Итоговая работа по алгебре за курс 10 класса.
Вариант 1
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область определения функции ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_3.png)
№4. Решите уравнение ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_4.png)
№5. Известно, что
и 2700 3600. Найдите сtg
.
№6. Вычислите: сos 100 · cos 200 – sin 100 · sin 200.
№7. Найдите наименьший, положительный период функции
f(x) = sin3x · cos5x – cos3x · sin5x.
№8. Найдите наименьший, положительный корень уравнения 2sin2x – 7cosx – 5 = 0.
Часть 2
№9. Найдите значение выражения: ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_8.png)
№10. Укажите число целых решений неравенства:
из отрезка
.
№11. Найдите число корней уравнения
.
№12. Найдите наибольшее целое значение функции y = ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_12.png)
Часть 3
№13. Решите уравнение ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_13.png)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_16.png)
№16. Вычислите
.
№17. Решите неравенство
№18. Найдите все значения
, при которых уравнение
имеет хотя бы одно решение.
Итоговая работа по алгебре за курс 10 класса.
Вариант 2
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область определения функции ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_23.png)
№4. Решите уравнение ![](https://fsd.multiurok.ru/html/2017/10/03/s_59d3d62526c7f/702623_24.png)
№5. Известно, что
и 900 1800. Найдите tg
.
№6. Вычислите: sin 700 · cos 400 – sin 400 · cos 700.
№7. Найдите наименьший, положительный период функции
f(x) = sin7x · cos3x + cos7x · sin3x.
№8. Найдите наименьший, положительный корень уравнения
.
Часть 2
№9. Найдите значение выражения: ![](data:image/png;base64,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)
№10. Укажите число целых решений неравенства:
.
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наибольшее целое значение функции
.
Часть 3
№13. Решите уравнение ![](data:image/png;base64,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)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство
№16. Вычислите ![](data:image/png;base64,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)
№17. Решите уравнение
№18. Найдите все значения
, при которых уравнение
не имеет решений.
Итоговая работа по алгебре за курс 10 класса.
Вариант 3
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область определения функции
.
№4. Решите уравнение ![](data:image/png;base64,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)
№5. Известно, что
и 1800 2700. Найдите tg
.
№6. Вычислите: сos 750 · cos 300 + sin 750 · sin 300.
№7. Найдите наименьший, положительный период функции
f(x) = cosx · cos6x – sinx · sin6x.
№8. Найдите наименьший, положительный корень уравнения
.
Часть 2
№9. Найдите значение выражения:
.
№10. Укажите число целых решений неравенства:
из промежутка
.
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наибольшее целое значение функции
.
Часть 3 №13. Решите уравнение
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](data:image/png;base64,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)
№16. Вычислите
№17. Решите неравенство ![](data:image/png;base64,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)
№18. Найдите все значения
, при которых уравнение
имеет хотя бы одно решение.
Итоговая работа по алгебре за курс 10 класса.
