diff --git a/2nd/03_Calcul_litteral/1_exercises.tex b/2nd/03_Calcul_litteral/1_exercises.tex index 1769ca6..8413f6c 100644 --- a/2nd/03_Calcul_litteral/1_exercises.tex +++ b/2nd/03_Calcul_litteral/1_exercises.tex @@ -3,15 +3,15 @@ \begin{multicols}{2} \begin{enumerate} - \item $A = 3x - 7 + 10x - 6$ - \item $B = - 7t - 3 - 10t - 4t$ - \item $C = 8t - 4 - 3t - 8t$ - \item $D = - 9x + 2 + 9x - 4$ - \item $E = 6t - 4 + 4t + 4 + 6t$ - \item $F = \dfrac{- 3}{3} + 4a - 7a - 2$ - \item $G = 8x^{2} + 10 + 9x^{2} - 3 - 6x^{2}$ - \item $H = - 8x + 10 - 4x^{2} - 5 + 4x^{2}$ - \item $I = 5x - 3 + 3x^{2} - 5x - 7x^{2}$ + \item $A = - 6x - 7 + 10x + 3$ + \item $B = - 4t - 3 - 10t - 7t$ + \item $C = - 8t - 4 - 3t + 8t$ + \item $D = 4x + 5 - 4x - 9$ + \item $E = - 7t + 9 + 2t - 9 - 4t$ + \item $F = \dfrac{- 9}{9} + 9a + 4a + 8$ + \item $G = 6x^{2} + 4 - 2x^{2} + 4 - 5x^{2}$ + \item $H = - 9x - 10 - 3x^{2} + 5 - 4x^{2}$ + \item $I = - 9x - 5 + 7x^{2} + 9x + 9x^{2}$ \end{enumerate} \end{multicols} \end{exercise} @@ -21,55 +21,55 @@ \begin{enumerate} \item \begin{align*} - A & = 3x - 7 + 10x - 6 \\ & = 3x - 7 + 10x - 6 \\ & = 3x + 10x - 7 - 6 \\ & = (3 + 10) \times x - 13 \\ & = 13x - 13 + A & = - 6x - 7 + 10x + 3 \\ & = - 6x - 7 + 10x + 3 \\ & = - 6x + 10x - 7 + 3 \\ & = (- 6 + 10) \times x - 4 \\ & = 4x - 4 \end{align*} \item \begin{align*} - B & = - 7t - 3 - 10t - 4t \\ & = - 7t - 3 + (- 10 - 4) \times t \\ & = - 7t - 3 - 14t \\ & = - 7t - 14t - 3 \\ & = (- 7 - 14) \times t - 3 \\ & = - 21t - 3 + B & = - 4t - 3 - 10t - 7t \\ & = - 4t - 3 + (- 10 - 7) \times t \\ & = - 4t - 3 - 17t \\ & = - 4t - 17t - 3 \\ & = (- 4 - 17) \times t - 3 \\ & = - 21t - 3 \end{align*} \item \begin{align*} - C & = 8t - 4 - 3t - 8t \\ & = 8t - 4 + (- 3 - 8) \times t \\ & = 8t - 4 - 11t \\ & = 8t - 11t - 4 \\ & = (8 - 11) \times t - 4 \\ & = - 3t - 4 + C & = - 8t - 4 - 3t + 8t \\ & = - 8t - 4 + (- 3 + 8) \times t \\ & = - 8t - 4 + 5t \\ & = - 8t + 5t - 4 \\ & = (- 8 + 5) \times t - 4 \\ & = - 3t - 4 \end{align*} \item \begin{align*} - D & = - 9x + 2 + 9x - 4 \\ & = - 9x + 2 + 9x - 4 \\ & = - 9x + 9x + 2 - 4 \\ & = (- 9 + 9) \times x - 2 \\ & = 0x - 2 \\ & = - 2 + D & = 4x + 5 - 4x - 9 \\ & = 4x + 5 - 4x - 9 \\ & = 4x - 4x + 5 - 9 \\ & = (4 - 4) \times x - 4 \\ & = 0x - 4 \\ & = - 4 \end{align*} \item \begin{align*} - E & = 6t - 4 + 4t + 4 + 6t \\ & = 6t - 4 + (4 + 6) \times t + 4 \\ & = 6t - 4 + 4 + 10t \\ & = (6 + 10) \times t + 0 \\ & = 16t + E & = - 7t + 9 + 2t - 9 - 4t \\ & = - 7t + 9 + (2 - 4) \times t - 9 \\ & = - 7t + 9 - 9 - 2t \\ & = (- 7 - 2) \times t + 0 \\ & = - 9t \end{align*} \item \begin{align*} - F & = \dfrac{- 3}{3} + 4a - 7a - 2 \\ & = 4a + \dfrac{- 3}{3} - 7a - 2 \\ & = 4a - 7a + \dfrac{- 3}{3} - 2 \\ & = (4 - 7) \times a + \dfrac{- 3}{3} + \dfrac{- 2}{1} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 2 \times 3}{1 \times 3} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 6}{3} \\ & = - 3a + \dfrac{- 3}{3} + \dfrac{- 6}{3} \\ & = - 3a + \dfrac{- 3 - 6}{3} \\ & = - 3a + \dfrac{- 9}{3} + F & = \dfrac{- 9}{9} + 9a + 4a + 8 \\ & = 9a + \dfrac{- 9}{9} + 4a + 8 \\ & = 9a + 4a + \dfrac{- 9}{9} + 8 \\ & = (9 + 4) \times a + \dfrac{- 9}{9} + \dfrac{8}{1} \\ & = 13a + \dfrac{- 9}{9} + \dfrac{8 \times 9}{1 \times 9} \\ & = 13a + \dfrac{- 9}{9} + \dfrac{72}{9} \\ & = 13a + \dfrac{- 9}{9} + \dfrac{72}{9} \\ & = 13a + \dfrac{- 9 + 72}{9} \\ & = 13a + \dfrac{63}{9} \end{align*} \item \begin{align*} - G & = 8x^{2} + 10 + 9x^{2} - 3 - 6x^{2} \\ & = 8x^{2} + 10 + (9 - 6) \times x^{2} - 3 \\ & = 8x^{2} + 10 - 3 + 3x^{2} \\ & = (8 + 3) \times x^{2} + 7 \\ & = 11x^{2} + 7 + G & = 6x^{2} + 4 - 2x^{2} + 4 - 5x^{2} \\ & = 6x^{2} + 4 + (- 2 - 5) \times x^{2} + 4 \\ & = 6x^{2} + 4 + 4 - 7x^{2} \\ & = (6 - 7) \times x^{2} + 8 \\ & = - x^{2} + 8 \end{align*} \item \begin{align*} - H & = - 8x + 10 - 4x^{2} - 5 + 4x^{2} \\ & = - 4x^{2} - 8x + 10 - 5 + 4x^{2} \\ & = - 4x^{2} + 4x^{2} - 8x + 10 - 5 \\ & = (- 4 + 4) \times x^{2} - 8x + 5 \\ & = - 8x + 5 + H & = - 9x - 10 - 3x^{2} + 5 - 4x^{2} \\ & = - 3x^{2} - 9x - 10 + 5 - 4x^{2} \\ & = - 3x^{2} - 4x^{2} - 9x - 10 + 5 \\ & = (- 3 - 4) \times x^{2} - 9x - 5 \\ & = - 7x^{2} - 9x - 5 \end{align*} \item \begin{align*} - I & = 5x - 3 + 3x^{2} - 5x - 7x^{2} \\ & = 3x^{2} + 5x - 3 - 5x - 7x^{2} \\ & = 3x^{2} - 7x^{2} + 5x - 5x - 3 \\ & = (3 - 7) \times x^{2} + (5 - 5) \times x - 3 \\ & = - 4x^{2} - 3 + I & = - 9x - 5 + 7x^{2} + 9x + 9x^{2} \\ & = 7x^{2} - 9x - 5 + 9x + 9x^{2} \\ & = 7x^{2} + 9x^{2} - 9x + 9x - 5 \\ & = (7 + 9) \times x^{2} + (- 9 + 9) \times x - 5 \\ & = 16x^{2} - 5 \end{align*} \end{enumerate} \end{multicols} \end{solution} \begin{exercise}[subtitle={Développer 1 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] - Réduire les expressions suivantes + Développer puis réduire les expressions suivantes \begin{multicols}{2} \begin{enumerate} - \item $A = 10(- 8x + 8)$ - \item $B = 7(- 4 + 8t)$ - \item $C = t(3 + 7t)$ - \item $D = - 9x(7x - 3)$ - \item $E = 5x(10x - 5)$ - \item $F = \dfrac{9}{4} \times x(2x + 8)$ + \item $A = - 6(3x - 7)$ + \item $B = - 6(- 7 + 3t)$ + \item $C = t(7 - 5t)$ + \item $D = 10x(4x + 7)$ + \item $E = - 3x(- 5x - 4)$ + \item $F = \dfrac{2}{10} \times x(2x + 9)$ \end{enumerate} \end{multicols} \end{exercise} @@ -79,45 +79,45 @@ \begin{enumerate} \item \begin{align*} - A & = 10(- 8x + 8) \\ & = 10 \times - 8x + 10 \times 8 \\ & = 10(- 8) \times x + 80 \\ & = - 80x + 