Рівень стандарту та профільний рівень (демонстраційний варіант)

1. 1.
2.
3.
4.
5.
1.
2.
4.
5.
6.
.
1–26 31
11

2. 2
2
4
2 4 5
225
a2
b2
= (a b a + b
(a + b 2
= a2
+ 2ab + b2
(a b 2
= a2
ab + b2
ax2
+ bx + c a
D = b2
ac
x =
–b D—
2a
x2 =
–b + D—
2a
D
x = x2 =
–b
—
2 D
ax2
+ bx + c = a(x x x x2
a = n
= a a a
n
a R n N n 2
a a2
=
a–n
= —n n N
a
m—n
= amn
m Z n N n 2
ax
ay
= ax + y
x
—y = ax – y
(ax y
= ax y
(ab x
= ax
bx
(a
b
x
=
x
—
bx
a b c k
alogab
= b log
log (b c b + log c
log b
c = log b c
log bn
= n log b
log k b =
k
log b
an = a + d(n Sn =
a + n
—
2
n
Pn 2 n = n! Ck
n =
n!
—
k! (n k
Ak
n =
n!
—
(n kP(A = k
n
bn = b qn
Sn =
b (qn
—
q
(q
a =
a
–a
2
ax y
= ax
a
= a(x
=
–b—
2a
k
+ d(n
(
x
—y = ax
a x
N
n N
n N n
x = x2
x2
+
– DD—
2a
c a

3. 1.
200
150
100
350
300
250
50
0
2.

4. 3.
4. 2
5.
MBA = 25o
M B C
A D
?
25o
o o o o o
4
o
A
M
25o

5. 6. y = f(x
7. ( a 2 + a
2 2 4 2
8. F
F C
o
o
F o
F o
F o
F o
F
y
y = f(x)
x1–1 4
1
0
5
F
F
2
11
== f((ff x)x

6. (2x2
—
4x
2—
x
2—
x4
4—
x
—
2x4
—
2x
11.
x y
x + 4y =
x y
x y
4
x
x +x
x
—
2

7. 12. f(x x + tgx
f (x x2
+ —
tg x
f (x x —
tg x
f (x x4
+ —
cos2 x
f (x x2
+ —
cos2 x
f (x x4
—
tg x
13. x
+ + +
14. o
2 2
—
2
—
2
2—
2
o
+

8. 15.
2 4
16.
CNB
DM i DN
o
MBND
2 2 2 2 2
M N
A C
D
B
BNDD
M
2

9. -
-
17.
1
2
3
y = 2x
y x
y x
y
x1–3 3
1
0
y
x1–3 3
1
0
y
x1–3 3
1
0–33
1
33

10. 18.
=
1
2
3
1 a2
2 a
3 log2 (4 + a
5
1
2
3
1
2
3
CB K
DA
5

11. D
1
2
3
1
2 C
3
A1
B1 C1
D1
A D
CBB
D1

12. 21.
1.
2.

13. 22.
ACB o
1.
O
15o
A
C
B
O
o

14. 23.
1.
2. ACC

15. 24. an a2 a4
1.
2. S

16. 25.
5
26.

17. 27.
log5
—
log5 5
28. x

18. y = x
1.
x y
2. y = x
3.
4. F(x f(x x
5. S
f
6. S
xf(ff xx
S

19. 31. SABCD ABCD
1. SABCD
SA
SABCD
DCD

20. 32.
1. SABCD
2.
33. x4
+ y4
x y + xy4
+ y4
SABCD

21. 34. x
+ 2a x
+ a2 x
—
x
x a
1.
x
—
x
2. a

22. 22

23. (
x
( x = 2 x (ex
= ex
(ln x = x (sin x = cos x
(cos x = sin x (tg x = cos2x
(u + v = u + v (u v = u v
(uv = u v + uv (Cu = Cu
(u–v =
u v uv
v2
sin = y cos = x sin2
+ cos2
tg = 2
= cos2
sin2 = 2sin cos cos2 = cos2
sin2
o
= cos o
= sin
o
= sin o
= cos
o
= tg
o
= tg
a
b
f(x dx = F(x a
b
= F(b F(a
0–1
–1
1
1
y
x
M(x , y )
x
y
tg
cos
sin
o o
2
2
2—
2
—
2—
2
—
2
—
2
45
o
4
o o o o o
2
—
2
2
F(x C
C
f(x
C
x— + C
ln x + C
x + C
sin x x + C
cos x sin x + C
tg x + C—
cos2
x
ex
ex
+ C
x
x
=
= co
sin2
M
sin
2 = cos
o
s2
= s2
F(FF a
—
os x
x—
ln
C
x +x C
F(FF xx C

24. 24
S = ab sin
S = aha
V = S H
S = P H
V = S H
S =
2
P m
V = R2
H
S = 2 RH
V = R2
H
S = RL
V =
4
R
S = 4 R2
L = 2 R
(x x 2
+ (y y 2
= R2
S = R2
S = 2
d d2
d d2
S =
a + b—
2 h
a b
S = ab
p =
a + b + c—
2 + +
a2
= b2
+ c2
bc cos
a— =
b—
sin
=
c—
sin
= 2R
R –
ABC
a2
+ b2
= c2
b
c = cos a
c = sin a
b
= tg
c
ab
C
A B
ha
c
a
b
a
b ha
a
b
d1
d2
a
b
h
R
M(x0, y0)
H
M(x0, y0, z0)
A(x1, y1, z1) B(x2, y2, z2)
H m H
R
RH L
R
R
S = 2
a ha S = 2
b c S = p(p a p b p c
x =
x + x2
—
2
y =
y + y2
—
2
z =
z + z2
—
2
AB(x2 x y2 y z2 z AB (x2 x 2
+ (y2 y 2
+ (z2 z 2
a b = a b + a2b2 + a b
a b = a b
a(a1, a2, a3)
b(b1, b2, b3)
H
x y2 y
)
M y0
V =
S
H
R
d2
S = 2
d d
d2
c
n