Вариант 4
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область определения функции ![](data:image/png;base64,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)
№4. Решите уравнение ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAAOCAIAAABhDSNOAAADpUlEQVR4nO1YWyhsYRSeY4YHGffLQTEPzMuM0EQh5UG8US5PSh4VpjQvMgkxEm8ThrzxQAqleKB4kluSJHfKJaYQcp3E+Wb/p91/9v5t+xjn2KfO9zCtveb/1/rWXv9a/5rRvL6+qv5DGdD8aQcul8vHx+dvbvwUfAltdjK2trYeHh6SkpI+ZpTH8vJyfHz8x8gtLCxkZmZ6SOBj+Cra7GQEBwdPTk5+50DrKysru7q6Xl5eZFo/ODgwmUwyFxuNxv39/bCwsMbGxrKysqenp/v7e19fX4kt5+fncXFxV1dX0paVRnt1dbWoqAgXxOjoaEJCAq9nJ8PPzw8RajTCbzs6OhCVeP3l5eXj42NUVJRAv729LSsgDlqtFk43NjaysrIQFd7y4uIiZIktMzMzNzc371pWGm2r1Wqz2e7u7iCMjY3xevfr7uvra2ho2NnZAYnS0tKlpaX5+fmIiIizs7PQ0FCxrejoaJyy7u7u/Pz8tra2+vp6LLZYLFVVVUzfYvvMZXNzc/iMjIyENQiBgYGnp6cSIaGXgol8FwqhDSBbQ0NDz8/PNTU1tN6dDHianp5ubW1F1aM7QYPEooi8vLyYtgYHB3GgKioqEJXdbgebjIwMZkje3t5M+xLo7e3Fm1Jx1XlxcSGxcmJiorq6mshyXHwJbSTJ6XQS2WAwrK2tQbi+vkYfw8kQNNifjaiuri41NXV3dzcoKAiP3ziQr3AjHR8fFxYW8nvS09Nh6OjoCHJ5eXl2dnZLSwuTIolKbF/AMjExcWVlBcLw8LBer8/Ly4OMzstvZy62cICAQwM+AhdKoA0wqwTVgx6FyuDNEriTcXJy0tnZCWZms7m/v1+wMyUlJTk5mdbgTOGa0ul0RD48PKTvK3oSIwMJ076Y5cDAQGxsLF4ZeaSbJDMkciGTTIhdKIG26o3KALfx8XHkA5mmTbmTkZOTMzU1FR4ejkKDexQyvQLR8kMeaOEzNzc3ICCgp6cHcnFxsb+/P3paU1NTbW2t6tdJDJfbu/Z5lJSU0C8aUcXExDBXiiF2oRDazGPU3NxcUFAAhiMjI2iVs7OzRO9Oxvr6OnnY29uTjtnOgdY4HI7Nzc3b21tQJ1HRk1hISIh8+4LRE+cURKX58LukXSiNNuoP0zCR+UyoPP8Fjs6LSRmF2d7eTjT0JIYZHLcZie13gZOrVqs9pPcWlEnb02TYONAaehKT32fESEtL85CbBJRJ+/P/m6InsX8ISqD9A9M9/VrUIj6HAAAAAElFTkSuQmCC)
№5. Известно, что
и 00 900. Найдите sin
.
№6. Вычислите: sin 260 · cos 40 + sin 40 · cos 260.
№7. Найдите наименьший, положительный период функции
f(x) = cos2x · cos4x + sin2x · sin4x.
№8. Найдите число корней уравнения
из промежутка
.
Часть 2
№9. Найдите значение выражения: ![](data:image/png;base64,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)
№10. Укажите число целых решений неравенства:
.
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наибольшее целое значение функции
.
Часть 3 №13. Решите уравнение
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](data:image/png;base64,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)
№16. Вычислите ![](data:image/png;base64,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)
№17. Решите уравнение
№18. Найдите все значения
, при которых уравнение
не имеет решений.
Итоговая работа по алгебре за курс 10 класса.
Вариант 5
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область определения функции ![](data:image/png;base64,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)
№4. Решите уравнение ![](data:image/png;base64,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)
№5. Известно, что
и 1800 2700. Найдите cos
.
№6. Вычислите: sin 260 · cos 40 + sin 40 · cos 260
№7. Найдите наименьший, положительный период функции
.
№8. Найдите сумму корней уравнения
из промежутка
.
Часть 2
№9. Найдите значение выражения:
.
№10. Укажите число целых решений неравенства:
из промежутка
.
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наибольшее целое значение функции
.
