Сертифікаційна робота з математики 2021 року (основна сесія)

1. ǿǳǾȀǶȂǥǸǮȄǥǷǻǮǾǼǯǼȀǮ ǵǺǮȀǳǺǮȀǶǸǶ ǥțȟȠȞȡȘȤȳȭȧȜȒȜȞȜȏȜȠȖȐȕȜȦȖȠȳ 1. ǽȞȎȐȖșȎȐȖȘȜțȎțțȭȕȎȐȒȎțȪȕȎȕțȎȥȓțȜȝȓȞȓȒȘȜȔțȜȬțȜȐȜȬȢȜȞȚȜȬȕȎȐȒȎțȪ 2. ǾȖȟȡțȘȖ ȒȜ ȕȎȐȒȎțȪ ȐȖȘȜțȎțȜ ȟȣȓȚȎȠȖȥțȜ ȏȓȕ ȟȠȞȜȑȜȑȜ ȒȜȠȞȖȚȎțțȭ ȝȞȜȝȜȞȤȳȗ 3. ǰȳȒȝȜȐȳȒȎȗȠȓ șȖȦȓ ȝȳȟșȭ ȠȜȑȜ ȭȘ ǰȖ ȡȐȎȔțȜ ȝȞȜȥȖȠȎșȖ ȗ ȕȞȜȕȡȚȳșȖ ȕȎȐȒȎțțȭǰȖȘȜȞȖȟȠȜȐȡȗȠȓȭȘȥȓȞțȓȠȘȡȐȳșȪțȳȐȳȒȠȓȘȟȠȡȚȳȟȤȭȐȕȜȦȖȠȳ 4. ǻȎȚȎȑȎȗȠȓȟȭȐȖȘȜțȎȠȖȐȟȳȕȎȐȒȎțțȭ 5. ǰȖ ȚȜȔȓȠȓ ȟȘȜȞȖȟȠȎȠȖȟȭ ȒȜȐȳȒȘȜȐȖȚȖ ȚȎȠȓȞȳȎșȎȚȖ țȎȐȓȒȓțȖȚȖ țȎ ȟȠȜȞȳțȘȎȣǲșȭȕȞȡȥțȜȟȠȳǰȖȚȜȔȓȠȓȴȣȐȳȒȜȘȞȓȚȖȠȖȐȳȒȳȞȐȎȐȦȖ ǥțȟȠȞȡȘȤȳȭȧȜȒȜȕȎȝȜȐțȓțțȭȏșȎțȘȳȐȐȳȒȝȜȐȳȒȓȗǮǯȠȎǰ 1. ȁȏșȎțȘǮȕȎȝȖȟȡȗȠȓȥȳȠȘȜȕȑȳȒțȜȕȐȖȚȜȑȎȚȖȳțȟȠȞȡȘȤȳȴȒȜȘȜȔțȜȴȢȜȞȚȖ ȕȎȐȒȎțȪșȖȦȓȝȞȎȐȖșȪțȳțȎǰȎȦȡȒȡȚȘȡȐȳȒȝȜȐȳȒȳ 2. ǻȓȝȞȎȐȖșȪțȜȝȜȕțȎȥȓțȳȝȳȒȥȖȧȓțȳȐȳȒȝȜȐȳȒȳȐȏșȎțȘȡǮȏȡȒȓȕȎȞȎȣȜ ȐȎțȜȭȘȝȜȚȖșȘȜȐȳ ȍȘȧȜ ǰȖ ȝȜȕțȎȥȖșȖ ȐȳȒȝȜȐȳȒȪ ȒȜ ȭȘȜȑȜȟȪ ȳȕ ȕȎȐȒȎțȪ ² ȡ ȏșȎțȘȡ Ǯ țȓȝȞȎȐȖșȪțȜȠȜȚȜȔȓȠȓȐȖȝȞȎȐȖȠȖȴȴȕȎȚȎșȬȐȎȐȦȖȝȜȝȓȞȓȒțȬȝȜȕțȎȥȘȡ ȗȝȜȟȠȎȐȖȐȦȖțȜȐȡȭȘȝȜȘȎȕȎțȜțȎȕȞȎȕȘȎȣ 4. ȍȘȧȜ ǰȖ ȕȎȝȖȟȎșȖ ȐȳȒȝȜȐȳȒȪ ȒȜ ȭȘȜȑȜȟȪ ȳȕ ȕȎȐȒȎțȪ ² țȓȝȞȎȐȖșȪțȜ ȠȜȚȜȔȓȠȓȐȖȝȞȎȐȖȠȖȴȴȕȎȝȖȟȎȐȦȖțȜȐȖȗȐȎȞȳȎțȠȐȳȒȝȜȐȳȒȳȐȟȝȓȤȳȎșȪțȜ ȐȳȒȐȓȒȓțȖȣȚȳȟȤȭȣȏșȎțȘȎǮ 5. ǰȖȘȜțȎȐȦȖ ȕȎȐȒȎțțȭ ȳ ² Ȑ ȕȜȦȖȠȳ ȎȘȡȞȎȠțȜ ȕȎȝȖȦȳȠȪ ȴȣțȳȞȜȕȐ·ȭȕȎțțȭȐȏșȎțȘȎȣǯȠȎǰ 6. ǰȎȦ ȞȓȕȡșȪȠȎȠ ȕȎșȓȔȎȠȖȚȓ ȐȳȒ ȕȎȑȎșȪțȜȴ ȘȳșȪȘȜȟȠȳ ȝȞȎȐȖșȪțȖȣ ȐȳȒȝȜȐȳȒȓȗ ȕȎȝȖȟȎțȖȣ ȡ ȏșȎțȘȡ Ǯ ȳ ȝȞȎȐȖșȪțȜȑȜ ȞȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ²ȐȏșȎțȘȎȣǯȠȎǰ ǼȕțȎȗȜȚȖȐȦȖȟȪ ȳȕ ȳțȟȠȞȡȘȤȳȭȚȖ ȝȓȞȓȐȳȞȠȓ ȭȘȳȟȠȪ ȒȞȡȘȡ ȕȜȦȖȠȎ ȗ ȘȳșȪȘȳȟȠȪ ȟȠȜȞȳțȜȘǦȣȚȎȱȏȡȠȖ ǽȜȕțȎȥȠȓțȜȚȓȞǰȎȦȜȑȜȕȜȦȖȠȎȡȐȳȒȝȜȐȳȒțȜȚȡȚȳȟȤȳȏșȎțȘȎǮȠȎȘ ǵȖȥȖȚȜǰȎȚȡȟȝȳȣȡ ǾȜȏȜȠȎȟȘșȎȒȎȱȠȪȟȭȕȕȎȐȒȎțȪȞȳȕțȖȣȢȜȞȚǰȳȒȝȜȐȳȒȳȒȜȕȎȐȒȎțȪ²ǰȖȚȎȱȠȓ ȝȜȕțȎȥȖȠȖ Ȑ ȏșȎțȘȡ Ǯ ǾȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ² ǰȖ ȚȎȱȠȓ ȕȎȝȖȟȎȠȖ ȐȏșȎțȘȎȣǯȠȎǰ. ǾȓȕȡșȪȠȎȠȐȖȘȜțȎțțȭȐȟȳȣȕȎȐȒȎțȪȏȡȒȓȐȖȘȜȞȖȟȠȎțȜȝȳȒȥȎȟȝȞȖȗȜȚȡȒȜ ȕȎȘșȎȒȳȐȐȖȧȜȴȜȟȐȳȠȖ ǾȓȕȡșȪȠȎȠȐȖȘȜțȎțțȭȕȎȐȒȎțȪ1–26, 30ȳ31ȏȡȒȓȕȎȞȎȣȜȐȎțȜȭȘȞȓȕȡșȪȠȎȠ ȒȓȞȔȎȐțȜȴȝȳȒȟȡȚȘȜȐȜȴȎȠȓȟȠȎȤȳȴȒșȭȐȖȝȡȟȘțȖȘȳȐȭȘȳȐȖȐȥȎșȖȚȎȠȓȚȎ ȠȖȘȡțȎȞȳȐțȳȟȠȎțȒȎȞȠȡ ǾȓȕȡșȪȠȎȠȐȖȘȜțȎțțȭȐȟȳȣȕȎȐȒȎțȪȏȡȒȓȕȎȞȎȣȜȐȎțȜȭȘȞȓȕȡșȪȠȎȠȒȓȞȔȎȐ țȜȴȝȳȒȟȡȚȘȜȐȜȴȎȠȓȟȠȎȤȳȴȒșȭȐȖȝȡȟȘțȖȘȳȐȭȘȳȐȖȐȥȎșȖȚȎȠȓȚȎȠȖȘȡțȎ ȝȞȜȢȳșȪțȜȚȡȞȳȐțȳ 1 ǵȜȦȖȠ ‹ȁȘȞȎȴțȟȪȘȖȗȤȓțȠȞȜȤȳțȬȐȎțțȭȭȘȜȟȠȳȜȟȐȳȠȖ ȅȎȟȐȖȘȜțȎțțȭ²ȣȐȖșȖț

