高一数学上学期综合压轴90题

U=1,2,3,4,5

A=1,2,4,B=2,3,4,5

∁UA⊆B

∁A∩∁B≠∅

U

U

A∪B=U

A∩B⊆A∪B

A=−2,−1,0,1,B=0,1,2,3

U=R

−2,−1

−2,1

−2,−1,1

−2,−1,0

x

x−a≤2

A=x0≤x≤4

B=x|m−3≤x≤m+3

a

①

②

m

①

②

−2,4⊆A∪B

A∩B=A

①A∩B=B②x∈A

x∈B

③B∩∁RA=∅

A={x∈R(x−1)(x+2)>0},B={x∈Ry=x+a,y∈R}

a=1

A∩∁RB

a

A=x,x,x,xxi∈−1,1,i=1,2,3,4

1

2

3

4

a,a,a,a,b,b,b,b∈A

ab+ab+ab+ab=0

a,a,a,a

b,b,b,b

1234

1

2

3

4

1

2

3

4

1

1

2

2

3

3

4

4

1

2

3

4

B⊆A

B

B

x,y∈M

x+y∈M

x−y∈M

M={x|x=3k,k∈Z}

M1M2

M1∪M2

B

A

n

m

=xx=,m∈A,n∈B

A=2,4

k

2

B

A

B=xx=−1,k∈A

∪B

k

A

N*

Pk

A

x

y

x−y≠k

B=1,4,5,8,11

A=a,a,a,a⊆1,2,3,4,5,6

A

P2

A

P3

1

2

3

4

A⊆1,2,⋯,11

P4

P7

A

Ω={xx⊆U}

A⊆Ω

①

M,N∈A

M∪N∈A

②

M∈A

∁UM∈A

U={1,2,3}

M,N∈A

∅∈A

M∩N∈A

3

m

1

n

2

2

m>0n>0m+4mn+3n=m+n

+

4+23

3+22

x,y

2x+y=2

1

4

xy

y+x2

1

2x

1

y

x

4+2y

+

11

M=max4x+,+y

yx

maxa,b

a

b

xy

M

22

3

8

9

3

a

3

b

a>0b>0

x>0y>0

+2b=2

2a+

2x+y=1

1

x

2

y

+

b

a

b

1−a

0<a<1

+

≥1

b

1

4

1

2

1

2

,+∞

,+∞

0,

0,4

2x+y−2xy=0

x>0,y>0

2x+y>k2+k−8

k

(−4,3)

[−4,3]

(−3,4)

y

[−3,4]

x

x−1y−2=2

3x+2y>m

m

−∞,4+62

−∞,7+43

6+42,+∞

8+43,+∞

a

b

2

a

a>0,b>0

2a+b=2

t2−3t≤

+

2

a+bc+d≥ac+bd

1

x

1

y

2m+2

m

x+y=1

+

≥

a−2x2−2a−2x−4<0

x∈R

a

−∞,−2∪2,+∞

−2,2

−∞,−2∪2,+∞

−2,2

a>0,b∈R

ax−2x2+bx−6≥0

0,+∞

4a−b

22

32

∃x∈R,mx2+2m−3x+4≤0

−∞,0

m

1,9

−∞,1∪9,+∞

−∞,1∪9,+∞

−x2+2x+m≤0

x∈[0,2]

x

2x−1>Kx2−1

K

x∈R

K

x∈1,+∞

K∈−2,2

x

R

fx

∀x,y∈Rfx−fy=fx−y+2x−yy

f6=0

f0=1

f3=9

∀x∈Rfx+f−x≥0

fx

f(x)

R

f(1)=−2

f(x)⋅f(y)=f(x+y)+f(x−y)

f(0)=0

f(x)

f(2)=1

f(x)

y=fx

−∞,0∪0,+∞

fxy=fx+fy−1

fx

1

f2=

x>1

f1024

2

fx<1

f2x+1>1

fx

x,y∈R

fx+y=fx+fy−2

f2=4

f1

gx=fx−2

gx

f−2025+f−2024+⋯+f−1+f0+f1+⋯+f2024+f2025

R

f(x)

∀x,y∈R

f(x+y)=f(x)+f(y)+1

f(1)=1f(x)