Часть 3 №13. Решите уравнение ![](data:image/png;base64,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)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALAAAAAPCAIAAADLSdKpAAAFh0lEQVR4nO1ZV0gdXRBeW2KNhogdFGPBYG+IPogg4oMgaBQLisYEoiaKBbFgwUawgd2QFwtI9CFCQgQ1KHmIiooVwY5YsKBiLyj6f94Dm3Xv3fV6jQbM/z2E2c2cnfPNfjNn9ip7cXFBSYTi4uKEhATJ1t4eVVVVUVFR9xbu3yErK9mysbExVVXVP7uVG0FKSmpwcNDW1vYeYv1TZG8giJmZmfX1dRsbGwUFhcbGRi8vr7vbFn90XJqbm7e0tNxPju6fLHWV732SvRTEu3fv0JTOz8/5XRUVFbG//Pz8nJyc7u5urMLNjY0NIyOj7e1tnoVmZmZzc3N6enpNTU329vaSbZQZHZf6+vo/f/7kcpaWliaGkpLS3t6emAS5QJOl/hJffrLA2tqat7d3b2/vyMjIy5cvMQZAQBYWFjxLuDwvBVFRUYF8iVy2tbV1fHyso6MDG/+2tbUFBgbCXl1dVVZWhtHV1bW7u8taNTk5aWpqSl8iNcPDw0NDQ69evRodHeVPBBeY0QFExx64Ivr5+eFlwCgvLxefIBdostRf4ssiy4q4ubmZlJTU19cHOy0tLS8v7+DgAMbXr195ns/l+fvI+Pbt29u3b1FGNTU1kFtBQUFmZqampiaGqffv38Ohuroa6+Xl5SlBjiBhbEtXV1c4GEqEWY4dHR1nZ2dY+/jx4/r6+qysrOnp6ampqdDQ0P7+fq4dszyRXDo6JSh9lAVXRKKGgYEBS0tL8QlygZClBK/hjvgKuzGzzSLLivjs2bO6urqGhgbYkEVzczOiJycn0861tbVubm5oM8wniPSkmIJITEz8/PkzyiU6Ohr5Kisr6+npcXFxoZMVGRlJO5+enmLSaW1tjYuL487kbzx69EhLSwtKRAvt7Oz88OEDem97ezvPEuSF6fn06VPm/8rIyIAMf9AfP34w2V5LkAuELIy748siS13NtjhkCXZ2dqBdaIV5qPn6+n769AmyDgsLe/HiBY8nxRTEwsKCs7MzPBYXF3GJYnJ3d8cZJjKwhoYG9JsgACU4s7FwdnbW2NiYOJBTHJJ//vw5DLwGnIJBQUGogPT0dEdHRwxN9DvW1tamK8DKygrNltjCnjQODw+xiifi/v4+3gpzyY0ICpPFh8ad8r2WLAyeiARqamrYKtTDfIiKikp8fDy2lJGRIScnh5OCy5NiCgItBRVzcnJiYGCAS9jIIGmVBMy5F50WjyNdi2QHBnbGukPg7++PQR2vB2JcXl6urKzEa4iJiSFdDlhZWRF+DSI9aSA6csQVEUAz8PHxYd65luDR0RGOfLwhNGqQRfZxTsOZkIUg7o6vOGR5ItJwcHD4/v07/KEt5v3x8XEcK1D2mzdv+D0vBYFNkGCYxdAbP378SAnmsidPnmAKxZSbmppKXZ178Tiw4p/FaODoxSmIFoou7eHhgSMWO8MRjhSge3Ot4vdcWlpizgfCmJiYeP36NbHFJIjtoQEUFhampKSg8vCZh9oiuROfrGR8b0MWXzSenp4wTExMSkpKQBZy+fLlC+1QWloKiWdnZ9MTGJCbm4uCoT1xdP769YsigigTgBUGQw1yisaLvZJ8MedePGtsbMzOzg62sFRZd/CFQ9sBAQHEQP1xMSSAqHk8kXT6i0PkHoqKimhbTIKwZWVlUTSUILloEnCIiIhgkr0jvjciy4poaGiIg4m+FP7JJDY2VviZ1tbWUBJ9SdRA8fwwhfMVn6fq6uqoGHKHOfe6uroKp/g+MT8/HxwcfJsnCBOECPApb2RkBN2jc6DEIRHqQZAVH5yCyBOAeYc199La/ysIDw8nk7/EECYYEhICHTg5OaFcyMmKMqIeBFnxIeHfMijBqPwH93FTiPw94PYgeceByrr/IMmKhOSC+B8PEv8Bh51tmy3LglsAAAAASUVORK5CYII=)
№16. Вычислите ![](data:image/png;base64,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)
№17. Решите уравнение ![](data:image/png;base64,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)
№18. Найдите все значения
, при которых уравнение
имеет хотя бы одно решение.
Итоговая работа по алгебре за курс 10 класса.