80 + A & = - 6(3x - 7) \\ & = - 6 \times 3x - 6(- 7) \\ & = - 6 \times 3 \times x + 42 \\ & = - 18x + 42 \end{align*} \item \begin{align*} - B & = 7(- 4 + 8t) \\ & = 7 \times 8t + 7(- 4) \\ & = 7 \times 8 \times t - 28 \\ & = 56t - 28 + B & = - 6(- 7 + 3t) \\ & = - 6 \times 3t - 6(- 7) \\ & = - 6 \times 3 \times t + 42 \\ & = - 18t + 42 \end{align*} \item \begin{align*} - C & = t(3 + 7t) \\ & = t \times 7t + t \times 3 \\ & = 7t^{2} + 3t + C & = t(7 - 5t) \\ & = t \times - 5t + t \times 7 \\ & = - 5t^{2} + 7t \end{align*} \item \begin{align*} - D & = - 9x(7x - 3) \\ & = - 9x \times 7x - 9x(- 3) \\ & = - 9 \times 7 \times x^{1 + 1} - 3(- 9) \times x \\ & = - 63x^{2} + 27x + D & = 10x(4x + 7) \\ & = 10x \times 4x + 10x \times 7 \\ & = 10 \times 4 \times x^{1 + 1} + 7 \times 10 \times x \\ & = 40x^{2} + 70x \end{align*} \item \begin{align*} - E & = 5x(10x - 5) \\ & = 5x \times 10x + 5x(- 5) \\ & = 5 \times 10 \times x^{1 + 1} - 5 \times 5 \times x \\ & = 50x^{2} - 25x + E & = - 3x(- 5x - 4) \\ & = - 3x \times - 5x - 3x(- 4) \\ & = - 3(- 5) \times x^{1 + 1} - 4(- 3) \times x \\ & = 15x^{2} + 12x \end{align*} \item \begin{align*} - F & = \dfrac{9}{4} \times x(2x + 8) \\ & = \dfrac{9}{4} \times x \times 2x + \dfrac{9}{4} \times x \times 8 \\ & = \dfrac{9}{4} \times 2 \times x^{1 + 1} + 8 \times \dfrac{9}{4} \times x \\ & = \dfrac{9 \times 2}{4} \times x^{2} + \dfrac{8 \times 9}{4} \times x \\ & = \dfrac{18}{4} \times x^{2} + \dfrac{72}{4} \times x + F & = \dfrac{2}{10} \times x(2x + 9) \\ & = \dfrac{2}{10} \times x \times 2x + \dfrac{2}{10} \times x \times 9 \\ & = \dfrac{2}{10} \times 2 \times x^{1 + 1} + 9 \times \dfrac{2}{10} \times x \\ & = \dfrac{2 \times 2}{10} \times x^{2} + \dfrac{9 \times 2}{10} \times x \\ & = \dfrac{4}{10} \times x^{2} + \dfrac{18}{10} \times x \end{align*} \end{enumerate} \end{multicols} \end{solution} \begin{exercise}[subtitle={Développer 2 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] - Réduire les expressions suivantes + Développer puis réduire les expressions suivantes \begin{multicols}{2} \begin{enumerate} - \item $A = (- 8x - 3)(- 7x - 10)$ - \item $B = (- 2t + 10)(2t + 6)$ - \item $C = (- 9x - 5)(3x + 4)$ - \item $D = (6x - 2)(9x + 10)$ - \item $E = (- 8x - 4)^{2}$ - \item $F = (- 8x - 10)^{2}$ - \item $G = (- 10x + 6)^{2}$ - \item $H = (\dfrac{- 6}{4} \times x - 7)^{2}$ + \item $A = (- 10x - 9)(3x - 5)$ + \item $B = (8t - 6)(4t - 2)$ + \item $C = (2x + 6)(- 6x - 7)$ + \item $D = (2x - 9)(2x + 8)$ + \item $E = (- 3x + 2)^{2}$ + \item $F = (8x + 5)^{2}$ + \item $G = (8x + 5)^{2}$ + \item $H = (\dfrac{10}{7} \times x - 10)^{2}$ \end{enumerate} \end{multicols} \end{exercise} @@ -127,35 +127,35 @@ \begin{enumerate} \item \begin{align*} - A & = (- 8x - 3)(- 7x - 10) \\ & = - 8x \times - 7x - 8x(- 10) - 3 \times - 7x - 3(- 10) \\ & = - 8(- 7) \times x^{1 + 1} - 10(- 8) \times x - 3(- 7) \times x + 30 \\ & = 80x + 21x + 56x^{2} + 30 \\ & = (80 + 21) \times x + 56x^{2} + 30 \\ & = 56x^{2} + 101x + 30 + A & = (- 10x - 9)(3x - 5) \\ & = - 10x \times 3x - 10x(- 5) - 9 \times 3x - 9(- 5) \\ & = - 10 \times 3 \times x^{1 + 1} - 5(- 10) \times x - 9 \times 3 \times x + 45 \\ & = 50x - 27x - 30x^{2} + 45 \\ & = (50 - 27) \times x - 30x^{2} + 45 \\ & = - 30x^{2} + 23x + 45 \end{align*} \item \begin{align*} - B & = (- 2t + 10)(2t + 6) \\ & = - 2t \times 2t - 2t \times 6 + 10 \times 2t + 10 \times 6 \\ & = - 2 \times 2 \times t^{1 + 1} + 6(- 2) \times t + 10 \times 2 \times t + 60 \\ & = - 12t + 20t - 4t^{2} + 60 \\ & = (- 12 + 20) \times t - 4t^{2} + 60 \\ & = - 4t^{2} + 8t + 60 + B & = (8t - 6)(4t - 2) \\ & = 8t \times 4t + 8t(- 2) - 6 \times 4t - 6(- 2) \\ & = 8 \times 4 \times t^{1 + 1} - 2 \times 8 \times t - 6 \times 4 \times t + 12 \\ & = - 16t - 24t + 32t^{2} + 12 \\ & = (- 16 - 24) \times t + 32t^{2} + 12 \\ & = 32t^{2} - 40t + 12 \end{align*} \item \begin{align*} - C & = (- 9x - 5)(3x + 4) \\ & = - 9x \times 3x - 9x \times 4 - 5 \times 3x - 5 \times 4 \\ & = - 9 \times 3 \times x^{1 + 1} + 4(- 9) \times x - 5 \times 3 \times x - 20 \\ & = - 36x - 15x - 27x^{2} - 20 \\ & = (- 36 - 15) \times x - 27x^{2} - 20 \\ & = - 27x^{2} - 51x - 20 + C & = (2x + 6)(- 6x - 7) \\ & = 2x \times - 6x + 2x(- 7) + 6 \times - 6x + 6(- 7) \\ & = 2(- 6) \times x^{1 + 1} - 7 \times 2 \times x + 6(- 6) \times x - 42 \\ & = - 14x - 36x - 12x^{2} - 42 \\ & = (- 14 - 36) \times x - 12x^{2} - 42 \\ & = - 12x^{2} - 50x - 42 \end{align*} \item \begin{align*} - D & = (6x - 2)(9x + 10) \\ & = 6x \times 9x + 6x \times 10 - 2 \times 9x - 2 \times 10 \\ & = 6 \times 9 \times x^{1 + 1} + 10 \times 6 \times x - 2 \times 9 \times x - 20 \\ & = 60x - 18x + 54x^{2} - 20 \\ & = (60 - 18) \times x + 54x^{2} - 20 \\ & = 54x^{2} + 42x - 20 + D & = (2x - 9)(2x + 8) \\ & = 2x \times 2x + 2x \times 8 - 9 \times 2x - 9 \times 8 \\ & = 2 \times 2 \times x^{1 + 1} + 8 \times 2 \times x - 9 \times 2 \times x - 72 \\ & = 16x - 18x + 4x^{2} - 72 \\ & = (16 - 18) \times x + 4x^{2} - 72 \\ & = 4x^{2} - 2x - 72 \end{align*} \item \begin{align*} - E & = (- 8x - 4)^{2} \\ & = (- 8x - 4)(- 8x - 4) \\ & = - 8x \times - 8x - 8x(- 4) - 4 \times - 8x - 4(- 4) \\ & = - 8(- 8) \times x^{1 + 1} - 4(- 8) \times x - 4(- 8) \times x + 16 \\ & = 32x + 32x + 64x^{2} + 16 \\ & = (32 + 32) \times x + 64x^{2} + 16 \\ & = 64x^{2} + 64x + 16 + E & = (- 3x + 2)^{2} \\ & = (- 3x + 2)(- 3x + 2) \\ & = - 3x \times - 3x - 3x \times 2 + 2 \times - 3x + 2 \times 