Soal untuk matematika cepat tepat

y = x 2 + ( p − 1) x + ( p + 1)
" "
&

#

'

$ #%

x 2 − 2 px + ( p 2 − 4 p ) = 0 " "

"

"
)

'

*

'

$

( a, b, c )

p !

" "

("

1+

$ #

$

•

−2 x + y − z = −3

•

x + 2y + z = 8

•

x − y = −1

#

!

(

$ #%

1
1

+
= ...
2 1− 2

!

"

"

$

+

a + b + c = ...

"

,

p !

'

x1

$ #

x2

-

( 5 − 2 log x ) log x = log1000 (

"

"

x12 + x2 2 = ...
.

x 2 + ( a − 1) x − ( a − 5 ) = 0 " "

"

/

x12 x2 + x1 x2 2 = 12 ( "

a>0

'
$

0

" "
3

$

!

$ "1
#

1

(x

"

!

“A Tribute To Mathematics”

2

$
3

$ , $ "1
1

x1

x2

$ #%

$ 2

( #

$ "

-

a = ...

+ 1) − 12 ( x 2 + 1) + 20 ≤ 0

1

3
!

2

!

$

3

$

#
'

$

#
!

& $ "1

"
(
( "

$ #%

1

4

$

z = 3x + 5 y !

" 5

y≥0

( x − 2 ) ( x2 + x − 6)

"

P=

6

x + 2 y ≤ 10 ( x + y ≤ 6 ( x ≥ 0 (

!

>0

x 2 + x − 20

a 2
−b 1

1 3
2 4

A=

& '

#

$ #%

$

'

" "

$ # P −1 =

$ #%

−3 6
("
3 c

2 3
( "
0 1

B=

$ #%

c

"

( A + B)

"

2

$ #%
)

-

1

U 7 = 16 ( "

,

U1 = ...
p, p + q, 4 ( p + q ) " "1

p > 0, q > 0 (

* '
$

" $
$

!

" $

U 4 = p 2 + 1 ( U10 = 2 p 2 + 4 (

$ # Un '

"

"

$
" "1

)

$

7

$ "

$

!

3

$

$ ( "

$ # 8

$ #
$

q = ...

("

!

3
5

'

" "1

$
&

$

$ #%
. 2

1

)

1
1 ( "

.
1

!

'
!

!

$ " , 1
1

!

9

$ "

1

$ #%
/ '

α " "

0 2 $ " ∆ABC ( 3

“A Tribute To Mathematics”

1
2

# cos 2 α + 2sin (π − α ) = sin 2 (π + α ) + 1 ( "
: 0( 8

: 4 2

∠ABC = 450 ( "

sin α = ...

tan ∠BAC = ...

2

4

"

&

lim

&

'

x→4

x 2 − 16

y = x+ x

$ # y ' = ...

6

f ( x ) = x2 + 2 ( x ≥ 0 ( "

= ...

5 − x2 + 9

y = g ( x)

$ #

$

$ #%

g

θ

&&

#

!

" "

#

cos 2 θ − cos 4 θ + cos 6θ + ... =

1
3

$ #%
&)

!

4p +

3

1500
− 40 3
p

# '

1 !

"

(

1 !

" "

!

#

1

!

$ # R 3

R = ...

#( "
&*

p #

$ "

1 a
(3
b c

A=

"

1 3 "$ #

)

1$

1, a, c " "1

1$

1, b, c " "1

1

1

"

"

( "

det A = ...
&, 8

&.

7 x 2 y −3 z 2
27 xy −1 z 8
×
54 x −1 y −5 z 4 84 x −6 y 4 z −2

#

$

k !

" "

&/ 2 1
*

&0

#
$ "
#

x a ( x a +1 )

"

!
&

#

$

"

< '

“A Tribute To Mathematics”

a 1− a

(x )

a , b, c " " $

&(

$ #

a

= x k −1

$ #%

ax 2 + bx + c = 0

"

$

;

#

$ #%

#
1

&

.(

# 1

!

"

%
"

1
1

!

! ("

$ #%
3

y = bx − a " "

&4 '

( x0 , y0 ) ( "
)

3
5
< 2
1 $
x − 3x + 2 x − 4 x + 3
"

$

x !

6 $%

$ #

1

8 : ) 9"(

)) 8

>

-

θ

: . 9"

?

$

#

1

1

@

!

1 1

1

=

450

l " "1

$ #%

l
# =(

ABCD.EFGH
#

1

#2 (

∆APS

$

$

#

∆APS

!

$ #%

ABCD

x − 1, 2 x − 1,3 x, 5 x − 3, 4 x + 3, 6 x + 2

3

"

"

). 2

"

" 1$ !

!
( 8(
" $

!

$ 8

(2

"

#

" "
1

)/ 2 $ " 1 1

cot an540 =

!

1
("
x

“A Tribute To Mathematics”

( &( )( *

)
1 $ #

#
" "1

0(

1

$

#
)&*( "

"
"1

1

!

!

$

$ #%

! #
!

$ #

$ #%

#

"
"

$ #

?

