МИНИСТЕРСТВО ОБРАЗОВАНИЯ И НАУКИ
ДОНЕЦКОЙ НАРОДНОЙ РЕСПУБЛИКИ
ОТДЕЛ ОБРАЗОВАНИЯ АДМИНИСТРАЦИИ ГОРОДА ЕНАКИЕВО
Лисиченская общеобразовательная школа
I-III cтупеней Амвросиевского района
Коммунальное учреждение
«Общеобразовательная школа I – III ступеней № 31 города Енакиево»
Программа элективного курса по выбору (факультатива)
«Модуль в школьном курсе математики»
Составили:
Проскуренко В.М. – учитель математики высшей категории,
учитель-методист Лисиченской общеобразовательной школы
I-III cтупеней Амвросиевского района, ДНР,
Романцов А.Н. Директор КУ «ОШ I-III ступеней № 31
г.Енакиево», учитель математики высшей категории, ДНР.
Енакиево 2016
Пояснительная записка.
Программа элективного курса по выбору (факультатива) «Модуль в школьном курсе математики» предназначена для систематизации и обобщения знаний, обучающихся в 10-11 классах общеобразовательных организаций и более эффективной их подготовки к ГИА и вступительным испытаниям в различном их виде.
Задача обучения математике в школе состоит не только в том, чтобы дать обучающимся определённую сумму знаний, но и в том, чтобы развить у них творческое математическое мышление, заинтересовать их математикой, привить им навыки самостоятельно выполнять исследования и решать сложные математические задачи.
Из опыта преподавания математики известно, что при решении уравнений и неравенств, при изучении функций и построении их графиков, когда необходимо действовать с выражениями, содержащими модули, и исследовать их, даже наиболее подготовленные обучающиеся делают ошибки, так как очень мало решают соответствующих упражнений и задач, вопреки тому, что этот материал имеет большое образовательное значение. И хотя таких упражнений и задач в нынешних учебниках стало значительно больше, уделять им достаточное внимание учителя не имеют полной возможности из-за дефицита учебного времени.
Настоящей программой и занятиями по ней предпринята попытка устранить в некоторой мере эти недостатки. Программа рассчитана на организацию занятий курса по выбору (факультатива) с учащимися 10-11 классов общеобразовательных организаций в количестве 70 часов, что даёт возможность их проведения по 1 часу в неделю в каждом из 10 и 11 классах. Возможно проведение по 2 часа в неделю, либо в 10 классе, либо в 11 классе (в зависимости от наличия часов школьного компонента в конкретном учебном учреждении и классе). В Программе предлагаются для обобщения, систематизации и углубления знаний учащихся по основным содержательным линиям:
Программа рассчитана и на самостоятельную, и на индивидуальную работу, желающих углубить знания по данной проблеме, так как в её содержательной части приведено достаточно большое количество упражнений и задач, в том числе и для самостоятельного решения.
Весь материал подобран и обобщён на основании многолетнего опыта работы с учащимися старшей школы
Учебно-тематический план курса по выбору (факультатива) «Модуль в школьном курсе математики для 10-11 классов (70 часов)
№ п/п | Разделы и темы программы | Всего часов | В том числе |
Теория | Практика | Контроль |
1 | 2 | 3 | 4 | 5 | 6 |
Раздел I. Модуль числа. (6 часов) |
Т-1 | Понятие модуля числа | 2 | 1 | 1 | |
Т-2 | Свойства модуля числа | 2 | 1 | 1 | |
Т-3 | Арифметическое значение корня квадратного | 2 | 1 | 1 | |
| Итого | 6 | 3 | 3 | - |
| | | | | |
Раздел II Линейные уравнения и неравенства с модулями(15часов) |
Т-1 | Графики линейных функций | 2 | 1 | 1 | |
Т-2 | Простейшие уравнения вида ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_1.png) | 3 | 1 | 2 | |
Т-3 | Более сложные линейные уравнения | 2 | 1 | 1 | |
Т-4 | Простейшие неравенства вида , | 2 | 1 | 1 | |
Т-5 | Более сложные линейные неравенства | 3 | 1 | 2 | |