2. 2 ȀȎȏșȖȤȭȘȐȎȒȞȎȠȳȐȐȳȒȒȜ ǮǹǱǳǯǾǮǥǽǼȅǮȀǸǶǮǻǮǹǥǵȁ ǲǼǰǥǲǸǼǰǥǺǮȀǳǾǥǮǹǶ ǼȒȖțȖȤȳ ǲȓȟȭȠȘȖ 0 100 1 400 2 3 1600 4 1 121 441 1681 2 144 484 1024 1764 3 4 576 1156 5 225 625 1225 2025 6 256 676 2116 7 8 324 361 784 841 1444 1521 2304 2401 ȂȜȞȚȡșȖȟȘȜȞȜȥȓțȜȑȜȚțȜȔȓțțȭ ǸȐȎȒȞȎȠțȓȞȳȐțȭțțȭ ǺȜȒȡșȪȥȖȟșȎ ǿȠȓȝȓțȳ ǹȜȑȎȞȖȢȚȖ ǮȞȖȢȚȓȠȖȥțȎȝȞȜȑȞȓȟȳȭ ȀȓȜȞȳȭȗȚȜȐȳȞțȜȟȠȓȗ ǸȜȚȏȳțȎȠȜȞȖȘȎ ǱȓȜȚȓȠȞȖȥțȎȝȞȜȑȞȓȟȳȭ a2 – b2 = (a – b)(a + b) (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 ax2 + bx + c = 0, a z 0 D = b2 – 4ac²ȒȖȟȘȞȖȚȳțȎțȠ x1 = –b – D — 2a , x2 = –b + D — 2a ȭȘȧȜD ! 0 x1 = x2 = –b — 2Ȏ ȭȘȧȜD = 0 ax2 + bx + c = a(x – x1)(x – x2) a1 = Ȏ, Ȏn = a ˜ a ˜ a nȞȎȕȳȐ Ȓșȭa R, n N, n 2 a0 ȒȓȎ z 0 a2 = ~Ȏ~ a–n = 1 — Ȏn ȒșȭȎ z 0, n N a m — n = am n , Ȏ ! 0, m Z, n N, n 2 ax ˜ ay = ax + y Ȏx — Ȏy = ax – y (ax )y = ax ˜ y (ab)x = ax ˜ bx (a – b) x = Ȏx — bx a ! 0, Ȏ z 1, b ! 0, c ! 0, k z 0 alogab = b logȎȎ = 1 logȎ1 = 0 logȎ(b ˜ c) = logȎb + logȎc logȎ b – c = logȎb – logȎc logȎbn = n ˜logȎb logȎk b = 1 – k ˜logȎb an = a1 + d(n – 1) Sn = a1 + Ȏn — 2 ˜ n Pn = 1 ˜ 2 ˜ 3 ˜˜ n = n! Ck n = n! — k! ˜ (n – k)! Ak n = n! — (n – k)! P(A) = k – n bn = b1 ˜ qn – 1 Sn = b1(qn – 1) — q – 1 , (q z 1) ~a~ = aȭȘȧȜȎ 0, –aȭȘȧȜȎ 0

3. ǵȎȐȒȎțțȭ²ȳ²ȚȎȬȠȪȐȳȒȝȜȐȳȒțȜȝȜȥȜȠȖȞȖȠȎȝ·ȭȠȪȐȎȞȳȎțȠȳȐȐȳȒȝȜȐȳȒȳ ȕ ȭȘȖȣ șȖȦȓ ȜȒȖț ȝȞȎȐȖșȪțȖȗ ǰȖȏȓȞȳȠȪ ȝȞȎȐȖșȪțȖȗ țȎ ǰȎȦȡ ȒȡȚȘȡ ȐȎȞȳȎțȠȐȳȒȝȜȐȳȒȳȝȜȕțȎȥȠȓȗȜȑȜȐȏșȎțȘȡǮȕȑȳȒțȜȕȳțȟȠȞȡȘȤȳȱȬǻȓȞȜȏȳȠȪ ȳțȦȖȣȝȜȕțȎȥȜȘȡȏșȎțȘȡǮȠȜȚȡȧȜȘȜȚȝ·ȬȠȓȞțȎȝȞȜȑȞȎȚȎȞȓȱȟȠȞȡȐȎȠȖȚȓ ȴȣȭȘȝȜȚȖșȘȖ ǯȡȒȪȠȓȜȟȜȏșȖȐȜȡȐȎȔțȳȝȳȒȥȎȟȕȎȝȜȐțȓțțȭȏșȎțȘȎǮ ǻȓȝȜȑȳȞȦȡȗȠȓȐșȎȟțȜȞȡȥțȜȟȐȜȑȜȞȓȕȡșȪȠȎȠȡțȓȝȞȎȐȖșȪțȜȬȢȜȞȚȜȬȕȎȝȖȟȡȐȳȒȝȜȐȳȒȓȗ 1. ǵȎ ȜȒțȎȘȜȐȖȣ ȘȜțȐȓȞȠȳȐ ȕȎȝșȎȠȖșȖ ȑȞț ǿȘȳșȪȘȖ ȐȟȪȜȑȜ ȠȎȘȖȣ ȘȜțȐȓȞȠȳȐ ȚȜȔțȎȘȡȝȖȠȖȕȎȑȞț Ǯ ǯ ǰ Ǳ 6 24 30 36 2. ǻȎ ȑȞȎȢȳȘȡ ȐȳȒȜȏȞȎȔȓțȜ ȕȚȳțȡ ȞȜȏȜȥȜȴ ȠȓȚȝȓȞȎȠȡȞȖ ȒȐȖȑȡțȎ șȓȑȘȜȐȜȑȜ ȎȐȠȜ ȚȜȏȳșȭ ȝȞȜȠȭȑȜȚ ȣȐȖșȖț ȕ ȚȜȚȓțȠȡ ȗȜȑȜ ȕȎȝȡȟȘȡ ǰȖȕțȎȥȠȓ ȕȎ ȑȞȎȢȳȘȜȚ ȘȳșȪȘȳȟȠȪȣȐȖșȖțȝȞȜȠȭȑȜȚȭȘȖȣȞȜȏȜȥȎȠȓȚȝȓȞȎȠȡȞȎȒȐȖȑȡțȎȏȡșȎțȓ ȏȳșȪȦȜȬ ȕȎo ǿ Ǯ ǯ ǰ Ǳ 7 4 3 2 ȅȎȟȣȐȖșȖțȖ ȀȓȚȝȓȞȎȠȡȞȎ Ȝ ǿ 0 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 3