R

f(0)

f(x)+1

∃x∈[−1,1]

f(x)>m2−m−2

m

f(2x2−8x+4)+3f(x)>0

fx1−fx

2

fx

∀x,x∈R

x1≠x2

>2

1

2

x1−x2

f2=12

−2,2

−∞,−2∪2,+∞

fm2≥2m2+8

m

−2,2

−∞,−2∪2,+∞

fx

R

fx+4=2fx

x∈0,4

fx=2x2−8x

3

4

∀x∈−∞,t

fx≥−

t

−∞,−11

−∞,−5

−∞,−7

−∞,−3

2

3

fx

−∞,0∪0,+∞

f3=

xxfx−fx

xfx−2

x

∀x1x2∈0,+∞

x1<x2

1

2

1

2

<2

x

>0

x2−x1

−∞,−3∪0,3

−3,3

−3,0∪3,+∞

0,3

fx=x2+5x+8gx=mx+3−5m

fx1=gx2m

x1∈−4,2

x2∈2,6

y=fx

−2,−6

f0=−2

fx−2

fx

x

gx=

y=fx

∀x∈1,2,∃x∈1,2

gx1≥mx2+4

m

1

2

fx

fx−1

1,0

fx+2

fx

0,2

f10<f19<f13

f13<f10<f19

f10<f13<f19

f13<f19<f10

fx

R

fx+1

fx+2

x1x2∈1,2x1≠x2

fx

x1−x2fx1−fx2>0

f2025=0

21

9

fx

−1,0

f−<f

5

8

x

x

x

x−x

x

x

fx=x

1

fx+=fx

2

gx=xx

hx=2xx−x−1

−1

(−2,3−a)

ax+b

4−x2

f(x)=

f(x)

f(x)

f(2t+1)+f(t−2)>0

x

fx=

x+1

fx

fx

0,+∞

x

fax2+3ax+f1−ax>0

x

a

fx=2x2−2x+1

fx

−∞,1

1,+∞

1,+∞

0,1

−∞,1

−∞,1

−∞,1

0,1

x

a−1

a+1

f(x)=

(a>0a≠1)

x

①

②

③

④

f(x)

f(x)

f(x)

f(x)

(0,1)

(0,0)

1

2

3

fx=a−

4

1

2+1

x

a

fx

x∈R

fmx2+f3−2mx>0

m

−ex+a

ex+1

R

f(x)=

a

y=f(x)

x

x

x

f(m⋅3)+f(3−9−2)>0

x≥0

m

x

x

fx=9−m⋅3−1

f2=−1

m=1

m

fx

−2,1

x+1

gx=2

x1∈−2,1

x2∈R

fx1≥gx2

m

f(x)=lnx−2−lnx

f(x)

f(x)

R

f(x)

(−∞,0)

3

1

(1,0)

4,5

f(log23)>f(−)

2

2

fx=logx−ax+6(1,2)

a

2

4,+∞

−∞,7

4,7

2

fx=2x−1−logx−2x+4

a=flog23b=flog34

1

2

c=flog45

abc

a>b>c

c>b>a

b>a>c

b>c>a

1+ax

f(x)=log2x−1

f(x)

5

x∈[,3]

f(x)<2m−1

3

fx=log1+2x−log1−2x(a>0,a≠1)

a

a

fx

fx

x

fx<0

fx=2025x+log2025x2+1+x−2025−x+1

fx2−2x+f(3x)>2

0,+∞

−1,0

−∞,−1

R

−∞,−1∪0,+∞

fx1−fx

2

fx

x1,x2

x1<x2

>−1

x1−x2

x

x

f1=1

1,+∞

−1,0∪0,3

flog3−1<2−log3−1

2

2

−∞,1

−∞,0∪0,1

2

fx=logx−ax+1

2

a=2

fx

fx

2,+∞

a

gx=4x−2x+1

x1∈0,1

x2∈−1,1

fx1≥gx2

a

3x+1

3x+a

fx=

a

x

x

gx=log⋅log+m

3339

x1∈3,27

x2∈0,2

gx1=fx2

m

1−ax

f(x)=log2x−1

f(x)(1,+∞)

x

−x

x

−x

f2+1+f2+1>logm2−2

x∈(0,+∞)

2

2x−2,0<x≤1

f(x)=1

2

g(x)=x2f(x)−1

f(x−1),x>1

log2x,x≤2

x2−8x+14,x>2

fx=

fx=k

x1

x2x3xx<x<x<x

4

x1+x2x3+x4

4

1

2

3

0,16

(18,+∞)

16,20

5−2x−2,x≥0

[16,+∞)

fx=

gx=f2x−m+2fx+2m

2x+3

x+1

,x<0

1,2∪3,4

1,2∪3,4

2,3∪4,+∞

log2x,x>0

4,+∞

f(x)=

f(x)=a

x,x,x,x

1234

1

x2+x+2,x≤0

4

x+xx

3

x<x<x<x

x4−

1

2

1

2

3

4

4

16

x+,x≥3

x

f(x)=

1

,x<3

x−3

f(x)(−∞,3)

