1. Jawab: E ~p ∨ q salah maka ~ p = S jadi p = B q = S
(A)p ⇒ q = B ⇒ S = S (B) p ⇔ q = B ⇔ S = S (C) p ∧ q = B ∧ S = S (D)~q ⇒ ~p = B ⇒ S = S (E) p ∨ q = B ∨ S = B
2. Jawab: E
10 3 3x+1+ 1−x =
10 3 3 3 .
3 x
1 1
x + =
10 p 3 p 3 + =
3p2 – 10p + 3 = 0
(p – 3)(3p – 1) = 0 p = 3 p = 1/3 3x = 31 3x = 3−1
x = 1 atau x = −1
3. Jawab : C
2 log 2 ) 3 x 2 log( ) 1 x log(
2 − ≤ + +
4 log ) 3 x 2 log( ) 1 x
log( − 2 ≤ + +
) 12 x 8 log( ) 1 x 2 x
log( 2 − + ≤ +
x2 – 2x + 1 ≤ 8x + 12
x2 – 10 – 11 ≤ 0
(x – 11)(x + 1) ≤ 0
–1 11
– +
+
syarat :
x – 1 > 0 2x + 3 > 0 x > 1 2
3
x>−
–1 11 2
3
− 1
1 < x ≤ 11
4. Jawab : D f(x) = 3x + 1
4 x
3 x 2 ) x ( g
+ − =
2 x
3 x 4 ) x ( g 1
− − − = → −
(
g f)
(x) )x (
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Hak Cipta dilindungi undang-undang
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www.ujiannasional.org
Hak Cipta dilindungi undang-undang
P(x) : (x – 5) sisa = 7 ⎯→ P(5) = 7
P(x) : (x2 – 8x + 15) sisa ax + b
P(x) = (x2 – 8x + 15)k(x) + ax + b
P(3) = 3a + b = 19 P(5) = 5a + b = 7
2a = –6 ⎯→ a = –3 ; b = 22 sisa = –3x +22
11. Jawab : D
0 10 x 6 x 7 kx
x4+ 3− 2+ − =
x1 = 1 maka
1 + k – 7 + 6 – 10 = 0 ⎯→ k = 10 x1 + x2 + x3 + x4 = –b/a
1 + x2 + x3 + x4 = –k
x2 + x3 + x4 = –k – 1 = – 11
12. Jawab : B x + 2y = 16 x + y = 12 _ y = 4 dan x = 8
f(x, y) = 4x + 10y f(0, 8) = 80 f(12, 0) = 48
f(8, 4) = 32 + 40 = 72 fmaks = 80
13. Jawab : C 2x + 3y + 4z = 20 x – y + 2z = 5 4x + 5y + z = 17 7x + 7y + 7z = 42 x + y + z = 6
14. Jawab : E
0 4 x 2 x2− − =
x1 + x2 = 2 x1.x2 = –4
(
x x)
3x .x (x x ) xx 1 2 1 2
3 2 1 3 2 3
1 + = + − +
= 23 – 3(– 4).2 = 32