4. 3. ǽșȎȟȠȖȘȜȐȳ ȘȡșȪȘȖ ȞȎȒȳȡȟȎ ȟȚ ȕȏȓȞȳȑȎȬȠȪ ȡ ȐȖȟȡȐțȳȗ ȦȡȣșȭȒȤȳ ȧȜ ȚȎȱ ȢȜȞȚȡ ȝȞȭȚȜ ȘȡȠțȜȑȜ ȝȎȞȎșȓșȓȝȳȝȓȒȎ ȒȖȐ ȞȖȟȡțȜȘ

5. ȍȘȜȬ ȕ țȎȐȓȒȓțȖȣ ȚȜȔȓ ȏȡȠȖ ȐȖȟȜȠȎ h Ȥȳȱȴ ȦȡȣșȭȒȘȖ Ǯ ǯ ǰ Ǳ ȟȚ ȟȚ ȟȚ ȟȚ 4. ȁȘȎȔȳȠȪȘȜȞȳțȪȞȳȐțȭțțȭ²x 5 4 Ǯ ǯ ǰ Ǳ 1 – – 5 1 – 5 5. ǿȡȚȎȠȞȪȜȣȘȡȠȳȐȝȎȞȎșȓșȜȑȞȎȚȎȒȜȞȳȐțȬȱȜ ǰȖȕțȎȥȠȓȑȞȎȒȡȟțȡȚȳȞȡȏȳșȪ ȦȜȑȜȘȡȠȎȤȪȜȑȜȝȎȞȎșȓșȜȑȞȎȚȎ Ǯ ǯ ǰ Ǳ ǲ 100o 80o 140o 40o 120o 4 h

6. 6. ǿȝȞȜȟȠȳȠȪȐȖȞȎȕ 3m – 2n — 8 – 3m — 8 n – – 4 n – – 8 n – – 6 m – – 4 3m – n — 4 Ǯ ǯ ǰ Ǳ ǲ 7. ȁȘȎȔȳȠȪȕȝȜȚȳȔțȎȐȓȒȓțȖȣȓȟȘȳȕȑȞȎȢȳȘȎȢȡțȘȤȳȴy = –2x Ǯ ǯ ǰ Ǳ ǲ y x 0 y x 0 y x 0 y x 0 y x 0 8. ǲșȭ ȚȳȟȤȓȐȜȟȠȳ ȧȜ șȓȔȖȠȪ țȎ ȞȳȐțȳ ȚȜȞȭ țȜȞȚȎșȪțȖȗ ȎȠȚȜȟȢȓȞțȖȗ ȠȖȟȘ ȟȠȎțȜȐȖȠȪȚȚȞȠȟȠǥȕȝȳȒțȭȠȠȭȚțȎȘȜȔțȳȚȓȠȞȳȐȡȑȜȞȡȎȠȚȜȟȢȓȞțȖȗ ȠȖȟȘ ȕțȖȔȡȱȠȪȟȭ țȎ ȚȚ ȞȠ ȟȠ ȁȘȎȔȳȠȪ ȕȝȜȚȳȔ țȎȐȓȒȓțȖȣ ȢȜȞȚȡșȡ ȕȎ ȭȘȜȬ ȐȖȕțȎȥȎȬȠȪ ȎȠȚȜȟȢȓȞțȖȗ ȠȖȟȘ Ȟ ȡ ȚȚ ȞȠ ȟȠ

7. țȎ ȐȖȟȜȠȳ h ȚȓȠȞȳȐ țȎȒ ȞȳȐțȓȚȚȜȞȭ Ǯ ǯ ǰ Ǳ ǲ 10h — 100 p = 760 – 100h — 10 p = 760 – 100h — 10 p = 760 + Ã — 10h p = 10h — 100 p = 760 + 5

8. ȍȘȳȕțȎȐȓȒȓțȖȣȠȐȓȞȒȔȓțȪȱȝȞȎȐȖșȪțȖȚȖ ǥ ǻȎȐȘȜșȜȏȡȒȪȭȘȜȑȜȞȜȚȏȎȚȜȔțȎȜȝȖȟȎȠȖȘȜșȜ ǥǥ ǲȳȎȑȜțȎșȳȏȡȒȪȭȘȜȑȜȞȜȚȏȎȐȕȎȱȚțȜȝȓȞȝȓțȒȖȘȡșȭȞțȳ ǥǥǥȁȏȡȒȪȭȘȜȚȡȞȜȚȏȳȐȟȳȟȠȜȞȜțȖȞȳȐțȳ Ǯ ǯ ǰ Ǳ ǲ șȖȦȓǥȠȎǥǥ șȖȦȓǥȠȎǥǥ, șȖȦȓǥ, șȖȦȓǥǥȠȎǥǥ, ǥǥǥȠȎǥǥǥ 10. ȁȘȎȔȳȠȪȝȞȜȚȳȔȜȘȭȘȜȚȡțȎșȓȔȖȠȪȘȜȞȳțȪȞȳȐțȭțțȭx Ǯ ǯ ǰ Ǳ ǲ [–12; –6) [–6; 0) [0; 6) [6; 12) [12; +’

9. 11. ȍȘȎȕțȎȐȓȒȓțȖȣȢȡțȘȤȳȗȱȝȓȞȐȳȟțȜȬȒșȭȢȡțȘȤȳȴf(x) = x–4 Ǯ ǯ ǰ Ǳ ǲ F(x) = – 1 — 5x5 F(x) = – 1 — 3x3 F(x) = – 3 — x5 F(x) = – 4 — x5 F(x) = – 5 — x5 6

10. 12. ǼȏȥȖȟșȳȠȪ 54 Ã4 — 203 Ǯ ǯ ǰ Ǳ ǲ 5 – 4 1 – 2 10 1 — 20 1 — 10 13. ǾȜȕȐ·ȭȔȳȠȪțȓȞȳȐțȳȟȠȪORJ (3x) ! Ǯ ǯ ǰ Ǳ ǲ ²’

11. ²’

12. (0,27; +’

13. (0,6; +’

14. (0; 0,27) 14. sin2 2x = Ǯ ǯ ǰ Ǳ ǲ 2sin2 x 2sin2 xcos2 x 4sin2 xcos2 x 4sin2 x sin4x2 7