Вариант 6
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область определения функции ![](data:image/png;base64,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)
№4. Решите уравнение ![](data:image/png;base64,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)
№5. Известно, что
и 900 1800. Найдите
.
№6. Вычислите: cos 1600 · cos 100 + sin 1600 · sin 100.
№7. Найдите наименьший, положительный период функции f(x) = ctg 5x.
№8. Найдите количество корней уравнения
из промежутка
.
Часть 2
№9. Найдите значение выражения:
.
№10. Укажите число целых решений неравенства:
из отрезка
.
№11. Найдите число корней уравнения ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAQCAIAAAD/IDQbAAADyUlEQVR4nO1XWyisURQeDHLNXUNRrrnlFhqiedI8IbyIpkmJmpoHRSLlngillPIgPExNoZSHGeVB7pIkyf2FjIYaTYjE+ebsc3a////9fudkzjyc9fC39p619lr7299ae4/07e1N8l8+EOm/TsChxUHRcXJy+o5lv1oov9B5fn52c3P7hnzYIj6QI5S8DZ3t7e3Y2Fj7oLOxsZGfn2+HQJDDw8PHx8e0tLQ/XsGGzvn5eWZmJuuHgoKCpaUlrkNycvLZ2VlwcHB7e7tarRYZ5vr6uri4eH19/enp6eHhwdPTU8AYZQXiMANVV1fTX19fX0UGDQgIMBqNISEhYWFhwpa7u7vl5eUIOjs7m5KSQudt6BwdHXEdeKGB+Pj4WCyWg4MDhUIhgA7OLT4+nui3t7eNjY2bm5vQY2JioMBXOF1WIMlXQKECZOH1KTSQlpaW7u7u+/t7KHNzc3T+XVceGBhobW318PBoaGhobm6WSqU4tKmpqfr6+s7OTmKztraGr0wmCw0NnZycbGtrOz4+Br4qlWpra4sulZCQQPcTGBg4MTGBdaD7+fldXV2J2Rsz0N3d3af23GT6+/sR7ubmJigoSNgXB6bX619eXpqampjzNnRcXV3JAKsvLy9nZGRABzqwHh0dBTSJiYkUHSJjY2N9fX1FRUWLi4u9vb3IABwWs2dvb29QSYwlM1BJSQkc3d3dx8fHEZTXEoiwksEZc80AN8qc6ElJSXt7e1CAPoodxwm2Mo3foTM4OIjuACCYJRMXF8di9fT0NCZJluBadnb2ycmJv78/hqenp2jwxMzZ2RlfHGZ0dDT1RdOh4dChLy4uysrKJL+vcNY9RQNhP1h/dXW1qqqKxGVuMjU1dWdnh5sMr/AyFxRDWYENLEcbOvS2qqmpQZHn5OQINBSdThcZGZmbmwv98vJyZGSkp6dHq9WSwgEQBEpAw9spTCYT5XlWVlZ6ejrRCS5MjJiBamtrwXwXFxcKH3eT3GR4hZc7yGR+fh4AAVw2Ouh/ZIA2ZrVawV4EIDNDQ0NkAyixuro6KJWVldQZzWVhYQGXAsiPzDQaDW9CuHqUSqXkJw07OjoolYCgwDOCGQj3iJeXV3h4OKJ8ZF9YWCgmGV7udHV1lZaWIp+ZmRkM8/LyVlZWJAQddE1iZDabiVJRUTE8PEydmSzgZQQKijXDNIuKiqLXosFgIH2NV0AN+kr+6iW1v7//UTKfCt5EOEI6JNBICDp4WaBTUoy+VXx9fVEgAgaO8ESmYkMnIiLCbvHkcrndYv29OOi/UAeRH1UI4TGDZ4GQAAAAAElFTkSuQmCC)
№12. Найдите наименьшее целое значение функции
.
Часть 3 №13. Решите уравнение ![](data:image/png;base64,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)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](data:image/png;base64,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)
№16. Вычислите
№17. Решите неравенство
№18. Найдите все значения
, при которых уравнение
не имеет решений.
Итоговая работа по алгебре за курс 10 класса.
