Aritmetica si Algebra

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Multimi numericeIn acest capitol definim si prezentam multimile numerice , si anume : 1 Multimea numerelor naturale ; 2 Multimea numerelor intregi ; 3 Multimea numerelor rationale ; 4 Multimea numerelor irationale ; 5 Multimea numerelor reale .

Multimea numerelor naturaleIn acest capitol definim si prezentam numerele naturale , multimea numerelor naturale precum si urmatoarele : aproximarea prin lipsa sau prin adaos a numerelor naturale , reprezentarea numerelor naturale pe axa , compararea numerelor naturale , scrierea numerelor naturale in baza 10 , operatii cu numere naturale si ordinea efectuarii operatiilor , impartirea cu rest a numerelor naturale , divizibilitatea numerelor naturale , proprietati ale relatiei de divizibilitate , multiplu unui numar natural , criterii de divizibilitate , numere prime , numere compuse , numere neprime , numere pare , numere impare , numere prime intre ele , puteri si operatii cu puteri in multimea numerelor naturale , descompunerea unui numar natural compus in produs de puteri de numere prime , descompunerea in factori primi , cel mai mare divizor comun , cel mai mic multiplu comun , media aritmetica a doua sau mai multe numere naturale .

Puteri . Calcule cu puteriIn acest capitol studiem puteri ale numerelor reale , calcule cu puteri si proprietati ale puterilor . Clasificam puterile astfel : 1 Puteri cu exponent natural ; 2 Puteri cu exponent intreg ; 3 Puteri cu exponent rational .

Multimea numerelor irationale . RadicaliIn acest capitol prezentam multimea numerelor irationale . Definim notiunea de numar irational si radical de ordinul doi . Capitolul cuprinde urmatoarele : 1. Radacina patrata a unui numar natural patrat perfect ; 2. Extragerea radacinii patrate dintr-un numar rational pozitiv - algoritmul de extragere a radacinii patrate ; 3. Scrierea unui numar real pozitiv ca radical din patratul sau ; 4. Reguli de calcul cu radicali ; 5. Introducerea factorilor sub radical ; 6. Scoaterea factorilor de sub radical ; 7. Rationalizarea numitorului unei fractii ce , contine expresii cu radicali ; 8. Formula radicalilor compusi ; 9. Ordinea efectuarii operatiilor ; 10. Factor comun ; 11. Exercitii propuse si rezolvate cu radicali .

MediiIn acest capitol definim si prezentam notiunea de medii , si anume : 1 Media aritmetica ; 2 Media aritmetica ponderata ; 3 Media geometrica ; 4 Media armonica . Capitolul cuprinde exercitii propuse si rezolvate cu medii .

Rapoarte . Procente . ProportiiIn acest capitol definim si prezentam notiunile : 1 Rapoarte ; 2 Probabilitati ; 3 Procente ; 4 Proportii ; 5 Sir de rapoarte egale ; 6 Marimi direct proportionale ; 7 Marimi invers proportionale ; 8 Regula de trei simpla . Capitolul curpinde exercitii propuse si rezolvate cu notiunile prezentate anterior .

Calcul algebricIn acest capitol definim si prezentam calculul algebric : calcul cu numere reale reprezentate prin litere .

FunctiiIn acest capitol al functiilor definim , prezentam si studiem : 1. Sistem de axe de coordonate - reper cartezian ; 2. Notiunea de functie ; 3. Moduri de definire a unei functii ; 4. Functii egale si numarul de functii ; 5. Graficul unei functii - definitie graficul unei functii , proprietatile graficului unei functii , intersectia graficului unei functii cu axele de coordonate , conditia ca un punct sa apartina graficului unei functii , reprezentarea grafica a unei functii ; 6. Functia de gradul 1 - definitie , graficul functiei de gradul 1 , determinarea formulei unei functii de gradul 1 cand cunoastem doua puncte care apartin graficului , intersectia graficelor a doua functii de gradul 1 .

EcuatiiIn acest capitol definim , prezentam si studiem ecuatii . Capitolul ecuatii contine : 1 Ecuatii cu o necunoscuta - definitii , caracteristici , ecuatii echivalente ; 2 Ecuatia de gradul intai ; 3 Ecuatia de gradul doi . Capitolul ecuatii cuprinde exemple propuse si rezolvate de ecuatii studiate .