Т-6 | Системы линейных уравнений с двумя переменными | 2 | 1 | 1 | |
| Итого | 15 | 6 | 8 | 1 |
Раздел III. Графики функций с модулями(5 часов) |
Т-1 | Простейшие геометрические преобразования графика функции ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_4.png) | 1,5 | 0,5 | 1 | |
Т-2 | Графики функций с модулями | 1,5 | 0,5 | 1 | |
Т-3 | Примеры построения графиков | 2 | 1 | 1 | |
| Итого | 5 | 2 | 3 | - |
Раздел IV. Квадратные и более высоких степеней уравнения и неравенства с модулями(13 часов) |
Т-1 | Квадратные уравнения | 3 | 1 | 2 | |
Т-2 | Некоторые уравнения более высоких степеней | 3 | 1 | 2 | |
Т-3 | Иррациональные уравнения | 3 | 1 | 2 | |
Т-4 | Квадратные неравенства | 3 | 1 | 2 | |
| Итого | 13 | 4 | 8 | 1 |
Раздел V. Показательные и логарифметические уравнения и неравенства с модулями(16 часов) |
Т-1 | Показательные уравнения с модулями | 4 | 1 | 3 | |
Т-2 | Логарифмические уравнения с модулями | 4 | 1 | 3 | |
Т-3 | Системы показательных и логарифмических уравнений с модулями | 3 | 1 | 2 | |
Т-4 | Показательные и логарифмические неравенства с модулями | 4 | 1 | 3 | |
| Итого | 16 | 4 | 11 | 1 |
Раздел VI. Модули в тригонометрии с модулями(15 часов) |
Т-1 | Определение тригонометрических функций угла и некоторые их свойства | 2 | 1 | 1 | |
Т-2 | Основные тригонометрические тождества. Формулы приведения | 3 | 1 | 2 | |
Т-3 | Теоремы сложения и их следствия | 2 | 1 | 1 | |
Т-4 | Тригонометрические уравнения | 3 | 1 | 2 | |
Т-5 | Примеры тригонометрических неравенств с модулями | 2 | 1 | 1 | |
Т-6 | Свойства и графики тригонометрических функций с модулями | 2 | 1 | 1 | |
| Итого | 15 | 6 | 8 | 1 |
| Всего | 70 | 25 | 41 | 4 |
Содержание Программы курса по выбору (факультатива) «Модуль в школьном курсе математики» для 10-11 классов (70 часов)
в двух вариантах (I вариант – 35 часов в 10 классе, 35 часов в 11 классе по 1 часу в неделю;
II вариант – 70 часов, либо в 10 классе, либо в 11 классе, но по 2 часа в неделю)
Разделы | Количество часов | Темы раздела | Количество часов | Основное содержание темы |
1 | 2 | 3 | 4 | 5 |
Раздел I Модуль числа | 6 | Понятие модуля числа | 2 | Определение модуля числа ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_5.png) Простейшие свойства: ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_6.png) |
Свойство модуля числа | 2 | | …+ …+ ; ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_10.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_11.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_12.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_13.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_14.png) |
Арифметическое значение корня квадратного | 2 | Определение арифметического квадратного корня; Тождество ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_15.png) |
Раздел II Линейные уравнения и неравенства с модулями | 15 | Графики линейных функций; | 2 | ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_16.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_17.png) |
Простейшие уравнения вида ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_1.png) | 3 | Решение уравнения при ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_19.png) Решение уравнения, если ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_20.png) |
Более сложные линейные уравнения | 2 | Примеры решения более сложных уравнений: ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_21.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_22.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_23.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_24.png) ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_25.png) |