8

$

$

3

300

>

), '

# 1 $

$ #%

sin 2θ = ...

8 2

)0 '

# 1 − 2x ≥ 2 − x

" "

)& ABCD.EFGH

)* 2

(1,1)

x0 + y0 = ...

2

)

y = ax 2 + bx + ( a − 2b )

1 $

"
!

( &,
3

9

" $

1

$ #%

cos ec90 = ...

4

)4

$

*

*

d
12 cos x − 5sin x + 16

" 5

"1

8

tan θ + tan y = p

8$

*& 2

#

1

'

$ #)

cos θ cos y
= ...
sin (θ + y )

p ≠0("

!

$

$ #%

d

a+b
= ...
b

1 $

#$

$

"

!

1
y= x 3
3

"1 !

y= 3("

$

3

!

$ #%
*) 2

h ( x ) = x2 + 3x − 4

#

"

g ( x ) = x 4 + 2 x3 − ax 2 − 14 x − b
**

1

0&

*, f ( x ) = x + 2

(f

−1

x→

*0 lim
4

9

x +1 1

1
1

x−2 1

%

/ 8$

1

a 2 − 4ab + 4b 2 = ...

x>0

g −1 ) ( x ) = 1

*/ lim x 2 sin

*4 8 $

$

g ( x) =

15
x

x>0 2

"

x = ...

f ( x ) = 2 − x A g ( x ) = x2 + 1

*. '

x →π

g ( x)

x 4 + ax 3 + 2 x 2 + bx + 5 3

!

x+3 1

1

$ #

h ( x ) = 3x ( "

(h

g f )( 3) = ...

1
1
tan = ...
x
x

cos x − sin x
2x −

π

= ...

2

y = xe 2 x ( "

“A Tribute To Mathematics”

dy
= ...
dx

5

,

2

f ( x ) = ax + b ( f ( x ) < 0

#

f ( x) ≥ 0

0≤ x≤4

x≥4 '

8

f ( x )dx = 0

$

# !

$ # y = f ( x ) , x = 0, x = 8

1

0

"1
,

$

f ( x ) = ...

$ # .( "

x
"

z = x + 3y

" "

x + 2y ≥ 8 ( x + y ≥ 8

y≥0

k " "

,& '

,) 8 !

M ( x, y )

2 −1
1 0

$

!

" "

3 x + 2 y ≥ 12 (

"

$ #%

#

x −1
0
=
("
y −1
k

k 1
1 0

"

$ #

"

−3 2
0 1

3

#

!

x + y = ...

1

"

$ # M '(−50,5) ( "

M

$ #%
,*

x !

$

,,

" "

#

"

2

3

x2 − 2 x + 3 = 0 " "

"

1

-

,.

log x +

x

1
>
log 3

!

+

α

"

x

2

3

1

β

#%

"

$ #%

β

+y

$

log 81

α

-

1

(α + β )

3

2

3

=1

!

1

!

2
B
4
,/
,0

,4

+ 32 x + 2 + 8.3x − 1 = 0

! $
#

1

$

+

ABCD.EFGH

“A Tribute To Mathematics”

$ #%

1
1
1
1
+
+
+ ... +
B
1+ 2
2+ 3
3+ 4
99 + 100
9"(

3

2 B
6

.

@

!

$

" "
.

"1

4

,1

%

y

+ C a C : &( C b C : )

'

π

y = tan x

6

Ca D b C :

$ #

5

$

Ca E &b C

e

ln xdx = ...

.&
1

.)

"

!

-

$ #

"1

y

P

1

(1, 0 )

" "1

%

$ # + 12 + 22 + 32 + 42 + 52 + ... + 20 2 B

., =
..

$
6

x !

y = 12 − x 2
"1

π

-

" "

y = x2 − x

1 $

x

1 $

P B

.* @

./

1

x 2 − 3ax + 2a 2 = 0

"

"1

!

" "

# 22 x + 2 − 2 x +3 + 4 = 0 B

$ #$

" 5
2

x

3

$

ABCD 3
6

1

8 1 #"
B

2

x cos xdx = ...

.0
0

.4

x2 − 9 x + p = 0 " "

"
$ #

/

="

/

=

$

α
! $

$ #+

!

-

α

β '

α = β +1 ( "

β B
"

+

1 12
− + 27 = 0
32 x 3x

$ #%

1
1
1
1
+
+
+ ... +
B
1.3 2.4 3.5
8.10

“A Tribute To Mathematics”

7

/&

1

9"

ABCD.EFGH

#-

#

=

$ #3

82 B
/) @
"

!

6

/* 2
5 9"

1

$ 1

!

!

12 x − y = 17

3 3

%
"

3

π

y = x2 + 5

6

1

"

"

! 9"

$

-"

24m 2

$
"

"

$ #5

3
!B

2

sin 3 xdx = ...

/,
0

( f ) ' ( 2) B

f ( x ) = x3 − 4 x 2 + 2 x + 9 (

/. '

−1

// tan 750 − tan150 = ...
/0 lim
x →0

/4

x
= ...
x −1 − x +1

1
9

#

3

5

$ #$
$ #

$

x !

