2.09.2021 Blok 1:
Vaardigheden.
1. a. 2 2 2 2 2 2 2 2 2 2 2 2 ( 2)( 1) 2 2 2 3 2 1 ( 1) ( 1) ( 1) ( 1) ( 1) x x x x x x x x x x x x x x x x x x x x x b. 2 2 1 4 ( 1)( 1) ( 4)( 4) 2 1 8 16 10 15 4 1 ( 4)( 1) ( 1)( 4) ( 4)( 1) ( 1)( 4) ( 1)( 4) x x x x x x x x x x x x x x x x x x x x x x x c. 2 2 4 4 4(2 ) (4 )(2 ) 8 4 8 2 6 2 2 (2 )(2 ) (2 )(2 ) (2 )(2 ) (2 )(2 ) (2 )(2 ) x x x x x x x x x x x x x x x x x x x x x d. 2 2 2 2 2 2 1 2 2 1 2 (2 1) 1 2 4 4 4 4 4 x x x x x x x x x x x e. 2 1 2 1 1 (2 1)(2 1) 1 4 1 2 1 1 (2 1)( 1) ( 1)(2 1) (2 1)( 1) ( 1)(2 1) x x x x x x x x x x x x x x x x 2 4 ( 1)(2 1) x x x x f. 3 2 2 1 4 3 (2 2 1)(2 1) 4 3 4 3 2 2 2 1 2 2 2 1 2 1 4 4(2 1) 4(2 1) 4(2 1) 4(2 1) 4(2 1) x x x x x x x x x x x x x x x x x 2. a. 2 2 2 3 4 4 4 4 4 2 3 4 2x 3x 4 2x 3x 4 x x x x x x x b. 3 3( 2) 3( 2) 2 6 2 2 2 2 2 x x x x x x x x x x x c. 2 2 2 ( 1) ( ) 1 1 1 1 1 1 1 x x x x x x x x x x x x x x x x x x x d. 2 2 3 ( 1) 2( 1) 3 ( ) (2 2) 3 5 2 1 1 1 1 1 1 x x x x x x x x x x x x x x x 3. a. 2 2 1 3 2 10 20 1 5 3 15 x x x x x d. 2 2 3 3 1 x 1 x x x x b. 3 3 2 8 8 2 4 4 x x x x x e. 1 5 3 9 5 5 3 9 x x x x c. 3 1 4 2 2 18 3 4 4 x x x x f. 1 2 2 2 5 15 5 1 3 6 2 x x x x x 4. a. 2 2 2 1 1 1 1 (2x ) (2x )(2x ) 4x 4 x x x x b. 3 3 3 3 2 3 2 2 4 3 8 6 2 (x 1) x x 2x 8x 6x 2x x x x x c. 2 2 1 1 1 (x )(x ) x x x x d. 2 2 2 2 2 2 2 3 3 9 6 9 6 (x 3x 2) x x 3 x x x x x x -2.09.2021 5. a. 2 1 1 6 x x x b. 2 2 1 5 1 x x c. 2 4 1 3 x x x 2 2 1 1 3 4 12 1 12 1 0 (3 1)(4 1) 0 3 1 0 4 1 0 x x x x x x x x x x 2 2 2 2 2 1 2 1 1 2 2 1 5( 1) 5 5 4 6 1 6 6 x x x x x x x 2 2 6 132 6 132 8 8 2( 3) 4 ( 1) 2 6 4 4 4 6 6 0 ABC formule x x x x x x x x x x d. 2 1 2 1 3 4 x x 1 2 8 2 6 12x x 6. a. 1 3 3( 1) p p p p b. 21 1 1 x x x x x 7. a. x 1 0 1 : , 1 1, f x D b. 2 2 3 (2 5)( 1) 3 2 3 5 3 2 3 2 ( ) 2 5 1 1 1 1 1 1 x x x x x x f x x x x x x x x c. f x( ) 0 2 1 2 2 3 2 (2 1)( 2) 0 2 1 0 2 0 2 x x x x x x x x 8. a. Df : , 0 0, 4 4, b. ( ) 3 2 3( 4) 2 3 12 2 5 12 4 ( 4) ( 4) ( 4) ( 4) ( 4) x x x x x f x x x x x x x x x x x x x 9. a. 1 2 3 2 2 3 1 2 2 1 ( ) 3 3 3 p p p p p p p p b. 2 2 3 3 2 4 4 ( 6) 6 4 3p 9p 9p c. 2 2 2 2 2 2 2 (p 1) (p 1) p 2p 1 (p 2p 1) 4p 4 p p p p d. 3 2 3 2 2 2 2 2 2 2 2 2 8 6 4 6 4 (p 4p 3p 2) p p p 2p 8 p p p p p p p
-2.09.2021 10. a. f x( ) 0 2 2 2 2 2 2 2 2 1 1 1 1 1 0 1 0 x x x x x x x x x x x x
De discriminant is kleiner dan 0. De vergelijking heeft geen oplossing. b. 2 2 2 2 2 2 2 2 2 1 1 ( 1) 1 1 2 1 1 1 1 ( ) 1 1 ( 1) ( 1) ( 1) ( 1) ( 1) ( 1) x x x x x x x g x x x x x x x x c. 2 2 2 2 2 2 2 2 2 2 1 1 ( 1) 1 ( 2 1) ( ) 1 ( 1) ( 1) ( 1) ( 1) ( 1) x x x x x x x x x h x x x x x x 2 2 2 2 1 2 1 ( 1) ( 1) x x x x x x x 11. a. 3x2y4 b. 2 3 4 x y 1 2 2 3 4 1 2 y x y x 1 2 2 3 2 6 4 1 2 3 4 x x x x c. 2 2(3 4) 6 12 8 4 (3 4) (3 4) 3 4 x x x x x x x x x 2 2 2 3 2 3 4(3 4 ) 12 16 12 8 12 4 8 4(3 2) 4(3 2)( 1) 0 3 2 0 1 0 1 x x x x x x x x x x x x x x x d. 2 3 ( , 3) en 1 2 (1, )
12. Uit de eerste vergelijking y2x 2 volgt y2x2. Dit invullen in de tweede vergelijking: 2x 2 1 x
x 2 2 2 2 1 2 2 ( 1) 3 2 ( 1)( 2) 0 1 2 (1, 0) (2, 2) x x x x x x x x x x x x x x en