15. 15. ǿȠȜȞȜțȎȜȟțȜȐȖȝȞȎȐȖșȪțȜȴȥȜȠȖȞȖȘȡȠțȜȴȝȳȞȎȚȳȒȖȒȜȞȳȐțȬȱȟȚȎȝȜȢȓȚȎ² ȟȚǰȖȕțȎȥȠȓȝșȜȧȡȝȜȐțȜȴȝȜȐȓȞȣțȳȤȳȱȴȝȳȞȎȚȳȒȖ Ǯ ǯ ǰ Ǳ ǲ ȟȚ2 ȟȚ2 ȟȚ2 ȟȚ2 ȟȚ2 ǽȞȭȚȜșȳțȳȗțȜȬ ȒȜȞȜȑȜȬ Ǯǰ ȞȡȣȎȱȠȪȟȭ ȠȞȜșȓȗȏȡȟ ȒȖȐ ȞȖȟȡțȜȘ

16. ǹȳțȳȭ CD ȓșȓȘȠȞȖȥțȜȑȜ ȒȞȜȠȡ ȝȎȞȎșȓșȪțȎ Ǯǰ ȗ ȒȎȣȡ MN ȠȞȜșȓȗȏȡȟȎ ȆȠȎțȑȎ KN, ȧȜțȎȞȖȟȡțȘȡȱȐȳȒȞȳȕȘȜȚȡȠȐȜȞȬȱȕǺNȘȡȠƒǰȳȒȟȠȎțȳȚȳȔȝȞȭȚȖȚȖCD ȗ Ǯǰ, ǺN ȗ Ǯǰ ȒȜȞȳȐțȬȬȠȪ Ț ȳ Ț ȐȳȒȝȜȐȳȒțȜ ȁȘȎȔȳȠȪ ȝȞȜȚȳȔȜȘ ȭȘȜȚȡ țȎșȓȔȖȠȪ ȒȜȐȔȖțȎ ȡ Ț

17. ȦȠȎțȑȖ KN ȁȐȎȔȎȗȠȓ ȧȜ Ȑȟȳ ȕȎȕțȎȥȓțȳ ȝȞȭȚȳ șȓȔȎȠȪȐȜȒțȳȗȝșȜȧȖțȳ B A 30Ȝ Ț N M K D ǿ Ț Ǯ ǯ ǰ Ǳ ǲ [1; 3) [6; 8) [5,5; 6) [5; 5,5) [3; 5) 8

18. ȁȕȎȐȒȎțțȭȣ²ȒȜȘȜȔțȜȑȜȕȠȞȪȜȣȞȭȒȘȳȐȳțȢȜȞȚȎȤȳȴȝȜȕțȎȥȓțȖȣȤȖȢ ȞȎȚȖȒȜȏȓȞȳȠȪȜȒȖțȝȞȎȐȖșȪțȖȗțȎǰȎȦȡȒȡȚȘȡȐȎȞȳȎțȠȝȜȕțȎȥȓțȖȗȏȡȘ ȐȜȬǽȜȟȠȎȐȠȓȝȜȕțȎȥȘȖȐȠȎȏșȖȤȭȣȐȳȒȝȜȐȳȒȓȗȒȜȕȎȐȒȎțȪȡȏșȎțȘȡǮțȎ ȝȓȞȓȠȖțȳȐȳȒȝȜȐȳȒțȖȣȞȭȒȘȳȐȤȖȢȞȖ

19. ȳȘȜșȜțȜȘȏȡȘȐȖ

20. ȁȟȳȳțȦȳȐȖȒȖǰȎȦȜȑȜ ȕȎȝȖȟȡȐȏșȎțȘȡǮȘȜȚȝ·ȬȠȓȞțȎȝȞȜȑȞȎȚȎȞȓȱȟȠȞȡȐȎȠȖȚȓȭȘȝȜȚȖșȘȖ ǯȡȒȪȠȓȜȟȜȏșȖȐȜȡȐȎȔțȳȝȳȒȥȎȟȕȎȝȜȐțȓțțȭȏșȎțȘȎǮ ǻȓȝȜȑȳȞȦȡȗȠȓȐșȎȟțȜȞȡȥțȜȟȐȜȑȜȞȓȕȡșȪȠȎȠȡțȓȝȞȎȐȖșȪțȜȬȢȜȞȚȜȬȕȎȝȖȟȡȐȳȒȝȜȐȳȒȓȗ 17. ȁȟȠȎțȜȐȳȠȪ ȐȳȒȝȜȐȳȒțȳȟȠȪ ȚȳȔ ȑȞȎȢȳȘȜȚ ²

21. ȢȡțȘȤȳȴ ȐȖȕțȎȥȓțȜȴ țȎ ȝȞȜ ȚȳȔȘȡ²@ȠȎȴȴȐșȎȟȠȖȐȳȟȠȬǮ²ǲ

22. ǱȞȎȢȳȘ ȢȡțȘȤȳȴ y y = f(x) x –4 1 1 4 0 y y = f(x) x –4 1 1 4 0 y y = f(x) x –4 1 1 4 0 1 2 3 1 2 3 ǮǯǰǱǲ Ǯ ȢȡțȘȤȳȭȱțȓȝȎȞțȜȬ ǯ țȎȗȚȓțȦȓȕțȎȥȓțțȭȢȡțȘȤȳȴțȎȝȞȜȚȳȔȘȡ@ ȒȜȞȳȐțȬȱ ǰ ȢȡțȘȤȳȭȱȝȎȞțȜȬ Ǳ ȑȞȎȢȳȘȢȡțȘȤȳȴțȓȚȎȱȟȝȳșȪțȖȣȠȜȥȜȘȳȕȑȞȎȢȳȘȜȚ ȞȳȐțȭțțȭx – 3)2 + (y – 4)2 = 4 ǲ ȑȞȎȢȳȘȢȡțȘȤȳȴȠȞȖȥȳȝȓȞȓȠȖțȎȱȝȞȭȚȡy = 1 ǰșȎȟȠȖȐȳȟȠȪ ȢȡțȘȤȳȴ

23. ȁȟȠȎțȜȐȳȠȪ ȐȳȒȝȜȐȳȒțȳȟȠȪ ȚȳȔ ȐȖȞȎȕȜȚ ²

24. ȳ ȠȐȓȞȒȔȓțțȭȚ ȝȞȜ ȗȜȑȜ ȕțȎȥȓț țȭǮ²ǲ

25. ȭȘȓȱȝȞȎȐȖșȪțȖȚȭȘȧȜa = –21 – 3 1 2 3 ǮǯǰǱǲ 1 a2 2 a + ~a~ 3 log55a Ǯ ȏȳșȪȦȓȐȳȒ ǯ țȎșȓȔȖȠȪȝȞȜȚȳȔȘȡ

26. ǰ ȱȐȳȒ·ȱȚțȖȚȥȖȟșȜȚ Ǳ țȎșȓȔȖȠȪȝȞȜȚȳȔȘȡ

27. ǲ ȒȜȞȳȐțȬȱ ǰȖȞȎȕ ȀȐȓȞȒȔȓțțȭ ȝȞȜ ȕțȎȥȓțțȭ ȐȖȞȎȕȡ ǸȐȎȒȞȎȠ ǮǰǿD ȗ ȝȞȭȚȜȘȡȠțȎ ȠȞȎȝȓȤȳȭ ǰMNǿ șȓȔȎȠȪ Ȑ ȜȒțȳȗ ȝșȜȧȖțȳ ȒȖȐ ȞȖȟȡțȜȘ

