of combined and conditional events.

Introduced in 4.6 Venn diagrams, tree diagrams and combined events