1 sur 9. Yvan Monka – Académie de Strasbourg – www.maths-et-tiques.fr. MATRICES Propriétés : Soit A B et C trois matrices carrées de même taille.
Yvan Monka – Académie de Strasbourg – www.maths-et-tiques.fr. TRANSLATION ET VECTEURS Soit t la translation qui envoie A sur A' B sur B' et C sur C'.
Le dénominateur d'un quotient ne doit pas être nul. Sous cette condition a
Ensembles équipotents. Soient E = {ab
Yvan Monka – Académie de Strasbourg – www.maths-et-tiques.fr Si a divise b et b divise c alors il existe deux entiers relatifs k et k' tels que b = ka ...
and d be numbers. (a
= = = ×. Page 2. 2. Yvan Monka – Académie de Strasbourg – www.maths-et-tiques.fr b) Calculons le discriminant de l'équation 2x2 ? 3x +. 9. 8. = 0 : a = 2 b =
Si a et n sont premiers entre eux alors il existe une solution x de ax ? b. (mod n)
Yvan Monka – Académie de Strasbourg – www.maths-et-tiques.fr. 1. PGCD ET NOMBRES PREMIERS c) Si b divise a alors PGCD(a ; b) = b. Démonstration de c :.
Règle 3 : simplifier des fractions. Attention à la position du « = » : a c ac a b b.
Exercise 1 Show that the inclusion-exclusion rule follows from the axioms Hint: A[B= (ABc)[B and A= (AB) [(ABc) Deal two cards A= face on the second cardg B= face on the rst cardg P(A[B) = P(A) + P(B) P(AB) Pfat least one aceg= 1 13 + 1 13? To complete this computation we will need to compute P(AB) = Pfboth cards are acesg 3
(A) (B) and (C) and (D) and Learning Objectives Essential Knowledge Mathematical Practices for AP Calculus LO 2 2B: Recognize the connection between differentiability and continuity EK 2 2B1: A continuous function may fail to be differentiable at a point in its domain MPAC 4: Connecting multiple representations MPAC 2
a b c x y Mathematical understanding and procedural skill are equally important and both are assessable using mathematical tasks of sufficient richness The Standards set grade-specific standards but do not define the intervention methods or materials necessary to support students who are well below or well above grade-level expectations
A?(B ?A) = ? 37 [2] (A?B)?(A?B) = A 38 [2] (A?B)?C ? A?C 39 [2] (A?C)?(C ?B) = ? 40 Argue that the symmetric di?erence operator does or does not always satisfy the associative property List the elements in the following sets Assume the universe is Z+: 41 {xx < 8} 42 {xx = 6?x ? 4} 43
1 Fractions Let abc and d be numbers (a) You can break up a fraction from a sum in the numerator but not in the denom-inator: a+b c = a c + b c but a b+c 6= a b + a c (b) Cancellation of the c here requires that it appears in each additive term of the numerator and denominator: ca+cb cd = c(a+b) cd = a+b d but ca+b cd 6= a+b d
understands the mathematics and may have a better chance to s?d at a less familiar task such as expanding (a + b + c)(x + y) Mathematical understanding and procedural skill are equally important and both are assessable using mathematical tasks of sufficient richness The Standards set grade-specific standards but do not define the
AP Calculus AB and AP Calculus BC Curriculum Framework, published in fall 2014. The AP Calculus AB and AP Calculus BC Course and Exam Description , which is out now, includes that curriculum framework, along with a new, unique set of exam questions.
2.1C2: Specific rules can be used to calculate derivatives for classes of functions, including polynomial, rational, power, exponential, logarithmic, trigonometric, and inverse trigonometric. Te Collee oar 1 Sample uestions AP Calculus AB/BC Exam Return to Table of Contents 2. is (A) 1 (B) 3 (C) 9 (D) nonexistent
13 Sample uestions A Calculus AB/BC Exam Return to Table of Contents 13. The temperature of a room, in degrees Fahrenheit, is modeled by , a differentiable function of the number of minutes after the thermostat is adjusted.
Mathematical Practices for AP Calculus LO 1 .1A(b): Interpret limits expressed symbolically. EK 1.1A2: The concept of a limit can be extended to include one-sided limits, limits at infinity, and infinite limits. MPAC 1: Reasoning with definitions and theorems MPAC 2 Connecting concepts MPAC 3: Implementing algebraic/computational processes MPAC