28. ǽșȜȧȎ ȘȜȔțȜȴ ȳȕ ȤȖȣ ȢȳȑȡȞȒȜȞȳȐțȬȱȟȚ2 , ǮǺ ȟȚ ȁȟȠȎțȜȐȳȠȪ ȐȳȒȝȜȐȳȒțȳȟȠȪ ȚȳȔ ȐȳȒȞȳȕȘȜȚ ²

29. ȳ ȗȜȑȜ ȒȜȐȔȖțȜȬǮ²ǲ

30. 1 2 3 ǮǯǰǱǲ 1 ȟȠȜȞȜțȎȘȐȎȒȞȎȠȎǮǰǿD 2 ȐȖȟȜȠȎȠȞȎȝȓȤȳȴǰMNǿ 3 ȚȓțȦȎȜȟțȜȐȎȠȞȎȝȓȤȳȴǰMNǿ Ǯ ȟȚ ǯ ȟȚ ǰ ȟȚ Ǳ ȟȚ ǲ ȟȚ ǰȳȒȞȳȕȜȘ ǲȜȐȔȖțȎ ȐȳȒȞȳȕȘȎ 10 M N B C A D

31. 20. ǻȎ ȞȖȟȡțȘȡ ȕȜȏȞȎȔȓțȜ ȝȞȭȚȜȘȡȠțȖȗ ȝȎȞȎ șȓșȓȝȳȝȓȒ ABCDA1B1C1D1 ȡ ȭȘȜȚȡ AB = 3, AD = 4, AA1 ȁȐȳȒȝȜȐȳȒțȳȠȪȝȜȥȎȠȜȘȞȓȥȓț țȭ²

32. ȳȕȗȜȑȜȕȎȘȳțȥȓțțȭȚǮ²ǲ

33. ȠȎȘȧȜȏ ȡȠȐȜȞȖșȜȟȭȝȞȎȐȖșȪțȓȠȐȓȞȒȔȓțțȭ 1 2 3 ǮǯǰǱǲ 1 ǰȳȒȟȠȎțȪȐȳȒȠȜȥȘȖǿȒȜȝșȜȧȖțȖǮǮ1ǰ1

34. ȒȜȞȳȐțȬȱ 2 ǰȳȒȟȠȎțȪȐȳȒȠȜȥȘȖAȒȜȝȞȭȚȜȴCC1ȒȜȞȳȐțȬȱ 3 ǰȳȒȟȠȎțȪȚȳȔȝșȜȧȖțȎȚȖABC

35. ȳǮ1ǰ1C1

36. ȒȜȞȳȐțȬȱ Ǯ ǯ ǰ Ǳ ǲ ǽȜȥȎȠȜȘ Ȟȓȥȓțțȭ ǵȎȘȳțȥȓțțȭ Ȟȓȥȓțțȭ 11 A1 B1 C1 D1 A D C B

37. ǾȜȕȐ·ȭȔȳȠȪȕȎȐȒȎțțȭ²ǼȒȓȞȔȎțȳȥȖȟșȜȐȳȐȳȒȝȜȐȳȒȳȕȎȝȖȦȳȠȪȡȕȜȦȖȠȳ ȠȎ ȏșȎțȘȡ Ǯ ǰȳȒȝȜȐȳȒȪ ȕȎȝȖȟȡȗȠȓ șȖȦȓ ȒȓȟȭȠȘȜȐȖȚ ȒȞȜȏȜȚ ȡȞȎȣȡȐȎȐȦȖ ȝȜșȜȔȓțțȭ ȘȜȚȖ ȝȜ ȜȒțȳȗ ȤȖȢȞȳ Ȑ ȘȜȔțȳȗ ȘșȳȠȖțȤȳ ȐȳȒȝȜȐȳȒțȜ ȒȜ ȕȞȎȕȘȳȐ țȎȐȓȒȓțȖȣȡȏșȎțȘȡǮ 21. ǼșȓțȎ ȘȡȝȖșȎ ȥȓȞȓȕ ȐȓȏȟȎȗȠ ȝȜȟȎȒȜȥțȖȗ ȒȜȘȡȚȓțȠ ȒȖȐ ȢȞȎȑȚȓțȠ ȒȜȘȡȚȓțȠȎ

38. țȎ ȝȜȠȭȑ ȧȜ ȘȜȦȠȡȱ ȑȞț ȁ ȗȜȑȜ ȐȎȞȠȳȟȠȪ ȐȣȜȒȭȠȪ ȐȎȞȠȜȟȠȳ ȘȐȖȠȘȎ ² ȑȞț ȝșȎȤȘȎȞȠȖ ² ȑȞț ȗ ȳțȦȖȣ ȐȖȠȞȎȠ ² ȑȞț ǵȎ ȑȜȒȖț ȒȜ ȐȳȒȝȞȎȐșȓțțȭ ȝȜȠȭȑȎ ǼșȓțȎ ȐȖȞȳȦȖșȎ ȝȜȐȓȞțȡȠȖ Ȥȓȗ ȝȜȟȎȒȜȥțȖȗ ȒȜȘȡȚȓțȠ ǰȳȒȝȜȐȳȒțȜ ȒȜ ȝȞȎȐȖș ȕȎ ȠȎȘȖȣ ȡȚȜȐ ȴȗ ȝȜȐȓȞȠȎȬȠȪ șȖȦȓ ȐȎȞȠȳȟȠȪ ȘȐȖȠȘȎ ȗ ȝȜșȜȐȖțȡ ȐȎȞȠȜȟȠȳ ȝșȎȤȘȎȞȠȖ ǸȞȳȚ ȠȜȑȜ ȕȎ ȝȜȐȓȞțȓțțȭ ȝȜȟȎȒȜȥ țȜȑȜȒȜȘȡȚȓțȠȎȕǼșȓțȖȒȜȒȎȠȘȜȐȜȟȠȭȑțȡȠȪȕȏȳȞȑȞț ɐȿɃɉɈɋȺȾɈɑɇɂɃȾɈɄɍɆȿɇɌȯɉȱȾɋɌȺȼɈɘȾɅəɉɊɈȲɁȾɍ ǬǯǱ ǯȤȻțȖȜȭșřȇȠŨȳ ǠȕȖȗȘșȝȞȢǮȟșȡȔ ǢȻȘȣȤȔȖȟșȡȡȳ ǯȤȜțȡȔȫșȡȡȳ 2200001 ǪǨȈǢŞǯǠǱǠǦǨǰǱǼǪǨǩ 2200200 ǢȇǭǭǨǶǿ ǤȔȦȔŵȫȔȥȖȻȘȣȤŜ ǤȔȦȔŵȫȔȥȣȤȜȕŜ ǯȢȼțȘ ǢȔȗȢȡ ǬȻȥȪș ǱșȤȖȻȥ 12.12.2020 06:50 12.12.2020 09:09 ǢǠǰǲʰ240,00ǣǰǭ 1. ȍȘȡȟȡȚȡȑȞȜȦȓȗǾȡȑȞț

39. ȜȠȞȖȚȎȱǼșȓțȎȝȜȐȓȞțȡȐȦȖȤȓȗȒȜȘȡȚȓțȠ ǰȳȒȝȜȐȳȒȪ 2. ǿȘȳșȪȘȖȐȳȒȟȜȠȘȳȐȐȳȒȐȎȞȠȜȟȠȳȒȜȘȡȚȓțȠȎȟȠȎțȜȐȖȠȪȟȡȚȎȑȞȜȦȓȗǾ ǰȳȒȝȜȐȳȒȪ 12

