1000 soal untuk matematika spmb
log 1 − log
+ 4 % log ( 4 × 4 x ) = 2 − x &
x = ...
2 . log x + log 6 x − log 2 x − log 27 = 0 &
x = ...
25 2 +( x % log 5 = 8 &
x = ...
2 2 2 +* 2 % log a + log b = 12 3 . log a − log b = 4 &
a +b = ...
1 1 ++ log x = log 8 + log 9 − log 27 " x = ...
+- %
p = log 8 &
log '
2 2 +0 2 % log x + 5 . log x + 6 = 0
2 x +y = 8 log( x +y ) = log 2 . log 36 &
x +y 3 = ...
2 - 3 % log 2 = 0 , 3010 log 3 = 0 , 4771 & log
x - +y x 5 = 49 x −y = 6
3 x + 2 - 5 x log 27 = log 3
3 5 -$ 4 % log 5 = p log 4 = q log 15 = ...
-( 2 x log log (
2 + 3 ) = 1 + log x
log x = 4 log ( a + b ) + 2 log ( a − b ) − 3 log ( a − b ) − log
x 2 + 16
log
2 1 3 16 a 1
-- %
log =
log b = 5 &
log 3 = ...
x >y > 1 x + 4 y = 12 xy &
log
2 4 2 x −y
log x + 2 . log y = 2 log
x +y = ...
MATRIKS
a b 5 − 2 2 13
a +b = ...
2 A − B + 3 C 10 &
a = ...
q +t 2 = ...
ab = ...
0* A =
det A = det B &
1 +x 2 = ...
x +y = ...
0- A =
( A . B ) = ...
x −y = ...
01 A =
( A . B ) = ...
K .M =
K = ...
det A = det B &
( A . B ) = ...
2 − 1 − 7 1$ z x 5 + y − 6 = − 21 − 2 5 2 z − 1
1( x +
1 2 4 3 m n 1 2 24 23
1- %
AB = I I "
B = ...
U 6 = 18
U 10 = 30 &
A = ...
11 A =
AB −2 B = C
x +y = ...
− 1 & T B = A =C & " A B = ...
2 x − xy 2 = ...
AP = B &
P = ...
1 2 4 10 − 1 1 − 1 − 4 x
( A . B ) = ...
4 1 − 1 a 1 15
b = ...
3 a 2 a + b 7 7 20
PQ =
x −y = ...
MN = I N =
M = ...
− 5 2 2 y − 1 − 16 5 x
( A . B ) = ...
1 3 + 15 2 2 A = ...
− - 1 f ( x ) =x 2 + 5 g ( x ) =x + 2 & ( f g )() x = ...
0 f ( x ) =x 3 − 4 g ( x ) =2 x + p ; ( f g )( = g f ) &
p = ...
( g f ) () 2 = ...
f ( 1 ) = ...
f ( x ) =x + 2 g ( x ) =
( g f )( ) x = ...
g ( x ) =x + 3 &
( g ( f ( x ) ) ) = ...
g ( x ) = ...
g ( x ) = ...
+ f ( x ) = x − 1 g ( x ) =x 2 + 4 &
( g f )() 10 = ...
( f g )() 6 = ...
g ( x ) =x − 2 &
( g f )() x = ...
g ( x ) =x 2 − 1 &
( f g )() x = ...
$ 2 % f ( x ) =x 2 − 2 g ( x ) =x − 1 &
( f g )( x + 1 ) = ...
( f g )( ) x = ...
f ( x ) = ...
$$ 2 % f ( x ) = x + 1 g ( x ) =x − 1 &
( g f )( ) x = ...
$( 2 % g ( x ) =x + 1 ( f g )( ) x = x + 3 x + 1 &
f () x = ...
$* f ( x ) =
& ( f g )( ) x =
g () x = ...
f ( x ) = x + 1 ( f g )( ) x =
g ( x − 3 ) = ...
$- %
f ( x ) =x 2 − 3 g ( x ) =
( f g )() x = ...
f ( − 3 ) = ...
f ( x ) =x 2 − 3 ( g f )( ) x =x 2 + 1 &
g () x = ...
( f g )() x = ...
2 − ( 1 % ( f g )( ) x = 4 x + 8 x − 3 g ( x ) =x 2 + 4 & f ( x ) = ...
( 2 % f ( x ) =2 − x & g ( x ) =x + 1 & h () x = 3 x &
( h g f )( ) 3 = ...
