tal n ruimt wi 1 vwo l Uitwrkinn
Gtal n ruimt 1VWO l - Hst 6 6.1 Kwaratn 1 40 x 40 = 1600 m 3 x 1600 4800. D kwkr poot 4800 ahlia's. tal 1 3 4 5 6 7 8 9 10 11 1 13 14 15 0 5 kwaraat 1 4 9 16 5 36 49 64 81 100 11 144 169 196 5 400 65 3a 5 4 = 5 16 = 80 5 4 = 5 4 = 100 5 4 = 5 16 = 9 8 3 = 64 3 4 = 64 1 = 5 h (8 3) 5 = 5 5 = 15 6 : 9 = 36 : 9 = 4 1 + 5 = 1 + 4 5 = -0 8 : 4 = 8 : 16 = 8 4 1 16 8 4a 3 + 4 3 = 3 + 16 3 = 3 + 48 = 51 ( 4 + ) : 3 = 6 : 9 = 36 : 9 = 4 3 (5 ) : 3 = 3 3 : 3 = 3 9 : 3 = 3 3 = 0 (17 + 3) : 80 40 = 0 : 80 40 = 400 : 80 40 = 5 40 = -35-6 (1 : 4) 3 = -6 3 9 = -6 81 = -87 (5 + 7) 18 : 3 = 144 18 :9 = 144 - = 14 5a 1,5 16 :,3 153,3 131 5 0, 7 87 (-,4 + 3,6) 5,4 : 3,7 1,05 4,3 6,83 61 15,18 57 3,1 6a -8-8 = 64 n -8 8 = -64-8 -8 is ht kwaraat van -8-5 = -5-10 = -100-1 = -1 7a (-9) = -9-9 = 81-11 = - 11 11 = -11 13 = 13 13 = 169 - (-13) = -169 (-15) = -15-15 = 5 (-4) = -4-4 = 16
8a -1,7 5 (-3,1) = -50,94 -(1,5 3,) = -86,49 8-1,3 = -47,3
9a -5-8 = -5-64 = 30 5 8 = 5 64 = -59 5 (-8) = 5 64 = 30 (5-8) = (-40) = 1600 h -(5 8) = -(-3) = - -3-3 = -9-5 (-8) = -5 64 = -69-5 + 8 3 = -5 + 8 9 = 47 (-8) : 4 = 64 : 16 = 4 i j k l 18 : -3 = 18 : -9 = - 18 (-7) = 18 49 = -31 -(-8) + 4-3 = -64 + 4-9 = -64 36 = -100-15 4-5 = -5 4-5 = -5 + 100 = -15 10a 1 + 3 + 5 + 7 = 16 Bij iuur 6 hoort 1 + 3 + 5 + 7 + 9 + 11 = 36 Er staan 11 onvn talln, ht antwoor is us 11 = 11 D som van rst 100 talln is 100 = 10000 11 -
Gtal n ruimt 1VWO l - Hst 6 6. Kwaratish ormuls 1a Fiuur 6 staat uit 6 6 = 36 virkantjs. Ht iuur ht nummr 1 want 1 * 1 = 144 Ht aantal virkantjs van n iuur mt nummr n is n n = n 13a n = 10 a = 10 + 3 = 103 Ht aantal virkantjs van iuur 10 is 103 n = 5 a = 5 + 3 = 68 Ht aantal virkantjs van iuur 5 is 68 17 3 = 169 13 13 = 169 us iuur ht nummr 13 14a a = 5 O = 6 5 = 3750 a = 8,3 O = 6 8,3 = 413,34 15a x = 3 y = 3 8 = 1 x = 7 y = 7 8 = 41 x 0 1 3 4 5 8 y -8-7 -4 1 8 17 56 16a x = 6 y = 5 6 = 5 36 = 180 x = -3 y = 5 (-3) = 5 9 = 45 x = 0 y = 5 0 = 5 0 = 0 x = -1 y = 5 (-1) = 5 1 = 5 17a x = 4 y = 4 1 = 16 1 = 4 x = -6 y = (-6) 1 = 36 1 = 4 x = 1 y = 1 1 = 1 1 = -11 x = -10 y = (-10) 1 = 100 1 = 88 18a x = 3 y = (3 7) = ( -4) = 16 x = -4 y = (-4 7) = ( -11) = 11 x = 0 y = (0 7) = ( -7) = 49 x = 8 y = (8 7) = ( 1) = 1 19a x -4-3 - -1 0 1 3 4 y -64-36 -16-4 0-4 -16-36 -64 D uitkomstn ij n positiv x-waar n n nativ x-waar zijn sts lijk! Bij x = -6 is ook y = -704