40. 22. ǻȎ ȞȖȟȡțȘȡ ȕȜȏȞȎȔȓțȜ ȝȞȭȚȜȘȡȠțȖȘ ABCD ȗ ȘȜșȜ ȭȘȓ ȒȜȠȖȘȎȱȠȪȟȭ ȒȜ ȟȠȜȞȜțȖ Ǯǰ ȗ ȟȠȜȞȳț ǰǿ ȗ ǮD Ȑ ȠȜȥȘȎȣ M ȳ K ȐȳȒȝȜȐȳȒțȜ ǽȓȞȖȚȓȠȞ ȥȜȠȖȞȖȘȡȠțȖȘȎ ǮǰǺK ȒȜȞȳȐțȬȱȟȚȎȒȜȐȔȖțȎȐȳȒȞȳȕȘȎKǿ²ȟȚ 1. ǰȖȕțȎȥȠȓȞȎȒȳȡȟȡȟȚ

41. ȕȎȒȎțȜȑȜȘȜșȎ ǰȳȒȝȜȐȳȒȪ 2. ǼȏȥȖȟșȳȠȪȝșȜȧȡȡȟȚ2

42. ȝȞȭȚȜȘȡȠțȖȘȎABCD ǰȳȒȝȜȐȳȒȪ 13 M C B A K D

43. 23. ȁ ȝȞȭȚȜȘȡȠțȳȗ ȟȖȟȠȓȚȳ ȘȜȜȞȒȖțȎȠ ȡ ȝȞȜȟȠȜȞȳ ȕȎȒȎțȜ ȐȓȘȠȜȞ A ń B(–3; 8; 1) ȳȠȜȥȘȡǰ²

44. ȠȜȥȘȎǼ²ȝȜȥȎȠȜȘȘȜȜȞȒȖțȎȠ 1. ǰȖȕțȎȥȠȓȜȞȒȖțȎȠȡyȠȜȥȘȖ A(x; y; z

45. ǰȳȒȝȜȐȳȒȪ 2. ǼȏȥȖȟșȳȠȪȟȘȎșȭȞțȖȗȒȜȏȡȠȜȘO ń AÃA ń B ǰȳȒȝȜȐȳȒȪ 14

46. ǮȞȖȢȚȓȠȖȥțȡȝȞȜȑȞȓȟȳȬan

47. ȕȎȒȎțȜȢȜȞȚȡșȜȬnȑȜȥșȓțȎan = 2,6n² 1. ǰȖȕțȎȥȠȓȟȪȜȚȖȗȥșȓțȤȳȱȴȝȞȜȑȞȓȟȳȴ ǰȳȒȝȜȐȳȒȪ 2. ǰȖȕțȎȥȠȓȞȳȕțȖȤȬa4 – a1 ǰȳȒȝȜȐȳȒȪ 15

48. 25. ȁȝȓȞȦȜȚȡȘșȎȟȳȒȳȐȥȎȠȜȘȕȭȘȖȣșȖȦȓȜȒțȎțȎȳȚ·ȭǲȎȞȖțȎȳȣșȜȝȥȖ ȘȳȐ ǻȎ ȝȓȞȦȜȚȡ ȡȞȜȤȳ ȐȥȖȠȓșȪȘȎ țȎȐȚȎțțȭ ȢȜȞȚȡȱ ȝȎȞȖ ȒȳȠȓȗ ȭȘȳ ȟȖȒȳȠȖ ȚȡȠȪȕȎȜȒțȳȱȬȝȎȞȠȜȬǽȓȞȦȜȬȐȜțȎȐȖȏȖȞȎȱȝȎȞȡȒșȭǲȎȞȖțȖȍȘȎȗȚȜȐȳȞțȳȟȠȪ ȠȜȑȜȧȜǲȎȞȖțȎȟȖȒȳȠȖȚȓȕȎȜȒțȳȱȬȝȎȞȠȜȬȕȒȳȐȥȖțȘȜȬ ǰȳȒȝȜȐȳȒȪ ǲșȭ ȝȞȖȑȜȠȡȐȎțțȭ ȒȓȕȳțȢȳȘȡȐȎșȪțȜȑȜ ȞȜȕȥȖțȡ ȘȜțȤȓțȠȞȎȠ ȞȜȕȐȜȒȭȠȪ ȐȜȒȜȬ ȐȚȎȟȜȐȜȚȡȐȳȒțȜȦȓțțȳȐȳȒȝȜȐȳȒțȜȝȳȟșȭȥȜȑȜțȎȘȜȔțȳȑȐȜȒȖȒȜȏȎȐ șȭȬȠȪ ȑ ȎȞȜȚȎȠȖȥțȜȴ ȞȳȒȖțȖ ǿȘȳșȪȘȖ ȑȞȎȚȳȐ ȘȜțȤȓțȠȞȎȠȡ ȝȜȠȞȳȏțȜ Ȓșȭ ȝȞȖȑȜȠȡȐȎțțȭȑȞȜȕȥȖțȡ ǰȳȒȝȜȐȳȒȪ 16

49. 27. ǼȏȥȖȟșȳȠȪȕțȎȥȓțțȭȐȖȞȎȕȡa2 – 24a + 16 – 3 27a3 ȕȎȎ ǰȳȒȝȜȐȳȒȪ 28. ǾȜȕȐ·ȭȔȳȠȪȞȳȐțȭțțȭx4 – x2 ² ȁȐȳȒȝȜȐȳȒȳȕȎȝȖȦȳȠȪȒȜȏȡȠȜȘȡȟȳȣȗȜȑȜ ȒȳȗȟțȖȣȘȜȞȓțȳȐ ǰȳȒȝȜȐȳȒȪ ǾȓȒȎȘȠȜȞ ȟȠȞȳȥȘȖ țȜȐȖț ȐȖȞȳȦȡȱ ȡ ȭȘȳȗ ȝȜȟșȳȒȜȐțȜȟȠȳ ȞȜȕȚȳȟȠȖȠȖ ȞȳȕțȖȣ țȜȐȖț ȝȜșȳȠȖȥțȳ ȟȡȟȝȳșȪțȳ ȗ ȟȝȜȞȠȖȐțȡ ǿȘȳșȪȘȖ ȐȟȪȜȑȜ ȱ ȞȳȕțȖȣ ȝȜȟșȳȒȜȐțȜȟȠȓȗ ȞȜȕȚȳȧȓțțȭ ȤȖȣ țȜȐȖț ȡ ȟȠȞȳȥȤȳ ȕȎ ȡȚȜȐȖ ȧȜ ȝȜșȳȠȖȥțȳ țȜȐȖțȖȚȎȬȠȪȝȓȞȓȒȡȐȎȠȖȳțȦȖȚȎȟȝȜȞȠȖȐțȎțȜȐȖțȎ²ȏȡȠȖȜȟȠȎțțȪȜȬȁȐȎ ȔȎȗȠȓȧȜȘȜȔțȡȳȕȤȖȣțȜȐȖțȡȟȠȞȳȥȤȳțȓȝȜȐȠȜȞȬȬȠȪ ǰȳȒȝȜȐȳȒȪ 17