0

$ #

$

m"

0) F
1

3

" 5

0

0& =

" "$

" "

$ 1
3

# + 2 log

1

(

3

"

-"

5

B

)

log ( 2 log x ) = 1

y = x+m "

!

1 $

y=

1 2
x −2 B
2

$ # + cos 20.cos 40.cos 60.cos80 B
1

1

"1 # ! 6 $ "

“A Tribute To Mathematics”

"1 #

3

$ 3
3

7 cm

s

$ # $ 3

: , 9" B

8

2

0*

$ #

$

"

2 x dx

$ # 1$

x

1 $

$ 1#

9$

−2

"

x B

0, lim nr 1 − cos
n→

0. 2

#

2π
= ...
n

( 4, 6 )

x 2 + y 2 − px − 4 y + 8 = 0 " $ $

$

=

$ # 3

-3

! B
0/

1

@
00 '

log ( 2a − 2 )

log ( b − 4 )

1

3 = xx

'

4

$

-

$

-

4& '

...
xx

"

a

log a 1

7
3

,) =

b

23 = 5 ( 23 = 10 ( c = 2
"

$ #

1 1
+ + ...
a a2

log b 1

=

!

1

$ # 4a ( "

$

a = ...

x = ...

("

x = ...

("
"

1

4) =

+ a +1+

#

$ #

sin α = ...

82@( "

log a

x

04 '

4

1

3 "$ #

α

'

ABCD.EFGH

$ # ,, '
$ #

1
b−a

x

216 = 162

#

x2 ( x2 − 5x + 6)
x2 −1

4* 8 $

f ( x ) = a ( x − 1)( x − 3)

4, 8 $

f ( x) =

3 − 2x
(
−4 x + 7

“A Tribute To Mathematics”

$
x

5( "

9
#

1

$

,

7

,
1

$ #

7 (

B
"

3 "$ #

1

B

≥ 0, x ∈ R B
f ' (1) = −4 (
$ #

$

$ #

9

f ( x) B

f −1 (1) B

9

4.

$ #1

-1

$

5

00 ≤ x ≤ 900 !

"

" "

#

"

tan 2 x
=1 B
1 + sec x
x = 0,999..... + 0, 666..... + 0, 444..... ( "

4/ 8 $

40 f ( x ) = x3 + ax + b

a≠b

x ( x 2 − 4 x + 4 ) cos x

44 lim

x3 + 7 sec2 x − 1

x →0

'

1

x+

8$

x4 +

=

3

1
= ...
x4

)

'

f (1) = ...

$

$ # 96 3 9" 2

$ # f ( x) B

& f x + x −1 = x3 + x −3 ( "
)

3 3

B

1
= 3( "
x

(

x=a

= ...

" 1
"

$ #%

6

x=b("

6

tan 5 11π x

$

x1 , x2 , x3 , x4 , x5 "

! $

2.35 x − 34 x +1 + 33 x + 5.32 x + 2.3x − 12 = 0
*

1

!

-

x1 + x2 + x3 + x4 + x5 = %

$
! , $ 1# !

-

x2 + 2 x − 4 = 0 B
,

2

#

x12 + x2 2 = −

x 2 − 3x + n = 0 " " $

" $ $

“A Tribute To Mathematics”

$ #

"

!

;&( 0< B

( p + 1) x 2 − 2 ( p + 1) x + 12 = 0 "
α 2 β 3 + α 3 β 2 = 18 ( "

x2 '

x1

1
( x1 + x2 ) − ( x12 x2 + x1 x2 2 ) "
3

1
.

-

"$

-

α

β '

:%
10

20 − 20 − 20 − ..... = .....

/

x 2 − ax + 2a − 3 = 0 " " $

0

α

-

α 2 β + αβ 2 = 35 ("

β '

a :%
4

$ #
'

!

-

3 "$ #

-

3 "$ #

x1 , x2 , 2 x1 " "1

1

'

3sin x − 4 cos x = 0 ( "

)

'

sin A + sin B =

'

α

cos (α − β )

(

n :%

x1 > x2 . '

x2
$ #

$

bB

sin 2 x :%

3
2

cos A + cos B =

$

9 ( cos (α − β ) =

β

1
2

A≥0

B ≤ 180

'

1
3
2

cos α .cos β = 1 ( "

:%

2 $ "

tan b =

.

x1

$

E8:%

cos (α + β )

,

$

"

x2 + x − n = 0 ( "
-

"

&

*

x 2 − 3x + n = 0

"

x 2 + bx + 8 = 0 " " $

#

+ x2 + 2 x − 1 = 0

$ 1# !
"

-

2

"

!

8 (

4
("
3

sin 2α =

(1

9

$ #

-

!

'

tan a =

3
4

9:%

1
1
( sin 2α =
4
4

( sin α + cos β )( cos α − sin β ) = 0 ( "

$

cos (α + β ) :%

“A Tribute To Mathematics”

11

/

2

#

2 sin 3 x − cos 2 x − 2sin x = 0

! $

"

20
0

'

4

'

&

'

&

2n

1

6

A = a +2 a −5
3
−2

"

;&( &(