Вариант 7
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область определения функции ![](data:image/png;base64,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)
№4. Решите уравнение ![](data:image/png;base64,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)
№5. Известно, что
и 900 1800. Найдите sin
.
№6. Вычислите: sin 360 · cos 240 + sin 240 · cos 360.
№7. Найдите наименьший, положительный период функции
f(x) = sin7x · cosx + cos7x · sinx.
№8. Найдите наибольший, отрицательный корень уравнения
Часть 2
№9. Найдите значение выражения:
.
№10. Укажите число целых решений неравенства:
.
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наименьшее целое значение функции
.
Часть 3 №13. Решите уравнение ![](data:image/png;base64,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)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](data:image/png;base64,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)
№16. Вычислите ![](data:image/png;base64,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)
№17. Решите неравенство
№18. Найдите все значения
, при которых уравнение
имеет хотя бы одно решений.
Экзаменационная работа по алгебре в 10 классе.
Вариант 8
Часть 1
№1. Упростите выражение
№2. Вычислите значение выражения
№3. Найдите область определения функции ![](data:image/png;base64,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)
№4. Решите уравнение ![](data:image/png;base64,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)
№5. Известно, что
и 1800 0. Найдите соs
.
№6. Вычислите: sin 560 · cos 260 – sin 260 · cos 560
№7. Найдите наименьший, положительный период функции
f(x) = sin8x · cos2x – cos8x · sin2x
№8. Найдите сумму корней уравнения
из промежутка
.
Часть 2
№9. Найдите значение выражения:
.
№10. Укажите число целых решений неравенства:
из отрезка
.
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наибольшее целое значение функции
.
Часть 3 №13. Решите уравнение ![](data:image/png;base64,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)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство
№16. Вычислите ![](data:image/png;base64,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)
№17. Найдите все значения
, при каждом из которых расстояние между
соответствующими точками графиков функций
и ![](data:image/png;base64,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)
меньше, чем 0,5.
№18. Найдите все значения
, при которых уравнение ![](data:image/png;base64,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)
не имеет решений.
Итоговая работа по алгебре за курс 10 класса.
Вариант 9
Часть 1
№1. Найдите значение выражения
№2. Вычислите значение выражения
№3. Найдите область значений функции ![](data:image/png;base64,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)
№4. Решите уравнение ![](data:image/png;base64,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)
№5. Известно, что
. Найдите cos
.
№6. Вычислите: cos 110 · cos 790 – sin 110 · sin 790
№7. Найдите наименьший, положительный период функции
f(x) = - sin9x ·sin5x + cos9x ·cos5x
№8. Найдите наименьший, положительный корень уравнения
Часть 2
№9. Найдите значение выражения:
.
№10. Укажите число целых решений неравенства:
.
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наименьшее целое значение функции
.