− 1 x + 2 5 − ($ 1
g (x )
g ( 1 ) = ...
2 (( 2 % g ( x ) = x + x + 2 ( f g )( ) x = 2 x + 2 x + 5 &
f () x = ...
(* 1 − 1 − f ( x ) = ; x ≠ 3 % f # f & f ( x + 1 ) = ...
(+ f ( x ) =
f ( x + 1 ) = ...
(- f ( x ) =
f ( x + 2 ) = ...
(0 2 f ( x ) =x + 2 ( g f )( ) x = 2 x + 4 x + 1 &
g () 2 x = ...
(1 f ( x ) =x 3 − 2 g ( x ) =
( f g )( ) x = ...
− 1 − * 1 2 " f ( x ) =x 2 − 3 % f # f & f () − 1 = ...
* 2 2 " f ( x ) =x 2 − 4 ( g f )( ) x = 4 x − 24 x + 32 &
g () x = ...
f ( x − 2 ) = ...
*$ 2 ( f g )( ) x = x + 3 x + 5 " g ( x ) =x + 1 &
f () x = ...
f ( x − 2 ) = ...
f ( x ) =x 3 + 2 g ( x ) = 2 ( 4 x − 1 ) &
( f − g )( ) x = ...
*+ 2 2 " f ( x ) = 2 x − 3 x + 1 & g ( x ) =x − 1 ( f g )( ) x = 0
− 1 f ( x ) = & f () 3 = ...
f ( x ) =x 8 + 5 g ( x ) = 2 ( 3 x − 1 ) 6 ( f − g )( ) x = ...
*1 2 2 " f ( x ) = x − 3 x + 5 & g ( x ) =x + 2 & ( f g )( ) x = 15 x
f − () 1 = ...
f ( x ) =x 5 + 1 g ( x ) = 2 ( 3 − 2 x ) 6 ( f − g )( ) x = ...
+ 2 2 " f ( x ) = x + 2 x + 1 & g ( x ) =x − 1 ( f g )( ) x = 4 x
+$ f ( x ) =x 6 − 3 & g ( x ) =x 5 + 4 ( f g )( ) a = 81 &
a = ...
+( 2 ; g ( x ) =x 2 + 1 ( g f )( ) x = 6 x + 4 x − 7 &
f ( x ) = ...
h () x = ( g f ) () x
f ( x ) =x 2 + 4 & g ( x ) =
− f 1 (x ) h () x = ...
f ( x ) = x + 1 ( f g )( ) x = 2 x − 1 &
g ( x ) = ...
+- %
f ( 2 x − 1 ) = ...
f ( x ) = ...
+1 2 f ( x ) = x − x + 3 g ( x ) = 1 − 2 x
( f g )( ) x = ...
- g () x = x + 4 x − 5 ( f g )( ) x = 2 x + 8 x − 3 &
f ( x ) = ...
LIMIT
1 − x - lim
- lim
2 2 = → ... x − 2 x
-$ lim x 1 2 = → ...
x − x -( lim
-* lim
0 = → ... 3 − 9 + x
x − 2 -+ lim
= x → 4 x ... − 4
1 +− x 1 -- lim
0 3 = → ... 1 +− x 1 x 2 − 1
-0 lim
x → 1 2 = ...
x +−− 3 x 1
-1 lim
( x + a )( xb + ) −= x → ...
ax b +− x 3
0 lim
a b ...
++ 1 2 ... + x
0 lim
0 lim x → 8 3 = x ... − 2
0$ lim
0( lim
x → 4 2 = x ... − 4 x
0* lim1 + + + ... + n = ...
sin 6 x 0+ lim
= ... x → 0 sin 2 x = ... x → 0 sin 2 x
0- lim x → 0 2 = x ... + 2 x
( 2 x − 5 x + ) 6 sin ( x − 2 )
00 lim
( x −− x 2 )
cos 2 x − 1
01 lim
0 2 = → ... x sin x
sin ( π x − π )
lim 0 = 1 x &
lim
sin 4 x + sin 2 x
1 lim
0 = → ... x 3 cos x x tan x
1 lim x → 0 = − ... 1 cos 2 x cos x − cos 3 x
1$ lim
− 1 cos 2 x − 1 cos x
1( lim
0 → ... 2 tan 2 = x cos 4 x − 1
1* lim
x → 0 x tan 2 x
a sin x
b lim
0 = → ... tan cx sin x
1- %
lim 0 = 1 &
lim π − x tan x = ...