0a x = 5 y = 5 + 7 = 5 + 7 = 3 x = -3 y = 7 (-3) = 7 9 = 63 x = y = ( 7) = (-5) = 5 1a x = 3 y = 5 3 7 = 5 9 7 = 38 x = -4 y = 5 (-4) 7 = 5 16 7 = 73 x = -1 y = 5 (-1) 7 = 5 1 7 = - a x = -4 y = 3 (-4) 1 = 3 16 1 = 36 x = -7 y = -(-7) = -49 x = 6 y = - 6 + 1 = -36 + 1 = -4 3a T = 4 L = 0,5 4 = 4 D lnt van slinr is 4 mtr T = 0,8 L = 0,5 0,8 = 0,16 D slinr is 16 m lan. T = 6 L = 0,5 6 = 9 T = 5 L = 0,5 5 = 6,5 Dus ij 8 mtr is slinrtij minr an 6 sonn. In één minuut ( = 60 sonn) 1 x hn n wr Dus pr kr 60 : 1 = 5 sonn. T = 5 L = 0,5 5 = 6,5 D slinr is 6,5 mtr. 4a t = 3 a = 5 3 = 45 hoot = 60 45 = 15 mtr. t = a = 5 3 = 0 Dus in r son 45 0 = 5 mtr valln t = 4 a = 5 4 = 80 D stn is innn 4 sonn op ron omat torn maar 60 m hoo is n astan an 80 m zou motn zijn.
Gtal n ruimt 1VWO l - Hst 6 6.3 Graikn 5a x = -3 y = (-3) + 5 = 9 + 5 = 14, klopt! x = 3 y = 3 + 5 = 9 + 5 = 14 D uitkomst is htzl! Dat komt omat 3 zl uitkomst ht als (-3). 6a x -3 - -1 0 1 3 y 10 5 1 5 10 7a x -1 0 1 3 4 5 y 9 4 1 0 1 4 9
8a x = -3 y = -(-3) + 4 = -9 + 4 = -5 klopt! x -3 - -1 0 1 3 y -5 0 3 4 3 0-5 9a x -3 - -1 0 1 3 y 0,5 4 4,5 4,5 0 Ht viaut is 4,5 mtr hoo. D w is 6 mtr r. D vrahtauto is maximaal,5 mtr hoo. 30a x = 0 y = 0,005 0 + 5 = 0,005 400 + 5 = + 5 = 7 In punt A: x = 50 y = 0,005 50 + 5 = 0,005 500 + 5 = 1,5 + 5 = 17,5 Punt A is us 17,5 m ovn ht watr. x = 0 y = 0.005 0 +5 = 0 + 5 = 5 Punt B is 5 m ovn ht watr. 13 5 = 8 8 : 0,005 = 1600 n 40 = 1600 us x = 40 hoort ij punt C
31a x -80-40 -0 0 0 40 80 y 0 48 60 64 60 48 0 64 + 5 = 69 D spoorlijn loopt op 69 mtr hoot. 80-80 = 160 D astan tussn in- n inpunt van oo is 160 mtr. x = 45 y = -0,01 45 + 64 = -0,01 05 + 64 = -0,5 + 64 = 43,75 Punt A lit op 43,75 m hoot. 69-43,75 = 5,5 D staa AB is 5,5 mtr. x = 30 y = -0,01 30 + 64 = -9 + 64 = 55 69 55 = 14 D staa PQ is 14 m lan. 3a AB = 80 m us OA = 40 m x = 40 y = 0,015 40 = 0,015 1600 = 0 Punt A lit 0 m ovn X-as. Hir is OA = 50 m 50 = 500 us y =.. 500 = 0 Op plaats van puntjs mot 0 : 500 = 0,008 komn t staan. D ormul is us y = 0,008x AB = 60, us OA = 30 30 = 900 us y =.. 900 = 18 Op plaats van puntjs mot 18 : 900 = 0,0 komn t staan. D ormul wort: y = 0,0x
33a y = x 1 is n linair ormul y = x 1 is n kwaratish ormul. Dat kun j zin oorat ij kwaratish ormul r ook n kwaraat ij x in ormul staat x -3 - -1 0 1 3 y 5 0-3 -4-3 0 5 x 0 3 y -1 5 33 D raikn snijn lkaar in (-1,-3) n (3,5) 34a x -3 - -1 0 1 3 y 9 4 1 0 1 4 9 x -1 y -4 Lt ns op ho vrlin van Y-as hir is D oörinatn van snijpuntn zijn (-,4) n (0,0)
