Jawab : A x2 – 5x + 7 = 2x – 3 x2 – 7x + 10 = 0 (x – 2)(x – 5) = 0 x = 2 atau x = 5 y = 2x – 3 x = 2 ⎯→ y = 1 x = 5 ⎯→ y = 7 Koordinat titik potong (2, 1) dan (5, 7 )
6.
Jawab : D f ( x ) = ax 2 − ( 2a − 4) x + a + 4 selalu positif maka a>0 D<0 (2a – 4)2 – 4a.(a + 4) < 0 4a2 – 16a + 16 – 4a 2 – 16a < 0 −32a < −16 a>½
7.
Jawab : B 10 − 5
a + b 2 =
= =
8.
10 + 5
.
10 − 5 10 − 5
10 − 2 50 + 5 10 − 5 15 − 10 2 5
= 3−2 2
a=3 b = −2 a+b=1 Jawab : C 2
⎛ 5 ⎞ 3 1 ⎜ x −3 ⎟ = 125 ⎝ 5 ⎠
(5 − + )
1 x 3 2
(5 )
4− x 2
=
=5
1 5 −1
= 5 −1 8 – 2x = −1 9 = 2x → x = 4½ 5
8− 2 x
WWW.UMBPTN.COM
WWW.UMBPTN.COM
9.
Jawab : D 2 log 3 = a ; 3 log 5 = b 2log 3.3log 5 = ab 2log 5 = ab 2 5
log
12
=
2
5 2
= 2
5 log 5
log 12− 2 log 5 log 5
log 4+ 2 log− 2 log 5 2
log 5
2 + a − ab
=−
10
12
2
= =
log
ab ab − a − 2 ab
Jawab : D x log 3 x 3x log x
x log 3x x log x
= 81 = 243
x log 3x −log x = 243 log 3 x
= 35 x log 3 = 35 log x log 3 = log 35 log 3. log x = 5 log 3 log x = 5 x = 100000 x
11.
x
Jawab : D C
p 3
o
60 WWW.UMBPTN.COM p B A T
WWW.UMBPTN.COM
CT2 = AC2 – AT2 = 3p2 – p2 = 2p2 CT = p 2 sin 60° = 3 2
=
CB =
CT CB
p 2 CB 2 p 2 3
12.
2
= p 6 3
Jawab : B Un – Un − 1 = Un + 1 – Un Merupakan sifat barisan aritmetika U1 = 2x + 1 U2 = −x + 21 U3 = 5x + 14 U2 – U1 = U3 – U2 −x + 21 –(2x + 1) = 5x + 14 – ( −x + 21) −3x + 20 = 6x – 7 −9x = −27 → x = 3 a = 2x + 1 = 7 U2 = −x + 21 = 18 b = U2 – a = 11 U3 + U5 + U7 = a + 2b + a + 4b + a + 6b = 3a + 12b = 21 + 132 = 153
13.
Jawab : C a, a + b, a + 2b memiliki jumlah 30 a + a + b + a + 2b = 30 3a + 3b = 30 a + b = 10 ⎯→ a = 10 – b ketiga bilangan menjadi 10 − b, 10 − b + b, 10 − b + 2b 10 − b, 10, 10 + b Jika bilangan ketiga ditambah 5 maka diperoleh deret geometri 10 − b, 10, 15 + b Sehingga 10 15 + b = 10 − b 10
WWW.UMBPTN.COM
WWW.UMBPTN.COM 100 = (15 + b)(10 – b) 100 = 150 – 15b + 10b – b 2 b2 + 5b – 50 = 0 (b + 10)(b – 5) = 0 b = −10 atau b = 5 Untuk b = −10 ketiga bilangan adalah 20, 10, 5 Untuk b = 5 ketiga bilangan adalah 5, 10, 20 Jadi bilangan terkecil adalah 5
14.
Jawab : C a4 = 8 a9 = 256 a9
r 5 =
a
4
256
=
8
ar3 = 8 → a =
= 32 → r = 2 8 r 3
8
=
8
=1
a1 + a7 = a + ar 6 = 1 + 64 = 65
15.
Jawab : B cos 2 θ − cos4 θ + cos6 θ + ... = a
=
1 3
1
1 − r 3 cos 2 θ 1 + cos θ 2
=
1 3
cos2θ =
3 1 + cos2 θ 2 cos2θ = 1 cos2θ = 1 cos2θ = ½ cos θ = −
1
θ = 135° =
16.
2
2 3 4
π
Jawab : B lim
x 2 − 16
x→4
5− x +9
=
=
lim x→4
lim x
→4
=
2
0−
2x 2x 2 x2 + 9
−2
2
x
+ 9 = −10
WWW.UMBPTN.COM
WWW.UMBPTN.COM 17.
18.
Jawab : E lim
sin 8x + tan 7 x
x→0
5x − sin 2x
8x + 7 x
=
15x
=
5x − 2 x
3x
=5
Jawab : B 1 ⎛ ⎞ y = x + x = ⎜x + x 2 ⎟ ⎝ ⎠ 1 1 2 ⎞ y' = ⎛ x x + ⎜ ⎟ 2 ⎝ ⎠
=
=
−1 2
⎛ ⎝
.⎜1 +
1 2
−1
2
x
−1 2
⎛
1 ⎞
x ⎝
2 x ⎠
1
1
2
x+
1
⎛ 2 x + 1 ⎞ ⎟ ⎜ 2 x ⎟ ⎠ x + x ⎝
2
1
.⎜⎜1 +
⎞ ⎟ ⎠
⎟⎟
.⎜
⎛ 2 x + 1 ⎞ ⎟ =⎜ ⎜ ⎟ 2 ⎝ 4 x + x x ⎠
19.
Jawab : D B p
= 4 p +
1500 p
− 40
B = 4p2 – 40p + 1500 B’ = 0 ⎯→ 8p – 40 = 0 ⎯→ p = 5 B = 100 – 200 + 1500 = 1400