2 \\ & = - 3(- 3) \times x^{1 + 1} + 2(- 3) \times x + 2(- 3) \times x + 4 \\ & = - 6x - 6x + 9x^{2} + 4 \\ & = (- 6 - 6) \times x + 9x^{2} + 4 \\ & = 9x^{2} - 12x + 4 \end{align*} \item \begin{align*} - F & = (- 8x - 10)^{2} \\ & = (- 8x - 10)(- 8x - 10) \\ & = - 8x \times - 8x - 8x(- 10) - 10 \times - 8x - 10(- 10) \\ & = - 8(- 8) \times x^{1 + 1} - 10(- 8) \times x - 10(- 8) \times x + 100 \\ & = 80x + 80x + 64x^{2} + 100 \\ & = (80 + 80) \times x + 64x^{2} + 100 \\ & = 64x^{2} + 160x + 100 + F & = (8x + 5)^{2} \\ & = (8x + 5)(8x + 5) \\ & = 8x \times 8x + 8x \times 5 + 5 \times 8x + 5 \times 5 \\ & = 8 \times 8 \times x^{1 + 1} + 5 \times 8 \times x + 5 \times 8 \times x + 25 \\ & = 40x + 40x + 64x^{2} + 25 \\ & = (40 + 40) \times x + 64x^{2} + 25 \\ & = 64x^{2} + 80x + 25 \end{align*} \item \begin{align*} - G & = (- 10x + 6)^{2} \\ & = (- 10x + 6)(- 10x + 6) \\ & = - 10x \times - 10x - 10x \times 6 + 6 \times - 10x + 6 \times 6 \\ & = - 10(- 10) \times x^{1 + 1} + 6(- 10) \times x + 6(- 10) \times x + 36 \\ & = - 60x - 60x + 100x^{2} + 36 \\ & = (- 60 - 60) \times x + 100x^{2} + 36 \\ & = 100x^{2} - 120x + 36 + G & = (8x + 5)^{2} \\ & = (8x + 5)(8x + 5) \\ & = 8x \times 8x + 8x \times 5 + 5 \times 8x + 5 \times 5 \\ & = 8 \times 8 \times x^{1 + 1} + 5 \times 8 \times x + 5 \times 8 \times x + 25 \\ & = 40x + 40x + 64x^{2} + 25 \\ & = (40 + 40) \times x + 64x^{2} + 25 \\ & = 64x^{2} + 80x + 25 \end{align*} \item \begin{align*} - H & = (\dfrac{- 6}{4} \times x - 7)^{2} \\ & = (\dfrac{- 6}{4} \times x - 7)(\dfrac{- 6}{4} \times x - 7) \\ & = \dfrac{- 6}{4} \times x \times \dfrac{- 6}{4} \times x + \dfrac{- 6}{4} \times x(- 7) - 7 \times \dfrac{- 6}{4} \times x - 7(- 7) \\ & = \dfrac{- 6}{4} \times \dfrac{- 6}{4} \times x^{1 + 1} - 7 \times \dfrac{- 6}{4} \times x - 7 \times \dfrac{- 6}{4} \times x + 49 \\ & = \dfrac{- 7(- 6)}{4} \times x + \dfrac{- 7(- 6)}{4} \times x + \dfrac{- 6(- 6)}{4 \times 4} \times x^{2} + 49 \\ & = \dfrac{42}{4} \times x + \dfrac{36}{16} \times x^{2} + \dfrac{42}{4} \times x + 49 \\ & = 49 + \dfrac{36}{16} \times x^{2} + \dfrac{42}{4} \times x + \dfrac{42}{4} \times x \\ & = 49 + \dfrac{36}{16} \times x^{2} + (\dfrac{42}{4} + \dfrac{42}{4}) \times x \\ & = 49 + \dfrac{36}{16} \times x^{2} + \dfrac{42 + 42}{4} \times x \\ & = \dfrac{36}{16} \times x^{2} + \dfrac{84}{4} \times x + 49 + H & = (\dfrac{10}{7} \times x - 10)^{2} \\ & = (\dfrac{10}{7} \times x - 10)(\dfrac{10}{7} \times x - 10) \\ & = \dfrac{10}{7} \times x \times \dfrac{10}{7} \times x + \dfrac{10}{7} \times x(- 10) - 10 \times \dfrac{10}{7} \times x - 10(- 10) \\ & = \dfrac{10}{7} \times \dfrac{10}{7} \times x^{1 + 1} - 10 \times \dfrac{10}{7} \times x - 10 \times \dfrac{10}{7} \times x + 100 \\ & = \dfrac{- 10 \times 10}{7} \times x + \dfrac{- 10 \times 10}{7} \times x + \dfrac{10 \times 10}{7 \times 7} \times x^{2} + 100 \\ & = \dfrac{- 100}{7} \times x + \dfrac{100}{49} \times x^{2} + \dfrac{- 100}{7} \times x + 100 \\ & = 100 + \dfrac{100}{49} \times x^{2} + \dfrac{- 100}{7} \times x + \dfrac{- 100}{7} \times x \\ & = 100 + \dfrac{100}{49} \times x^{2} + (\dfrac{- 100}{7} + \dfrac{- 100}{7}) \times x \\ & = 100 + \dfrac{100}{49} \times x^{2} + \dfrac{- 100 - 100}{7} \times x \\ & = \dfrac{100}{49} \times x^{2} + \dfrac{- 200}{7} \times x + 100 \end{align*} \end{enumerate} \end{multicols} diff --git a/2nd/03_Calcul_litteral/3E_remplacer_dans_formules.pdf b/2nd/03_Calcul_litteral/3E_remplacer_dans_formules.pdf new file mode 100644 index 0000000..5311500 Binary files /dev/null and b/2nd/03_Calcul_litteral/3E_remplacer_dans_formules.pdf differ diff --git a/2nd/03_Calcul_litteral/index.rst b/2nd/03_Calcul_litteral/index.rst index 7b7f0f2..b4dc892 100644 --- a/2nd/03_Calcul_litteral/index.rst +++ b/2nd/03_Calcul_litteral/index.rst @@ -2,7 +2,7 @@ Calcul littéral ############### :date: 2022-09-13 -:modified: 2022-09-13 +:modified: 2022-09-14 :authors: Benjamin Bertrand :tags: Calcul littéral :category: 2nd @@ -22,3 +22,10 @@ La solution des exercices techniques .. image:: ./solutions.pdf :height: 200px :alt: Les solutions + + +Exercices pour remplacer dans une formule + +.. image:: ./3E_remplacer_dans_formules.pdf + :height: 200px + :alt: Exercices pour remplacer dans une formule diff --git a/2nd/03_Calcul_litteral/plan_de_travail.pdf b/2nd/03_Calcul_litteral/plan_de_travail.pdf index b285702..96f984a 100644 Binary files a/2nd/03_Calcul_litteral/plan_de_travail.pdf and b/2nd/03_Calcul_litteral/plan_de_travail.pdf differ diff --git a/2nd/03_Calcul_litteral/tpl_exercises.tex b/2nd/03_Calcul_litteral/tpl_exercises.tex index cd439da..fe57aa3 100644 --- a/2nd/03_Calcul_litteral/tpl_exercises.tex +++ b/2nd/03_Calcul_litteral/tpl_exercises.tex @@ -36,7 +36,7 @@ \end{solution} \begin{exercise}[subtitle={Développer 1 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] - Réduire les expressions suivantes + Développer puis réduire les expressions suivantes \Block{ set reduction = { "A": random_expression("{a}({c}x + {d})", global_config={"rejected":[1, 0, -1]}), @@ -70,7 +70,7 @@ \end{solution} \begin{exercise}[subtitle={Développer 2 - technique}, step={2}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }, mode={\trainMode}] - Réduire les expressions suivantes + Développer puis réduire les expressions suivantes \Block{ set reduction = { "A": random_expression("({a}x + {b})({c}x + {d})", global_config={"rejected":[1, 0, -1]}),