sin 2 x 1 − x
lim
x → 1 = x ... sin ( ππ − x ) xx ( + ) 2 tan x
1 lim
11 lim = x ... → 0
( x + )( 1 1 cos 2 − x )
tan x
lim
lim
x → a 3 = x − 3 a + tan ( x − a )
lim x 2 +
2 2 2 x + 2 x −− 3 2 x − 2 x − 3
lim x
x − 2 x + 3 $$ lim
3 2 = → ... x − 9
( 45 + x )( 2 − x )
$( lim
( x + 21 )( − x )
( 2 x − ) 1 sin 6 x
$* lim
0 3 2 = → ... x + 3 x + 2 x x − k
$+ lim
sin ( x − k ) + 2 k − 2 x
tan 2 .tan 3 x x $- lim x → 0 2 = 5 ... x
2 2 x + x $0 lim
0 = → ... sin x
− 2 1 cos ( x − 1 )
$1 lim 1 2 = ...
cos x − cos 2 x
lim 0 2 = x ... → x
x 2 +− x 6
lim x → 2 3 = ...
lim 1 3 = x ... → −
x 2 − 9 $$ lim
x → 3 = 3 ...
( 2 x + 2 ) ( x −− x 6 )
$( lim
x →− 2 2
3 x 2 − 16 x
$* lim
= ...
− 2 x − 2 $+ lim
− x = → ...
1 1 $- lim
0 − 1 = → ... t t + 1
10 x $0 lim x → 0 = 9 ... − 5 x + 81
6 x − sin 2 x $1 lim
...
2 x + 3 tan 4 x
2 − + 1 cos 2 x
lim x → 0 2 = ...
sin x sin 2 x
lim x → 0 = ...
3 − 2 x + 9 sin x − cos x
lim π
= ...
x → 4 cos 2 x x 2 − 5 x
$$ lim
= sin 2 x
...
sin 6 x $( lim
= ... tan 2 x
x sin 2 x $* lim
= ...
− 1 cos x − 1 cos x
$+ lim → 0 = x ... − 1 cos 2 x
Program Linier
4 x +y ≥ 4 , 2 x +y 3 ≥ 6 4 x +y 3 ≤ 12 &
$$- "
x ≥ 0 , y ≥ 0 & 2 x +y 5 ≤ 10 4 x +y 3 ≤ 12 &
x ≥ 0 , y ≥ 0 & 2 x +y ≤ 6 x +y 2 ≤ 6 F ( x , y ) = x + y &
$$1 4 x + 5 y
x ≥ 0 , y ≥ 0 & x +y 2 ≤ 10 x +y ≤ 7
$( 2 x + 5 y
x ≥ 0 , y ≥ 0 & x +y ≥ 12 x +y 2 ≥ 16
$( 8 x + 6 y
x ≥ 0 , y ≥ 0 & 4 x +y 2 ≤ 60 2 x +y 4 ≤ 48
$( 4 y − x
y ≤ 2 x & 3 y ≥ 2 x , 2 y +x ≤ 20 x +y ≥ 3
$($ 3 x + 6 y
4 x +y ≥ 20 , x +y ≤ 20 & x +y ≥ 10 & x ≥ 0 , y ≥ 0
$(( 2 x + 3 y
3 x +y 2 ≤ 28 & − x + 2 y ≤ 8 & x ≥ 0 , y ≥ 0
$(* 3 x + y
x ≥ 0 , y ≥ 0 & 2 x +y ≥ 4 , x +y ≥ 3
$(+ 4 x + 3 y
x ≥ 0 , y ≥ 0 & x +y ≥ 4 & 2 x +y 3 ≥ 9
$(- 6 x − 10 y
x +y ≤ 10 , x +y 2 ≤ 10 & x ≥ 2 & y ≥ 0
$(0 4 x + 5 y
x +y ≤ 8 & 3 ≤x ≤ 6 , x +y ≥ 5 y ≥ 0
STATISTIKA
"! " ' "' $ $$
& "! " '
"'
"'
$* '
"' =
+'
-& 0& -&* %
' .'