Gtal n ruimt 1VWO l - Hst 6 6.4 Rknn mt lttrs 35a a = 7 n = 8 3a = 3 7 8 = 1 16 = 5 a = 3 n = -5 -a + = - 3 + -5 = -6 5 = -11 a = -6 n = 5 a 3 = -6 3 5 = -6 15 = -1 36a p + p + p + p = 4 p = 4p x + x = x = x a + a + a + a + a + a + a + a = 8a r + r + r + r + r + r = 6r 37a 3a = a + a + a 7 = + + + + + + p = p + p 8q = q + q + q + q + q + q + q + q 38a Franin tlt 3 lijk ln mt tlkns 5 stukjs van x m. Elsk tlt all stukjs van x m ij lkaar. Ja 3 5x = 3 5 x = 15x 39a 5a 9 = 45a 5a -4 = -100a -8 4a = -3a -3p -q = 3pq 6x -5 = -30x -p -a = ap 40a 0,a 5 = a -8x -y 3z = 4xyz -a - -1 = -a 5y -3x -z = 15xyz 18y 0 -x = 0-0,5a -8 = 4a 41a 15a 3a = 45a 1 1 1 3 x x = 6 x 1 x y 3 6 3 3 5 x = 45 15a 3 = 45a 3 3 4 y = 1 y x 1 3 y 3z = xyz x y 4a Opp. = 5m k = 10km Opp. = 5x y = 10xy Opp. = 6p 1 = 7p Opp. = 3q q = 6q 43a 18a = 9a -4a = -1a 15xy = x 015y 15x = 5x 3x -3xy = -x 3y 100xy = -10x -10y 44a 3a = a + a + a 4a = a + a + a + a 3a + 4a = a + a + a + a + a + a + a Ja, 3a + 4a = 7a 45a 6a + 7a = 13a + 3 = 5 1096x + 4x = 1100x 15y + y = 16y 154x + 46x = 00x 1,5q + 0,5q = q h i a +8a = 10a 4,5p + p = 5,5p + 13 = 14
46a a + a = 3a 1,x + 8,7x = 9,9x xy + xy = xy a + 10a = 11a 16a + 9,5a = 5,5a x + 3x + 6x = 11x h i y + y + y = 4y 8z + z + z = 11z a + a + a = 4a 47a 3a + 10a = 13a 3x + 8 = k.n. 1 1 a1a a 3a + 10 = k.n. a + 6a = 8a h 1 1 a 3 k.n. + 8 = 9 a + 8a = k.n. i 1 1 3 a1 a 5a 48a ou lnt: 8 + 8a niuw lnt: 8 + 13a ou lnt: 8 + 3a niuw lnt: 8 + 4a ou lnt: 8 + 8a niuw lnt: 4 + 0a 49a 3a + 5a + 6 = 8a + 6 3a +5 +6 = 3a + 11 6a + 14a + 3 = 0a + 3 p + 5q + q = p + 6q p + 4p + q = 6p + q 4p + 16p +35p = 75p 50a 5a + + 3a + 4 = 8a + 6 8a + 6 + a + 9 = 10a + 15 6a + 14a + 3 = 0a + 3 a + 4 + 6a + 8 = 8a + 1 3a + + 8 + a = 4a + 10 6a + 5 + 6 = 6a + 11 51a 5a + 3 + + 6a + 7 + 8 = 11a + 10 + 10 3a + 5 + 7a + 8a + 9a + 10 = 11a + 16a + 15 7pq + 8p + 9q + 6pq + pq + p + q = 14pq + 9p + 10q 3a -5-8 = 40a 1a 5 0 30h = 0 1a 5 30h = 3600ah 5 Fiuur a Opprvlakt = 8y 5x = 40xy Omtrk = 8y + 5x + 8y + 5x Fiuur Opprvlakt = 5 3m = 15m Omtrk = 5 + 3m + 5 + 3m = 10 + 6m Fiuur Opprvlakt = y 3x + y x + 3y x Omtrk = y + 3x + y + x + y + x + y = 3xy + xy + 3xy = 8xy + x + 3y + x + 3y + 3x = 1x + 1y Fiuur Opprvlakt = 6y x + 4y x + y x Omtrk = 6y + x + 3y + x + y +3x +y + x = 6xy + 4xy + xy = 1xy = 1y + 8x 53a x = 40 ra = 8 + 0,1 40 = 8 + 4 = 1 Marln krijt 1 uro ra = 8 + 0,1x + 3 + 0,x = 11 + 0,3x Ik nk at z hrli ormul ruikt, at is vl minr rknwrk!