50. ǾȜȕȐ·ȭȔȳȠȪ ȕȎȐȒȎțțȭ ǵȎȝȖȦȳȠȪ ȡ ȏșȎțȘȡ ǯ ȝȜȟșȳȒȜȐțȳ șȜȑȳȥțȳ Ȓȳȴ ȠȎ ȝȜȭȟțȓțțȭ Ȑȟȳȣ ȓȠȎȝȳȐ ȞȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ȕȞȜȏȳȠȪ ȝȜȟȖșȎțțȭ țȎ ȚȎȠȓȚȎȠȖȥțȳȢȎȘȠȖȕȭȘȖȣȐȖȝșȖȐȎȱȠȓȥȖȳțȦȓȠȐȓȞȒȔȓțțȭȍȘȧȜȝȜȠȞȳȏțȜ ȝȞȜȳșȬȟȠȞȡȗȠȓȞȜȕȐ·ȭȕȎțțȭȕȎȐȒȎțȪȞȖȟȡțȘȎȚȖȑȞȎȢȳȘȎȚȖȠȜȧȜ 30. ǵȎȒȎțȜȢȡțȘȤȳȬy = x3 – 3x 1. ǲșȭ țȎȐȓȒȓțȖȣ ȡ ȠȎȏșȖȤȳ ȕțȎȥȓțȪ ȎȞȑȡȚȓțȠȎ ȣ ȐȖȕțȎȥȠȓ ȐȳȒȝȜȐȳȒțȳ ȴȚ ȕțȎȥȓțțȭȡ x y 0 –1 2 2. ǰȖȕțȎȥȠȓȗȕȎȝȖȦȳȠȪȘȜȜȞȒȖțȎȠȖȠȜȥȜȘȝȓȞȓȠȖțȡȑȞȎȢȳȘȎȢȡțȘȤȳȴy = x3 – 3x ȳȕȐȳȟȟȬȣ 3. ǵțȎȗȒȳȠȪȝȜȣȳȒțȡf cȢȡțȘȤȳȴf(x) = x3 – 3x 4. ǰȖȕțȎȥȠȓțȡșȳȢȡțȘȤȳȴf c 5. ǰȖȕțȎȥȠȓȝȞȜȚȳȔȘȖȕȞȜȟȠȎțțȭȳȟȝȎȒȎțțȭȠȜȥȘȖȓȘȟȠȞȓȚȡȚȡȗȓȘȟȠȞȓȚȡȚȖ ȢȡțȘȤȳȴf 6. ǽȜȏȡȒȡȗȠȓȓȟȘȳȕȑȞȎȢȳȘȎȢȡțȘȤȳȴf ǰȳȒȝȜȐȳȒȪ 18

51. 31. ǼȟȪȜȐȖȚȝȓȞȓȞȳȕȜȚȤȖșȳțȒȞȎȱȝȞȭȚȜȘȡȠțȖȘǮǰǿDȟȠȜȞȜțȎǮDȭȘȜȑȜșȓȔȖȠȪ Ȑ țȖȔțȳȗ ȜȟțȜȐȳ ȤȖșȳțȒȞȎ ǲȳȎȑȜțȎșȪ Ǯǿ ȝȓȞȓȞȳȕȡ ȒȜȞȳȐțȬȱ d ȗ ȡȠȐȜȞȬȱ ȕ ȝșȜȧȖțȜȬțȖȔțȪȜȴȜȟțȜȐȖȤȖșȳțȒȞȎȘȡȠᇗ 1. ǵȜȏȞȎȕȳȠȪțȎȞȖȟȡțȘȡȕȎȒȎțȖȗȤȖșȳțȒȞȳȗȜȑȜȜȟȪȜȐȖȗȝȓȞȓȞȳȕǮǰǿD 2. ȁȘȎȔȳȠȪȘȡȠᇗȧȜȡȠȐȜȞȬȱȝȞȭȚȎǮǿȳȕȝșȜȧȖțȜȬțȖȔțȪȜȴȜȟțȜȐȖȤȖșȳțȒȞȎ 3. ǰȖȕțȎȥȠȓȜȏ·ȱȚȤȖșȳțȒȞȎ ǰȳȒȝȜȐȳȒȪ

52. ǾȜȕȐ·ȭȔȳȠȪ ȕȎȐȒȎțțȭ ² ǵȎȝȖȦȳȠȪ ȡ ȏșȎțȘȡ ǰ ȝȜȟșȳȒȜȐțȳ șȜȑȳȥțȳ Ȓȳȴ ȠȎ ȝȜȭȟțȓțțȭ Ȑȟȳȣ ȓȠȎȝȳȐ ȞȜȕȐ·ȭȕȎțțȭ ȕȎȐȒȎțȪ ȕȞȜȏȳȠȪ ȝȜȟȖșȎțțȭ țȎ ȚȎȠȓȚȎȠȖȥțȳȢȎȘȠȖȕȭȘȖȣȐȖȝșȖȐȎȱȠȓȥȖȳțȦȓȠȐȓȞȒȔȓțțȭȍȘȧȜȝȜȠȞȳȏțȜ ȝȞȜȳșȬȟȠȞȡȗȠȓȞȜȕȐ·ȭȕȎțțȭȕȎȐȒȎțȪȞȖȟȡțȘȎȚȖȑȞȎȢȳȘȎȚȖȠȜȧȜ ȁȐȎȑȎȁȚȜȐȖȕȎȐȒȎțȪȳȚȎȬȠȪȟȝȳșȪțȡȥȎȟȠȖțȡǾȜȕȐ·ȭȕȎțțȭȕȎȐȒȎțȪ ²ȕȎȝȖȦȳȠȪșȖȦȓȐȏșȎțȘȡǰ. 32. ǼȟȪȜȐȖȚȝȓȞȓȞȳȕȜȚȤȖșȳțȒȞȎȱȝȞȭȚȜȘȡȠțȖȘǮǰǿDȟȠȜȞȜțȎǮDȭȘȜȑȜșȓȔȖȠȪ ȡ țȖȔțȳȗ ȜȟțȜȐȳ ȤȖșȳțȒȞȎ ǲȳȎȑȜțȎșȪ Ǯǿ ȝȓȞȓȞȳȕȡ ȒȜȞȳȐțȬȱ d ȗ ȡȠȐȜȞȬȱ ȕ ȝșȜȧȖțȜȬ țȖȔțȪȜȴ ȜȟțȜȐȖ ȤȖșȳțȒȞȎ ȘȡȠ ᇗ ǻȎ ȘȜșȳ țȖȔțȪȜȴ ȜȟțȜȐȖ ȐȖȏȞȎțȜ ȠȜȥȘȡKȠȎȘȧȜȑȞȎȒȡȟțȎȚȳȞȎȒȡȑȖǮKȒȜȞȳȐțȬȱƒ 1. ǵȜȏȞȎȕȳȠȪ țȎ ȞȖȟȡțȘȡ ȕȎȒȎțȖȗ ȤȖșȳțȒȞ ȳ ȐȘȎȔȳȠȪ ȘȡȠ Ȗ ȚȳȔ ȝșȜȧȖțȜȬ (KBD

53. ȳȝșȜȧȖțȜȬțȖȔțȪȜȴȜȟțȜȐȖȤȖșȳțȒȞȎǼȏȽȞȡțȠȡȗȠȓȗȜȑȜȝȜșȜȔȓțțȭ 2. ǰȖȕțȎȥȠȓȘȡȠȖ ǰȳȒȝȜȐȳȒȪ 33. ǲȜȐȓȒȳȠȪȠȜȠȜȔțȳȟȠȪ 2a2 + 5a – 3 — a + 3 = 1 – 2a — 2cos240 o 20

