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Kunci Latihan soal UM Undip 2010 Ujian Mandiri Universitas Diponegoro
Mata Ujian : Matematika Dasar
1. Jawab : C020)1x(12)1x( 222 +++
x4 + 2x 2 + 1 12x 2 12 + 20 0x4 10x 2 + 9 0(x2 1)(x 2 9) 0(x + 1)(x 1)(x + 3)(x 3) 0
1 31
+ + 3
+
3 x 1 atau 1 x 3
2. Jawab : D
01xx63xx2
2
2
7. Jawab : B
510
510.
510
5102 ba
+=+
510550210
+=
2235
21015 ==
a = 3 b = 2a + b = 1
8. Jawab : C
3
2
3x 12515 5 =
( )51
523x1 =+
( ) 12x4 55 = 1x28 55 =
8 2x = 19 = 2x x = 4
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9. Jawab : Da3log2 = ; b5log3 =
2log 3. 3log 5 = ab2log 5 = ab
5log5
12log
512
log2
2
5 =
5log
5log12log2
22 =
5log
5loglog4log2
222 +=
ababa2 +=
ab2aab
=
10 Jawab : D
81x3
xxlog
x3log
=
243xx
xlog
x3log
=
243x xlogx3log = 5log 3x x
x3=
53log 3x = 53log 3logxlog =
log 3. log x = 5 log 3log x = 5x = 100000
11. Jawab : D
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A B T
C
3 p
p
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CT2 = AC2 AT 2 = 3p 2 p 2 = 2p 2
CT = 2 p
CBCT60sin =
CB2 p
23 =
6 p32
3
2 p2CB ==
12. Jawab : BUn U n 1 = U n + 1 U n Merupakan sifat barisan aritmetikaU1 = 2x + 1U2 = x + 21U3 = 5x + 14
U2 U 1 = U 3 U 2x + 21 (2x + 1) = 5x + 14 ( x + 21)3x + 20 = 6x 79x = 27 x = 3
a = 2x + 1 = 7U2 = x + 21 = 18 b = U 2 a = 11U3 + U 5 + U 7 = a + 2b + a + 4b + a + 6b
= 3a + 12b = 21 + 132 = 153
13. Jawab : Ca, a + b, a + 2b memiliki jumlah 30a + a + b + a + 2b = 303a + 3b = 30a + b = 10 a = 10 b
ketiga bilangan menjadi10 b, 10 b + b, 10 b + 2b10 b, 10, 10 + b
Jika bilangan ketiga ditambah 5 maka diperoleh deret geometri10 b, 10, 15 + bSehingga
10 b15
b1010 +=
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100 = (15 + b)(10 b)100 = 150 15b + 10b b 2 b2 + 5b 50 = 0(b + 10)(b 5) = 0 b = 10 atau b = 5Untuk b = 10 ketiga bilangan adalah 20, 10, 5
Untuk b = 5 ketiga bilangan adalah 5, 10, 20Jadi bilangan terkecil adalah 5
14. Jawab : Ca4 = 8a9 = 256
2r 328
256aa
r 4
95 ====
ar 3 = 8 188
r
8a
3 ===
a1 + a 7 = a + ar 6 = 1 + 64 = 65
15. Jawab : B
31642 ...coscoscos =++
31
r 1a =
31
cos1cos
2
2
=+
3 cos 2 = 1 + cos2 2 cos 2 = 1cos 2 = 1cos 2 =
221
cos =
==43
135
16. Jawab : B
=+
9x5
16x4x
lim2
2
9x2
x20
x24x
lim
2 +
=
10924
lim 2 =+
= x x
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17. Jawab : E
x2sinx5x7tanx8sin
0x
lim
+ 5x3
x15x2x5x7x8 ==
+=
18. Jawab : B21
21
xxxxy
+=+=
+
+=
212
1
21
x21
1.xx21
'y
+
+=
x2
11.
xx
121
+
+=
x2
1x2.
xx
121
+
+=
xxx4
1x22
19. Jawab : D
40 p
1500 p4
pB +=
B = 4p 2 40p + 1500B = 0 8p 40 = 0 p = 5B = 100 200 + 1500 = 1400
20. Jawab : D
ax + by + c = 0 ba
m =
01y3x5 =+ 35
m 1 =
03y2x =+ 21
m 2 =
21
21
m.m1
mmtan +
=
66
.).(1 2
135
21
35
++
= 1356310 =
+=
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