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Moderne wiskunde 11e editie 5 Havo wiskunde A Hoofdstuk 6 uitwerkingen
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Moderne wiskunde 11e editie 5 Havo wiskunde A Hoofdstuk 6 uitwerkingen ISBN 1773
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14 januari 2020Hoofdstuk 6: Werken met formules
V-1
a. 2
7
+ 73 = 75 c. 7 56 − 2 31 = 7 56 − 2 62 = 5 21 e. 2
5
11
5
= 10
55
= 112
b. 3 91 + 95 = 3 96 = 3 32 d. 1
2
31 = 1
6
f. 3
8
91 = 723 = 241
V-2
a. 7
11
+ 51 = 35
55
+ 55
11
= 46
55
d. 7
11
− 52 = 35
55
− 55
22
= 13
55
b. 8
9
+ 61 = 16
18
+ 183 = 19
18
= 1181 e. 9
21
− 143 = 18
42
− 42
9
= 9
42
= 143
c. 2 57 + 3 = 2 35
3
25
5
+3 21
35
= 6 35
11
f. 2
3 11 − 1 59 = 3 18
99
−1 55
99
= 1 37
99
V-3
a. 5
13
32 = 10
39
c. 5
12
109 = 120
45
= 3
8
e. 1
3
5 73 = 31 387 = 38
21
= 117
21
b. 5
12
89 = 108
40
= 10
27
d. 18
7
52 = 36
35
=1 1
35
f. 2
5
8 31 = 52 253 = 50
15
= 3 31
V-4
5 3 10 3 13 2 9 x 18 x 6
a. + = + = d. = = x
p 2p 2p 2p 2p 3 17 51 17
9 3 45 6t 45 − 6t 2b 9a 18ab 6
b. − = − = e. = = 17 ab
2t 5 10t 10t 10t 3 17 51
p 3 p 2
15 p + 15
2
4 15q 60q 60
c. + = + = f. = = = 3 31
5 p 5p 5p 5p 9q 2 18q 18
V-5
15t + 16 15t 16 15
a. P= = + = t + 16 = 85 t + 32
24 24 24 24 24
9p + 7 9 12 x − 5 12
b. K= = 21 p + 21
7
= 37 p + 31 y= = 9 x − 95 = 1 31 x − 95
21 9
4P − 3Q + 7 4
w= = 5 P − 53 Q + 57 = 54 P − 53 Q + 1 52
5
V-6
a. y = 3a2 + 4a − a + a2 = 4a2 + 3a
b. Q = 5x 4 + 9x + 2x 3 − 14x = 5x 4 + 2x 3 − 5x
c. g = 6 + 3m − 17 + 8m = −11 + 11m
d. P = 4a 2 − 3a + 5b 2 + 8a = 4a 2 + 5a + 5b 2
e. B = 3 − 7 p6 − 11p5 + 1 = 4 − 7 p6 − 11p5
f. w = t 3 − 2t 2 + 3t − t + 2t 2 − 3t 3 = −2t 3 + 2t
V-7
a. K = 7( x − 5) = 7 x − 35 d. P = 4m(2m − 3k ) = 8m2 − 12mk
b. y = (5 x + 8) 3 = 15 x + 24 e. T = (3t 2 + 5q ) 2t = 6t 3 + 10qt
c. Q = p (3p + 1) = 3p2 + p f. L = −2y ( y − 11) = −2y 2 + 22y
1
Uitwerkingen 5 havo wiskunde A, hoofdstuk 6
, 14 januari 2020
V-8
a. y = 3 (5 x + 8) + 2 x − 11 = 15 x + 24 + 2 x − 11 = 17 x + 13
b. y = 4 x( x + 3) + 2( x 2 − 1) = 4 x 2 + 12x + 2x 2 − 2 = 6 x 2 + 12x − 2
c. y = (3x 2 + 7 x ) 5 − ( x 2 − 2) x = 15 x 2 + 35 x − ( x 3 − 2x ) = − x 3 + 15 x 2 + 37 x
d. P = 9 − 4(5 x + 3) + 11x 2 = 9 − (20 x + 12) + 11x 2 = 11x 2 − 20x − 3
e. Q = 8 x − 3 x (4 − x ) + 5 x 2 = 8 x − 12x + 3x 2 + 5x 2 = 8x 2 − 4x
f. R = a(3a + 4b) − b(7a − b) = 3a2 + 4ab − 7ab + b2 = 3a2 − 3ab + b2
1
a. 2700
1000
250 + 1000
1500
350 = 1200 cent
b. Je moet 2700 cent betalen voor 1000 gram walnoten. Dat is 2,7 cent per gram.
Voor w gram walnoten betaal je dus 2,7 w cent.
Je betaalt 1500 cent voor 1000 gram cashewnoten: 1,5 cent per gram. Voor c gram
cashewnoten betaal je dan 1,5 c cent.
In totaal betaal je 900 cent.
c. 2,7 100 + 1,5 420 = 900 ; 2,7 175 + 1,5 285 = 900 ; 2,7 225 + 1,5 205 = 915 ;
2,7 275 + 1,5 105 = 900 . Alleen de derde niet.
d. 600 − 1,8 100 = 420 ; 600 − 1,8 175 = 285 ; 600 − 1,8 225 = 195 en
600 − 1,8 275 = 105 . Weer alleen de derde niet.
e. 2,7 w + 1,5 c = 900
1,5 c = 900 − 2,7 w
c = 9001,5
− 2,7
1,5
w = 600 − 1,8 w
2
a. y = 8x + 9 b. F = 3 (2t + 1) + 2 (7t − 11) c. Q = 8 + 2 (5u + 1)
8x = y − 9 F = 6t + 3 + 14t − 22 Q = 8 + 10u + 2
x= 8y−8
1 9
20t = F + 19 10u = Q − 10
x = 0,125 y − 1,125 t = 201 F + 19
20
u = 101 Q − 1
d. 5(2 p + 5) = 3(3q − 1) e. a + 5 = 8b − 9(2b − 9a + 5)
10 p + 25 = 9q − 3 a + 5 = 8b − 18b + 81a − 45
10 p = 9q − 28 10b = 80a − 50
p = 0,9q − 2,8 b = 8a − 5
f. 2m(6n + 7) = 3n(4m + 21)
12mn + 14m = 12mn + 63n
14m = 63n
m = 1463
n = 4,5n
2
Uitwerkingen 5 havo wiskunde A, hoofdstuk 6
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