54. 34. ǵȎȒȎțȜȟȖȟȠȓȚȡȞȳȐțȭțȪ ax2 + 3ax + 41 + y = 8, xÃ y = 1, Ȓȓx, y²ȕȚȳțțȳa²ȒȜȐȳșȪțȎȟȠȎșȎ 1. ǾȜȕȐ·ȭȔȳȠȪȟȖȟȠȓȚȡȭȘȧȜa 2. ǰȖȕțȎȥȠȓȐȟȳȞȜȕȐ·ȭȕȘȖȕȎȒȎțȜȴȟȖȟȠȓȚȖȕȎșȓȔțȜȐȳȒȕțȎȥȓțȪa 21

55. ǰȳȒȝȜȐȳȒȪ 22

56. 23 ǽȜȣȳȒțȎȢȡțȘȤȳȴ ȀȞȖȑȜțȜȚȓȠȞȳȭ ȀȎȏșȖȤȭȕțȎȥȓțȪȠȞȖȑȜțȜȚȓȠȞȖȥțȖȣȢȡțȘȤȳȗȒȓȭȘȖȣȘȡȠȳȐ ǽȓȞȐȳȟțȎȢȡțȘȤȳȴ ȠȎȐȖȕțȎȥȓțȖȗȳțȠȓȑȞȎș ǿ, Ĵ²ȟȠȎșȳ (ǿ)Ļ = 0 ȣĻ = 1 (ȣĴ )Ļ ĴxĴ² ( x)Ļ = 1 – 2 x (ex )Ļ = ex (ln x)Ļ = 1 – x (sin x)Ļ = cos x (cos x)Ļ = –sin x (tg x)Ļ = 1 – cos2x (u + v)Ļ = uĻ + vĻ (u – v)Ļ = uĻ – vĻ (uv)Ļ = uĻv + uvĻ (Cu)Ļ = CuĻ (u – v)Ļ = uĻv – uvĻ – v2 sin Ĵ = yĴ cos Ĵ = xĴ sin2 Ĵ + cos2 Ĵ = 1 tg Ĵ = VLQĴ – FRVĴ 1 + tg2 Ĵ = 1 – cos2Ĵ sin2Ĵ = 2sin Ĵcos Ĵ cos2Ĵ = cos2 Ĵ²sin2 Ĵ VLQo Ĵ) = cos Ĵ sin(180o ²Ĵ) = sin Ĵ FRVo Ĵ) = –sin Ĵ cos(180o ²Ĵ) = –cos Ĵ WJo Ĵ) = – 1 – tgĴ tg(180o ²Ĵ) = –tg Ĵ a œ b f(x)dx = F(x)~a b = F(b) – F(a

57. ²ȢȜȞȚȡșȎǻȪȬȠȜțȎ²ǹȓȗȏțȳȤȎ 0 –1 –1 1 1 y x Ĵ M(xĴ, yĴ) xĴ yĴ tg D cos D sin D ȞȎȒ ȑȞȎȒ 0 o 0 D 0 1 0 0 0 30 o ʌ – 6 1 – 2 1 – 2 2 — 2 1 — 3 2 — 2 3 — 2 3 — 2 45 o ʌ – 4 1 3 60 o ʌ – 3 o 180 o 270 o 360 o ʌ – 2 ʌ 3ʌ — 2 2ʌ 1 0 0 –1 –1 0 0 1 țȓȳȟțȡȱ țȓȳȟțȡȱ ǵȎȑȎșȪțȖȗȐȖȑșȭȒ ȝȓȞȐȳȟțȖȣF(x) + C, C²ȒȜȐȳșȪțȎȟȠȎșȎ ȂȡțȘȤȳȭf(x) 0 C xĴ + 1 — + C Ĵ ln ~x~ + C x + C sin x –cos x + C cos x sin x + C tg x + C 1 — cos2 x 1 ex ex + C 1 – x xĴ Ĵz –1

58. 24 ǸȳțȓȤȪȕȜȦȖȠȎ ǱǳǼǺǳȀǾǥȍ ǲȜȐȳșȪțȖȗȠȞȖȘȡȠțȖȘ ǽȎȞȎșȓșȜȑȞȎȚ ǽȞȭȚȎ ȝȞȖȕȚȎ ȄȖșȳțȒȞ ǸȜțȡȟ ǸȡșȭȟȢȓȞȎ ǽȞȎȐȖșȪțȎ ȝȳȞȎȚȳȒȎ ǽȞȭȚȜȘȡȠțȖȘ ǾȜȚȏ ȀȞȎȝȓȤȳȭ ǽȞȭȚȜȘȡȠțȖȗȠȞȖȘȡȠțȖȘ ǸȜȜȞȒȖțȎȠȖȠȎȐȓȘȠȜȞȖ ȀȞȖȘȡȠțȖȘȖ ȅȜȠȖȞȖȘȡȠțȖȘȖ ǸȜșȜ Ǽȏ·ȱȚțȳȢȳȑȡȞȖȗȠȳșȎ ǸȞȡȑ S = ab sinȖ S = aha V = SȜȟț ˜ H Sȏ = PȜȟț ˜ H V = 1 – 3 SȜȟț ˜ H Sȏ = 1 – 2 PȜȟț ˜ m V = ʌR2 H Sȏ = 2ʌRH V = 1 – 3 ʌR2 H Sȏ = ʌRL V = 4 – 3 ʌR3 S = 4ʌR2 L = 2ʌR (x – x0)2 + (y – y0)2 = R2 S = ʌR2 S = 1 – 2 d1d2, d1, d2 ²ȒȳȎȑȜțȎșȳȞȜȚȏȎ S = a + b — 2 ˜ h, aȳb ²ȜȟțȜȐȖȠȞȎȝȓȤȳȴ S = ab p = a + b + c — 2 Ĵ + ȕ + Ȗ = 180Ȝ a2 = b2 + c2 – 2bc cosĴ a — VLQĴ = b — sinȕ = c — sinȖ = 2R R – ȞȎȒȳȡȟȘȜșȎȜȝȖȟȎțȜȑȜ țȎȐȘȜșȜȠȞȖȘȡȠțȖȘȎ ABC a2 + b2 = c2 ȠȓȜȞȓȚȎǽȳȢȎȑȜȞȎ

59. b – c = cosĴ a – c = sinĴa – b = tgĴ c a b C A B ȕ Ȗ ha Į c a b Į a b Ȗ 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 R H L R R S = 1 – 2 a ˜ ha S = 1 – 2 b ˜ c ˜VLQĴ S = p(p – a)(p – b)(p – c) x0 = x1 + x2 — 2 y0 = y1 + y2 — 2 z0 = z1 + z2 — 2 AB(x2 – x1, y2 – y1, z2 – z1) ~AB~ (x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2 a ˜ b = a1b1 + a2b2 + a3b3 a ˜ b = ~a~˜~b~FRVǗ Ǘ a(a1, a2, a3) b(b1, b2, b3)

Сертифікаційна робота з математики 2021 року (основна сесія)

Recommended

Recommended

More Related Content

What's hot

What's hot (13)

More from ErudytNet

More from ErudytNet (20)

Сертифікаційна робота з математики 2021 року (основна сесія)