F(x)=f(x)2−4af(x)+3a2

a

y=fx

x0fx0+f−x0=0

x0,fx0

x2+3x,x<0

kx+5,x≥0

y=fx

3−25,0

−∞,3+25

fx=

fx

k

0,3+25

−∞,3−25

D

fx

k

x∈D

fx−f−x≤k

fx

P0

P1

Pk

①

x

②fx=

1+x2

③

④

fx=x2+x+1

k

fx

Pk

a

1+2

a>0

fx=

Pk

a∈0,k

x

①

②

③

④

f(x)

x1≠x2

x

f(x)+f(−x)=0

f(x)−f(x)

x1,x2

1

2

<0

1

f(x)

x1−x2

①f(x)=−x②f(x)=x2③f(x)=|x|④f(x)=

x

y=fx

x1

x2

fx1fx2=1

gx=x

fx=2x−2

m,nn>m>0

mn

3

2

3

2

3

2

hx=x−a2a<

hx≥−t2+s−tx

,3

x∈,3

t∈R

s

A=yy=fx,x∈DB=yy=2m−x,x∈D

m∈R

B⊆A

y=fx

1,2

0,a

pm

y=3x

y=3x−1

p1

p1

fx=−x2+2tx+3

0,2

pm

π

6

π

4

x=

fx=cosωx−

ω>0

ππ

−,

312

fx

ω

3

2

5

3

15

2

π

3

π

2

f(x)=sin(ωx+)ω>0

T>

f(x)

ππ

(,)

63

2π

3

x=

ω

1

4

21

4

π

6

fx=3sinωx+ω>0

0,2π

ω

1913

66

138

63

1913

66

138

63

,

,

,

,

π

2

π

8

fx=sinωx+φω>0φ≤

x=−

fx

π

8

ππ

189

x=

y=fx

fx

,

ω

π

3

P3,1

φ

fx=sinωx−φω>0

0,

2π

3

,π

ω

2

3

5

3

0,

1,

58

23

1117

43

,

,

π

f(x)=2cos(ωx+)+2(ω>0)

ππ

[−,]

63

6

[0,π]

2

3

1

2

11

12

13

12

fx=sinxgx=cosxhx=fx+gx

y=fxgx

hx0,2π

hx

0,2π

y=fgx

π

3

fx=2sinωx+φ

ω

ω>00<φ<π

fx≤f

π

2

fx

0,

3

fx=22cosωx+φ(ω>0,0<φ<π)

fx

fx

π

2

0,

π

4

gx=fx+2

,m

m

π

f(x)=2cos(ωx+)(ω>0)

[0,2π]

6

ω

ππ

[−,]

24

ω∈N∗

ω∈N∗

|f(x)−m|<3

y=f(x)+t

ππ

[−,]

42

π

2

m−1sin2x−msinx+m−1>0

0,

1,+∞

−∞,4

2,+∞

4,+∞

2,4

3,4

4

2

cosx−tcosx+3>0

−∞,−4

−4,+∞

π5π

cos2x+2sinx−1−m≤0

−,

36

π

fx=23sin(2x−)+2

6

fx

fx

ππ

−,

64

ππ

124

f2x−2mfx+3m≥0

x∈−

,

fx=cos2x−2asinx+a+3a∈R

fx

R

π

2

fx>0

0,

a

fx=5

0,2π

a

π

6

π

6

π

2

fx=2sinx+

gx=2sinωx+

x1∈0,

π

2

x2∈0,

fx1=gx2+2

ω

π

6

1

ω

fx=2sinx+

ω>0

π

2

π

2

gx

x1∈0,

x2∈0,

fx1=gx2+2

ω

π

6

π

2

fx=asin2x−+ba>0,b∈R

0,

0,3

fx

x1∈0,

π

6

π

2

x2∈,m

fx1≥fx2

m

π

2

5π

12

fx=sin2x+φ0<φ<

f

=0

fx

ππ

−,

43

ω>0

gx=fx+

fωx

ω

ππ

π

12

x

2

x

π

3

4

+af−af

+

−2a+

,

a

24

123

π

3

fx=sin2x+,gx=2sin2x+acosx+1a∈R

y=fx

gx

ha

x2∈R

ha

fx1+1≥gx2

x1∈R

a

ππ

α∈−,

22

sinα=x

α=arcsinx

2y2−1=

α∈0,π

cosα=x

2

2

α=arccosx

2a

y∈0,1

(arccosy)−(arcsiny)=a

2a

π

cos

−sin

−sin

π

4a

π

4a