Часть 3 №13. Решите уравнение ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAAASCAIAAAAyt2BGAAAEtUlEQVR4nO1YWSh9WxjfhpAps4sMEZIxDxQvHlwZilKKkieiTA+GRKJ0Jby4hniQDAmvXmR6MoVChswPJEeGFA4y3Z+z7t1We++zz2Zv5/5v1+/htPY6e/++9X2/9X3r29v47e2N+d/j7u7OwsLiu62o1Wpzc3MFCY0V5PqPYmNjw8nJSQ/ira6uRkVFKUj4Ix5zfn4eFBSkB0O3t7f43dnZub+/DwsLk0/4Ix5zc3OjH0MGBgaoz3Z2duPj48h1V1dXmYQ/4jFXV1eC84i1soa2traQduHh4a+vr/KVY37EA15eXrT9pWw3p1Kp9vb2pqambGxsLi4uHBwcZBJ+QjwFi/UvhaenJ/4k0k6+cpyImZqaomyWlZXJpyJ4F6+goKCjowO5LP7814q1oaEhO4YJiba+gO3t7e7ubgxycnL8/PxYu2gjxU81QfH4hGdnZykpKQsLC9KXxImYmZkZxJP+uAgVwbt4bW1tCCj/ARwGDw8P7N2Ojo5fK9a0VBJtSQT2o7+/PxknJSVlZGTAVkJCwsHBQVpa2vDwMOZbW1vFSbSJRxMuLi6Wl5fj91PL40QMmUcaTp2+6KQi+Cibo6OjeXl5uKOzsxNENTU1zs7OJSUlhYWF5Iampia2WPf19dXW1qKC7+7uZmVlLS0tfcornbZoiNgKCAhgdwY0yM7OxuXAwAAuiXLLy8shISHii6FrAwGpmR4eHiyhvb19b29vf3+/CA9/nXTEGM3hCv20PU77opOK4EO80tLSoaEhbP/8/Hy1Wj0/Px8dHU1Hky7WYJyenm5oaAAd0lk8OpaWllh0T09PcnKyRFs0JNpqaWnx9vbGYHBwkJ2cnJysqKhgL11cXFD9yDgwMHB9ff09BMZ/B4FzzgkSioC/Ts7x9vj4iFAoQkXwId7R0RHe/yH+8fFxVVVVbGxsfX29iIHq6uqIiIj9/X1bW1syQ4cmNDR0ZWUFA8zghrm5uczMTFY8mbZQFX19fclfJG+wSYuLi5HEyL/ExMT09HRG81JsYmJC85yenvLJjYyMGKEXAz4hDUFn+TGhISieoC8+Pj7iVAQf4nl6eiIDYMDLywsDxJf+EMfpdk5OTtrb2xHxoqIitpgIhiY3N3dkZAQBoje1TFvwjVQYeMuWGrDNzMwg1khoMoPkTk1NpRcjmHmklJHl0cnHJ6TBd1YwJjTQrVhbW3MmBX3RSUXwLh7uICw45LH6rq6uy8tLmIEbdXV1lZWVzD/dzm8a4DIuLm5iYgLNT2NjI8yg+mkzgJ2Ffs/NzQ23fastnExohcDJVjm0izi06HsEt5eVlRV9yepHEx4eHsbHx2MSbefY2BgppxzoXCes43FtgZJOhSNmdnaWIeL9qQH9d2RkJDxH2QELCSjy/fr6mj0eNjc3yQDaiK9jbW2NvlTWFt3H/q4B/W9zc7P42gjoT9KQja2fHEL0DuI8OmMCH93d3bU9TvsiTkWUY7S9pOMQCg4ORmODJofM4P0GDaFKpZL/XeBftCUI5D36QHLyMUp/VaHx/PysLKGweH9oQM/ExMTAK35XLR/6tCUI9AXYKCjs321IsNjKgdTPYwYaKGv7V7AFoCPVg3IA21Uqhb8AvZSGEbZEoQsAAAAASUVORK5CYII=)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](data:image/png;base64,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)
№16. Вычислите
№17. Найдите все значения
, при каждом из которых расстояние между
соответствующими точками графиков функций
и
меньше, чем на 4,8.
№18. Найдите все значения
, при которых уравнение
имеет хотя бы одно решение.
Итоговая работа по алгебре за курс 10 класса.
Вариант 10
Часть 1
№1. Упростите выражение
№2. Вычислите значение выражения
№3. Найдите область значений функции ![](data:image/png;base64,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)
№4. Решите уравнение ![](data:image/png;base64,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)
№5. Известно, что
Найдите
.
№6. Вычислите: cos 1300 · cos 100 + sin1300 · sin 100.
№7. Найдите наименьший, положительный период функции
№8. Найдите количество различных корней уравнения
из отрезка
.
Часть 2
№9. Найдите значение выражения:
.
№10. Укажите число целых решений неравенства:
№11. Найдите число корней уравнения ![](data:image/png;base64,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)
№12. Найдите наименьшее целое значение функции
.
Часть 3 №13. Решите уравнение ![](data:image/png;base64,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)
№14. а) Решите уравнение
б) Укажите все корни этого уравнения, принадлежащие отрезку
№15. Решите неравенство ![](data:image/png;base64,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)
№16.Вычислите
№17. Найдите все значения
, при каждом из которых расстояние между
соответствующими точками графиков функций
и ![](data:image/png;base64,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)
меньше, чем 2.
№18. Найдите все значения
, при которых уравнение
имеет хотя бы одно решение.