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ЗНО-2021 (математика)
1. The diagram shows angles MBC and ABC measuring 25 degrees each. 2. Angle MBC and ABC are equal since they are vertical angles. 3. Therefore, the measure of angle CBD is also 25 degrees by angle substitution.
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ЗНО-2021 (математика)
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- 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
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- 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 iDN o MBND 2 2 2 2 2 M N A C D B BNDD M 2
- 9. - - 17. 1 2 3 y = 2x yx 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 3log2 (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 AD CBB D1
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- 15. 24. an a2a4 1. 2. S
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- 18. y = x 1. xy 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 + 2ax + a2 x — x x a 1. x — x 2. a
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- 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 = absin 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