Fx = x cosx = ux vx
F’x = u’ x vx + u x v’ x
= 1 cosx + x sinx
= cosx x sinx
F’x+
2 1
= cosx+
2 1
x+
2 1
sinx+
2 1
=
sinx x+
2 1
cosx =
sinx x cosx
2 1
cosx
17. Jawab A
Subtitusi : x
2
+ ax + b = cosx berpotongan di x = 0 dan x =
x = 0
0
2
+ a 0 + b = cos 0
b = 1 x =
2
+ a + b = cos
2
+ a + 1 = 1
a =
2
Sumbu simetri =
2 a
=
2 1
+
1
18. Jawab B
3 x
6 x
4 2
= 125
6 2x
6 x
2 2
=
3
5
6
2x 6
x
2
=
3
5
3x
2
=
3
5
x
2
= 5 Diperoleh
x
4
=
x
2
2
=
2
x
2
–
2
5
=
5 2
1
19. Jawab B
Kurva y = x
3
3x
2
9x Batas: 0
x 2 Cek batas: x = 0
y = 0 x = 2
y = 22 Cek puncak: y
= 0 3x
2
6x 9 = 0 X
2
2x 3 = 0 x + 1 x
3 = 0 x =
1 atau x = 3 Tetapi x =
1 dan x = 3 tidak terletak pada interval 0
x 2 Nilai minimum:
min
y =
22 Nilai maksimum:
max
y = 0
20.
Jawab E
2
log
x
3
logy = 0
2 1
2
logx
3
logy = 0
2
logx 2
3
logy = 0
2
logx +
3
logy
2
= 5
2
logx + 2
3
logy = 5 2
2
logx = 5
2
logx =
2 5
x =
2 5
2
= 4 2
21.
Jawab D
S
1
Persegi sisi 1, maka Luas S
1
= 1 S
2
persegi dengan sisi x Lihat gambar , 3x = 1
x = 3 1
Luas S
2
= x
2
= 9 1
Rasio r =
1 2
S Luas
S Luas
= 9 1
Jumlah luas semua persegi =
S
=
9 1
1 1
=
8 9
22. Jawab D
L = luas OABC = x
y = x
x 2
2
= x x
2
4x + 4 = x
3
4x
2
+ 4x Luas akan maksimum,
jika L
= 0 3x
2
8x + 4 = 0 3x
2x 2 = 0 x =
3 2
atau x = 2 Untuk x = 2
luas = 0 Untuk x =
3 2
luas = x x 2
2
= 27
32 Maksimum
23. Jawab B
ganjil
S
= jumlah suku-suku bernomor ganjil
=
1
U +
3
U +
5
U + ...
genap
S
= jumlah suku-suku bernomor genap
=
2
U +
4
U +
6
U + ... 9 = 5 +
genap
S
genap
S
= 4
SNMPTN 2009 Halaman 3 dari 6 halaman
+
45
o
45
o
x x
x x
C A
O Bx,y
=+
Rasio r =
r =
5 4
9 = 5
4 1
a
a =
5 9
24. Jawab C
p = 13
14 1
=
13 14
1
13 14
13 14
=
13 14
q = 13
14 1
=
13 14
1
13 14
13 14
=
13 14
p
2
+ pq + q
2
= p + q
2
p q = 2
14
2
1 = 55
25. Jawab C
Jika A
1
=
1
3 2
dan B
1
=
3 2
1
, maka A B
1
= B
1
A
1
=
3 2
1
1
3 2
=
3
3 4
BAHASA INDONESIA 26. Jawab: B
