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Cours mathématiques terminale A4
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MATHS Terminale A4 Table des matières CHAPITRE I : EQUATIONS -INEQUATIONS, SYSTEMES ................................ ................................ .............. 2 I. équation et inéquation du type : 𝒂𝒙+𝒃 (1er degré) ................................ ................................ ...... 2 A- équations ................................ ................................ ................................ ................................ ......... 2 B- inéquations ................................ ................................ ................................ ................................ ...... 3 C- équation et inéqu ation du second degré ................................ ................................ ........................ 5 D- équations et inéquations du degré 3 (ordre 3) ................................ ................................ ............... 9 E- équations et inéquations bicarrées ................................ ................................ ............................... 12 E1. équations bicarrées ................................ ................................ ................................ ......................... 12 F- équatio ns et inéquations liant deux fractions rationnelles ................................ ........................... 15 CHAPITRE 2 : ETUDE DE FONCTION ................................ ................................ ................................ ....... 17 I. Rappels sur la Notion de limites et de continuité ................................ ................................ ......... 17 II. notion de dérivée ................................ ................................ ................................ .......................... 25 III. étude d e fonction ................................ ................................ ................................ ...................... 31 A- parité : ................................ ................................ ................................ ................................ ........... 31 B. fonction logarithme népérien ................................ ................................ ................................ ....... 32 C. fonction exponentielle ................................ ................................ ................................ .................. 37 IV. Equation – Inéquations ................................ ................................ ................................ ............. 38 V. étude graphique de la fonction exponentielle ................................ ................................ .............. 39 CHAPITRE 3 : PROBABILITE ................................ ................................ ................................ .................... 41 I. dénom brement ................................ ................................ ................................ ............................. 41 II. Outils d’Analyse Combinatoire ................................ ................................ ................................ ...... 42 III. probabilité ................................ ................................ ................................ ................................ . 44 Bibliographie ................................ ................................ ................................ ................................ ............ 1 2 CHAPITRE I : EQUATIONS -INEQUATIONS, SYSTEMES I. équation et inéquation du type : 𝒂𝒙+𝒃 (1er degré) A- équations Une équation de la forme 𝑎𝑥+𝑏=0, où a et b sont des nombres réels est appelée équation du 1er degré ou équation d’ordre 1.Cette équation admet : Une solution unique si 𝑎≠0 Cette solution est −b2a⇒ 𝐒= {−𝐛
𝟐𝐚} Aucune solution si 𝑎=0 𝑒𝑡 𝑏≠0 ⇒ 𝑺=ф Exemple : Résoudre dans IR les équations suivantes : 𝑎) −3𝑥+2=0 𝑏) 𝑥+1=𝑥−2 𝑐) 4𝑥+6=0 𝑑) 3𝑥−1=0 𝑒) 2(𝑥−1) +3(𝑥+1) =𝑥−1 Solution a)−3x+2=0 ⇒ −3x= −2 ⇒ x= −2
3 ⇒ x= 2
3 ⇒ 𝑏) 𝑥 +1=𝑥−2 ⇒ 𝑥−𝑥+1−2=0 ⇒ 0𝑥−1=0; 𝑎=0⇒ c) 4𝑥+6=0 ⇒ 4𝑥= −6 ⇒ 𝑥 = −6
4 ⇒ 𝑥=−3 2⇒ d) 3𝑥−1=0 ⇒ 3𝑥=1 ⇒ 𝑋= 1 3 ⇒ 𝑒)
{ 2(𝑥−1) + 3(𝑥−1) = 𝑥−1 ⇒2𝑥−2+3𝑥−1= 𝑥−1
⇒5𝑥−𝑥−3+1=0
⇒4𝑥−2=0 4𝑥=2 𝑥=2 4 𝑥 = 1 2 𝐒= { 𝟐
𝟑 } S= ф S = {−3 2} S = { 1 3 } S = {1
2}
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