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 −b
2a⇒ 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}
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller mamoudoubakaryastaharam. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.16. You're not tied to anything after your purchase.