"'
' " : (0 & $+ & +* & - &+
$*- ,
? * &! @'
*@'
&! ? " ! " ' , ' $*0 )
4' & = '
4'
* = ?"! " '
$+$ & ;& 8 ' " "!" ""
8' " "!" " *+ +*&
f ( x ) = cos
f ' () x = ...
$++ 2 y = ( 1 − x )( 2 x + 3 )
$+- /
3 x − 900 +
. " '"
$+1 2 % f ( x ) = x . 4 − 6 x &
f ' () − 2 = ...
$- )
"" x = 2 # y =
$- %
f ( x ) = 6 x + 7 f ' () 3 = ...
$- % 5/
p = ...
3 $-$ 2 2 " # y = x − 6 x + 9 x + 1 #
$-( 4 " y = cos x sin x + cos x
$-* f ( x ) =
; sin x ≠ 0 &
sin x
$-+ 3 2 " " # y = 4 + 3 x − x " x ≥ 0 5 #" '"
"" P m &
3 $-- 2 4/ y = 5 x − 3 x
' x "" P %
2 m + 1 = ...
3 $-0 2 % " . f ( x ) = x − px − px − 1 x = p &
p = ...
$-1 2 f () x = px − ( p + 1 ) x − 6 3 ""
p = ... $0 3 ) # y = 2 x − 4 x + 3 ""
$0 f () x = tan a x + bx
a +b = ...
3 $0 2 ) / f () x = 2 x + 3 x + x "" ( − 1 , 0 )
4 $0$ 2 4/ y = x − 8 x − 9 "
3 $0( 2 "'. / y = x + 6 x + 9 x + 7
2 $0* 2 f ( x ) = 3 x − 5 x + 2 & g ( x ) = x + 3 x − 3 % h ( x ) = f ( x ) − 2 . g ( x ) &
h ' ( x ) = ...
$0+ ' "
x = ...
$0- %
f ' () x = ...
3 $01 2 6 y = x − 3x "
3 $1 2 # f ( x ) = x + 3 x − 9 x + 7 "#
3 $1 2 ) # y = x + 2 x − 5 x "" ( 1 , − 2 ) π
# y = tan x "" ( , 1 )
3 $1$ 2 2 " f ( x ) = 2 x + 9 x − 24 x + 5 %
"" ( 1 , − 1 ) # y = x −
3 $1* 2 6 y = 4 x − 18 x + 15 x − 20 3 5 " x = ...
$1+ 2 " / f ( x ) = ( x − 2 )( x − 1 ) 3 x = ...
x = ...
2 $1- 2 % f ( x ) = − (cos x − sin x ) &
f ' () x = ...
4 dy
y = 3 x + sin 2 x + cos 3 x &
dx
2 $11 3 4/ f () x = 5 + 15 x + 9 x + x
f () x =
f ( 0 ) + 6 . f ' () 0 = ...
f () x = x + x − 2 x + 5
f () x = + x − 2 x &
1 3 df ( x )
dx
($ 6 f () x =
2 + cos x
sin x
b = ...
3 (( 2 " # y = 2 x − 4 x − 5 x + 8 )
3 (* 2 " # y = x − 3 x + 1 ,,
18 x −y 2 + 3 = 0
3 (+ 2 % / y = − x + 6 x + 15 x − 2 − 2 < x < 6 a
a −b = ...
' x ' y "" (a , 0 )
(- 4 "" ( 2 , 8 ) # y = 2 x x + 2 .".
a +b = ...
2 2 (0 2 % x
x + kx + k = 0 &
k = ...
3 (1 2 / y = 2 x − 6 x − 48 x + 5 "# − 3 ≤ x ≤ 4
f () x =
f 'x ( )
4/ y = x x − 2 "#
3 x + ($ 5 " / y = e + ln( 2 x + 7 )
TRIGONOMETRI
0 (( 0 ) ∆ ABC " a +b = 10 ∠A = 30 ∠B = 45 &
b = ...
2 2 (* 2 % tan x + 1 = a & sin x = ...
∆ ABC
cos( B +C ) =
AC = 10 &
AB = 8 &
BC = ...
(- %
tan α = p &
sin α −
2 cos α
∆ ABC
sin( A +B ) = ...
cos t =
π <t < 2 π &
sin t = ...
sin α = 2 sin β &
tan( α − β ) = ...
( 2 % 3 cos 2 x + 4 cos 2 x − 4 = 0 &
cos x = ...