54a 6a + 8a + 5a = 19a 6a 8a = 48a 6a + 8 + a = 7a + 8 6a 8 = 48a 3x + 4y + x + y = 4x + 6y -3x -4y -x = -1x y 3x -y = -6xy h 3x + y +y + y = 3x + 4y i j k p + p + q = p + q p + 5 + q + 8 = p + q + 13 5 1 3 p 5 p 3 p 5 p 10 15 p 3 p 6p 3q 1pq l 3 55a 7a = a + 5a 10a = 9a + a 8a = - 1 / a -16a 5x = x + 4x 16xy = 8x y 3xy = 1 / 3 xy + / 3 xy h i 1a = -3a -4a 1a = 3a + 9a 18a = -1/3a 54a
Gtal n ruimt 1VWO l - Hst 6 6.5 Hrlin 56a 1 + -7 = 5-1 7 = -19-1 -7 = -5-4 + -8 = -1-4 8 = -1 4-8 = 1 h i -3 + -3 = -6-3 -3 = 0-3 3 = -6 57a 3a 5a = -a -3a 5a = -8a -3a + 5a = a 6 + - = 4-6 + - = -8-6 - = -4 h i 5x 4x = x -5x + 5x = 0 4x 5x = -x 58a 6p 1p = -6p -a 8a = -10a 0,6x + 1,4x = x 5a 1a = -7a -3pq 4pr = k.n. -1a + a = -11a h i 6a 7a = -a 3 = -5a +5 = k.n. 59a 8a = 0a 1a a = 5a 4a a = 1 1 / 3 a - 1 / 3 a -4a = a 6a 3a = a -a -4 1 / a = -a 3 1 / a h i 5a = 4a -a 6a = a -5a -5pq = 1 1 / 3 pq 6 1 / 3 pq 60 vrmnivuliinn: p 9q = 18pq 3pq 6 = 18pq -p -18q = 18pq 1 / p 36q = 18pq optllinn: 10pq + 8pq = 18pq 0pq + -pq = 18pq -10pq + 8pq = 18pq atrkkinn: 10pq -8pq = 18pq pq 4pq = 18pq -3pq -1pq = 18pq 61a waon1 = 7p + 3 waon1+ = 7p + 3 + 8p + = 15p + 5 waon1+ = 15p +5 5p 4 = 10p + 6a J krijt sts 8! uitkomst = x + 1 + x 4 3x = 8 D uitkomst is van tvorn kn omat r n x mr in ht (hrli) antwoor staat. Nm n tal in ahtn n tl r 3 ij. Tl r nu vij kr ht oorspronklijk tal ij. Trk r nu 10 vana.. Trk r ri kr ht oorspronklijk tal vana. Tl r nu wr 3 ij. En trk ri kr ht oorspronklijk tal r vana. Uitkomst is sts -4 63a x 3y 4y = -x 4y x 3y 4y = x 7y -3a 4a + = -7a + -3a 4 + a = -a 4 7p 4q 3q = 7p 7q -3t 4t 5t = -1t
64a a 3 + 5a = 7a 5-3a + a = -4a + 3a + + 8a = 11a 5x + 4y x 5y = 4x y -3x + 8y 8y + 3x = 0 x y + x + y = x 65a x 3 + 5x = 7x 5 -x + y + x y = 0 3x 1 + 8 x = x + 7 -a a + = -a 8a + 4 8a + = 6-7a a 3a + a = -6a 4a 66 3a 4a + 3 a + 3 a 3 a 3 3a + 6 a + a + -4 - a a + 7 a -a + a -a 3 5-7 a + 6 a + 67-68a x voor rst atum, x + 1 is voln a n x + 7 n x + 8 zijn n wk latr. x + (x + 1) + (x + 7) + (x + 8) = 4x + 16 "rst 16" t : 4x + 16 16 = 4x n "ln oor 4" t nu x x + (x + 1) + (x + ) + (x + 7) + (x + 8) + (x + 9) + (x + 14) + (x + 15) + (x + 16) = 9x + 7 x + (x + 7) + (x + 14) + (x + 1) + (x + ) = 5x + 66 x + (x + 6) + (x + 7) + (x + 8) + (x + 14) = 5x + 35 Nu kun j (som 35) rknn n i uitkomst oor 5 ln. -
