Comprehensive guide to Terminale speciality mathematics, covering logic, algorithms, sequences, limits, continuity, differentiability, and more.
Extract
[...] = Assign a value CHAPTER 1 : Sequences - def of a sequence: explicit formula, def implicit, by recurrence relation (un+1 = - graphical representation of a sequence ? on an axis ? in a plane ? recurrence relation: stair steps as a function of f and y=x - monotonicity of a sequence ? increasing: un un+1 ? decreasing: unun+1 ? monotone : increasing or decreasing ? constant : un = un+1 - study the monotony of a sequence ? sign of un+1 - un ? [...]
[...] distance of a point A yA ; zA) au plan P = the length AH where H is the orthogonal projection of A on P ? mediator plan: set of points equidistant from 2 planes - intersection ? of 2 planes: solve the system with 2 cartesian equations ? of a line and a plane: solve the system with 1 parametric representation of the line and 1 cartesian equation of the plane ? of 2 lines: solve the system with 2 parametric representations ? all their common points: confused ? no common point: strictly parallel ? a common point: secant ? [...]
[...] the norm is ? if or if then k ? properties of multiplication by a real - colinear vectors ? colinearity: colinear if or ? 2 non-zero vectors are collinear if they have the same direction ? zero vector is collinear with any vector ? and M are aligned if colinear (i.e. ) ? O point of space and vector not equal to zero: line D passing through O and directed by is the set of points M such that the vectors and colinear ? [...]
[...] possibility of an infinity of outcomes ? event = any subset of the universe ? elementary event = a single possibility ? impossible event = never occurs = ? certain event = always occurs = ? ? set of events: ? operations on events ? A or B ? A and B ? contrary to 1 ? A but not B ? incompatible events ? A implies B when A is included in B ? A and B are incompatible when - probability ? [...]
[...] f is differentiable to the right if THERE IS and it is FINISHED ? f differentiable on the left if THERE IS and it is FINISHED - theorem: differentiability at a point ? f differentiable at a if f differentiable on the left and on the right at a AND that = ? in this case: = = - interpretation graphique ? tangent at a point: ? if f is differentiable at a : the line passing through and with slope is the tangent at the point with abscissa a ? [...]