2 ∆ 3 ABC & sin C =
tan A . tan B = 13 &
tan A + tan B = ...
2 cos x +
= cos x −
tan x = ...
(( 2 % θ " 3 2 cos θ = 1 + 2 sin 2 θ
tan θ = ...
2 sin x − 7 sin x + 3 = 0 − < x < &
cos x = ...
3 tan P
PQR
sin P . cos Q = &
5 tan Q
(- 0 % α + β = 270 &
cos α + sin β = ...
(0 " '
BC = CD &
cos B = ... A "
,='
(1 0 ) ∆ ABC & , AC = b & BC = a a +b = 10 % ∠A = 30 ∠B 0 = 60 &
AB = ...
($ cos − sin
+ 8 sin cos
∆ ABC &
AC =
6 & BC = 10 ∠A = 60 &
∠C = ...
3 ($ 2 x " 0 2 π 2 cos x + cos x − 1 = 0
($$ 2 ) ∆ ABC & " a = 4cm , b = 3 cm " 6cm &
∠C = ...
tan
cos
+ tan
sin
sin cos
0 0 ($* 2 % 0 <x < 90 ' tan x 1 − sin x = 0 , 6 &
tan x = ...
0 ($+ 0 ) ∆ ABC & " ∠A = 30 ∠B = 60 % a +c = 6 &
b = ...
($- %
0 <x < 90 '
cot x =
cos ecx = ...
sin α = p
tan( β + γ ) = ...
cos α . cos β = &
cos( α − β ) = ...
4 (( 2 % α " 3 2 cos α = sin α &
tan α = ...
∆ ABC &
C % cos( A +) C = k &
sin A + cos B = ...
(( 0 ) ∆ ABC & ∠B = 45 CT
" C % BC = a
AT = a 2 &
AC = ...
(($ 0 ) ∆ ABC & ∠B = 60 CT
" C % BC = a
3 AT = a &
AC = ...
0 0 0 ((( 0 % sin x = a cos y = b 0 <x < 90 90 <y < 180 &
tan x + tan y = ...
cos x =
cot
−x = ...
sin x = &
cot
−x = ...
((- %
cot x = 3 &
sin
−x = ...
x = 3 tan α &
sin α cos α = ...
((1 f ( x ) = 5 sin x + 2 a b &
ab = ...
m (* 5 2 ' " m = ...
15 sin x − 8 cos x + 25 (* 2 % 0 <x < π sin x tan x − tan x − 6 = 0
tan x = − 3 &
cos x = ...
(*$ 0 cos 1110 = ...
1 sin A
(*( 0 % A + B + C = 360 &
sin ( B +C )
∆ ABC & a , b , c "!
tan a =
tan b = & sin c = ...
α − β = 30 sin γ = &
6 cos A . sin B = ...
(*- 2 "
A B "!
C % sin A =
tan B = &
cos C = ...
(*0 cos 150 + sin 45 + cot ( − 330 ) = ...
(*1 2 % − π < x < π x 6 sin x − sin x − 1 = 0 &
cos x = ...
tan x = 3 0 <x < &
3 cos x + cos x + π + sin ( π − x ) = ...
7cm . % AB = 2 7 cm &
ABC " "
tan A = ...
tan x = &
cos 3 x + cos x = ...
sin x − cos x = p &
sin x . cos x = ...
(+( %
sin θ = −
tan θ > 0 &
cos θ = ...
(+* 0 2 ∆ PQR & PQ = 3cm , PR = 4cm , ∠P = 60 '
cos R = ...
0 0 0 90 0 180 360 720
(++ P = 8sin
cos
cos
cos
17 17 17 17
(+- ( tan 20 .tan 40 .tan 60 .tan 80 ) = ...
(+0 cos π + cos π + cos π = ...
0 0 0 0 0 0 (+1 0 cos 84 .cos 72 .cos 60 .cos 48 .cos 36 .cos 24 cos12 = ...
(- 0 +
0 = ...
sin10 sin 50 sin 70
0 0 0 (- 0 sin 72 .sin 54 .sin 36 .sin18 = ...
2 0 2 0 2 0 2 (- 0 sin 6 + sin 42 + sin 66 + sin 78 = ...
2 0 2 0 2 0 2 0 4 0 2 0 6 (-$ 0 sin 15 + sin 15 cos 15 + sin 15 cos 15 + sin 15 cos 15 + ... ... =