69a Gtal n ruimt 1VWO l - Hst 6 Onr 6 komt 10 t staan want 5 = 10 3 3a 6 1p 9-1x 5 5a 10 0p 15-0x 6.6 Hrlin van rukn 70a 3 3a 5 10a a 8 16a 5 10a 7 14a 71a 3a 3 7a 6xy 6 3 7 8xy 8 1a 1 6 4 a p 1 8p 8 6 xy 6 y 3 y 1a 6a 4 8xz 8z 4z 7a 7a 7 a 7a 7a 14a 7 a 1 7 aa 3 1 8a 4 7 6a a 10a 5 73a 8a a 3a 8a 5a 4a5a 9a a3a a 4 6 a 8a 4 6 a xy 15x y 5x x 3 a a aa 0 74a 1 3 5 5 5 3 1 10 10 10 1 3 7 7 7 75a 3a a 5a 5a a 4a x x x 76a q q q q 4r 4r 4r r 9p 4p 5p p 5q 5q 5q q x 3x x x a 8a 10a y y y y 3 3 3 4y y 6y 0 0 3z 3z 3z y z 5p 6p 5 3 p p 1a 5a 7a a 7 7 7 7xy 1a 5a 17a 5x 7x5x y 7 7 7 1x
77a 1 6 5 11 5 3 15 15 15 1 0 3 17 3 10 30 30 30 3 1 6 5 1 5 10 10 10 78a 1 5 y 5x y 5x x y xy xy xy 3 7 3 7a 3 7a a a a a 5 3 5y 3x 5y 3x x y xy xy xy 1 y x x y xy xy yx xy 1 6a 6a 3a 3a 3a 3a 1 a 6 a 6 3 a 3a 3a 3a 79a a aq p aq p p q pq pq pq 5 3 5y 6x x 5y 10xy 10xy 5y6x 10xy 5 1 4 p p p p 4 1 4a 4a a a a a p q 7py qx x 7 y 14xy 14xy 7py qx 14xy 1 x 3 x3 3 x 3x 3x 3x
Gtal n ruimt 1VWO l - Hst 6 Dianostish Tots 1a 6 5 = 6 5 = 150 (15-3) 80 4 = 1 80 16 = 144 180 = -1136-5 (-3) = -5 9 = -45-4 (-4) = -16 16 = -3 (3 5) : - + 8 4 = (-) : - + 8 16 = 4 : - + 18 = - + 18 = 16-1 (-3) - = -1 9-4 = -1 + 36 = 35 a -,7 5 (-3,1) = -55,34 181 3,5 5 10 5 1, 35 3a x = 5 y = -3 5 + 7 = -3 5 + 7 = -75 + 7 = -68 x = - y = (- 5) 8 = (-7) 8 = 49 8 = 41 t = -5 A = 4 (-5) 1 = 4 5 1 = 100 1 = 88 4a l = 1,58 G = 5 1,58 = 6,41 Frits zijn wiht was 6,41 k l = 1,48 G = 5 1,48 = 54,76 l = 1,7 G = 5 1,7 = 73,96 73,96 54, 76 = 19, Hij is in z vir jaar 19, k zwaarr worn. 5a Talln: x -3 - -1 0 1 3 y -3 5 6 5-3 x -3 3 y 1 7 Graik: Coörinatn van snijpuntn zijn: (-, ) n (1, 5)
6a x = 0 y = 0,005 0 + 75 = 76 Hoot wk, an is x = 0 y = 0,005 0 +75 = 75. Ht wk is 75 m hoo. Bij torn A is x = -100 y = 0,005 (-100) +75 = 5 + 75 = 100 100 75 = 5. Torn A stkt 5 m ovn ht wk uit. x = -40 y = 0,005 (-40) +75 = 79 16 : 0,005 = 6400 80 80 = 6400 D x i ij punt C hoort is 80 B lit us 79 75 = 4 m ovn ht wk. D staa is us ook 4 m lan. 7a 7-3a = -1a 3x 0 -q = 0 1 1 1 a 4 114 xa 1p -q = -1pq 1 1 1 x a xa -x -z -x = -x z 3 6 8a 5a + 7a = 1a a a a 1 1 1 5 8x + 7y + x + y = 10x + 8y 8x 7y x = 11yx x + x = x 9x 6x 3 9a 5x 1x = -7x -5x 7x = -1x -15a -3a = -1a -a a = -3a -3x -3x = 0-3x 6x = -9x 10a 1a = 18a 6a 1a = -6a -a 8x = x 4x 1 6a a 1 18a = 6a -1a -7y = y 8y 11a -6p + 3q + p 7q = -5p 4q 3a 8-5 a = a 3 -x y x + 3y = -3x + y 1a 3pq 3p 1 1 p q 6xy 6y 3y 8xz 8z 4z 3a 3 1 6 6a 13a 3 5 a a a a a a 3 3 3 3x 4x 7x 7 7xy 7xy 7xy 7y 1 1 y y 14a 3 3a 3a a a a a 3 1 9x y y 3x 6xy 6xy 9x y 6xy 3 3p 14 7 p 7p 7p 3p 14 7 p