Простейшие неравенства вида , ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_3.png) | 2 | Неравенства: а) Если Если . |
| | | | Примеры неравенств этого вида: а) 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д) 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е) 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ж) 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з) 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и) 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Более сложные линейные неравенства | 3 | Основной способ – определение решений неравенства на каждом из промежутков ( промежутки, на которые числовая прямая делится корнями подмодульных функций); Примеры неравенств: а) ![](data:image/png;base64,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) б) 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в) 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г) д) ![](data:image/png;base64,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) |
Системы линейных уравнений с двумя переменными | 2 | Пример системы: Каждое из выражений может быть неотрицательным и отрицательным. Поэтому, возможны 8 комбинаций вариантов знаков этих трёх выражений, а потому решается 8 систем неравенств и уравнений. |
Раздел III Графики функций с модулями | 5 | Простейшие геометрические преобразования графика функции ![](https://fsd.multiurok.ru/html/2017/02/27/s_58b3da72b2432/574239_4.png) | 1,5 | График ; График ; График ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAVCAIAAABngU9+AAAD60lEQVR4nNVXWShtURg+OIZkTiIylEgZkilkylAISclJMiRj4kVmXnAevCgZiohHQ0JRxiIeJB5MDygkUngwZOZ+96zabXuvc/Y+15Fz/6e1//Xtf+9v/eOSfn5+SrRVrq6urK2tNQWTauKXfkqmpqZyc3MFYZOTk3l5eYIw7aX6/Px8fHwsBgnYy8uLgYGBapj2Ul1aWnJ2dhaDdHJyWl5ejomJUQ3TFqoPDw9ra2teXl62trZEg8eoqCgx77q4uAD8f1A9Pz+vqqrKz88PCws7ODggyp2dHZlMJuZ1nM7e3p4gTCuoVlRUgFVoaGh7ezujRAZaWlqKeR2wk5MTQdjvU8Vfjo+P9/b2SqXSxMRERn95eWliYiLGgqmp6dnZmSDs96mOjIwEBASYm5tz9Le3t0ZGRmIsGBoa3t/fC8K4VLe3t+vr6+3s7Hp6evCYk5NzdHS0srKC9cLCQmxsLNWKnp7e6+urmN9iy9bWlp+fH1nr6uoODg5mZWUxu09PT/Az8zgzM9PS0uLt7d3V1dXW1jYxMTE7O2tsbPyXg1T6+PjIthwUFDQ3N2dmZqaKKmpgXV1deHh4a2urlZVVU1MT8/no6OiPjw91+agQX19fGLS3t29sbCwsLOTscsa4+Pj4w8PDhoaG4ODglJSUyspKZktHRwdNmA329/eHqzkGKQEcGBgIr+LMMjIyNjc3MzMzxf+9up5H7bm4uIiMjOTjEb1gCxqMJjk5uby8HKfj5ubGRkLD9j+ks7OTb5Ceq6mpqQgYUEXBGBgYoGKooq7nV1dXbWxs3N3d+VsIThwNewZycHBAseWf19vbG4lk1UKniiBBqIyOjiJs9PX1iVLjuSpRUKW6VKKoq0hXNtWOjg5EJqYFdGA2EolqYWEh+C06VVhEYszPz5PiRETjuSpRUC0qKqJuOTo6oggzpWVsbAw1DCFQW1uLmD89PUXtIVt3d3fIOLJG65qeni4uLuYbpFPFqIVrUXV19XepqBQw2d3dTUpKou66urre3NwgaNfX17Ozs5ubmzFL4ZWamhqw7evrY5DX19cAkzVmrNLS0rS0NBwKxyCdKg6mu7tb5LT9z4KMCAkJARnqrqenJwZGdBeUyf39faKEk/mDEZzs4+ND1hhCEhIS+DwlHKo4M1Rt3HQxfBQUFHyXihJBVmM2KikpGRoaksvlymBxcXGLi4tiDKLzR0REkPXw8DAaLxX2hSqauFwhP8cT8v7+3t/fj76Xnp6OuVcZzMPDA3duMQYR5yguZI3QRY2kwr5QLSsrQ0JzepTGBQ1zY2NDDJKZpVQLQp1ZK+Mp4efqT/NUSwSvoEQwBYiB/QFpi5YM2EkmmQAAAABJRU5ErkJggg==) График ![](data:image/png;base64,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) График ![](data:image/png;base64,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) График ![](data:image/png;base64,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) 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Графики функций с модулями | 1,5 | График ![](data:image/png;base64,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) График ![](data:image/png;base64,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) |
| | Примеры построения графиков | 2 | ![](data:image/png;base64,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) ![](data:image/png;base64,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) -
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Раздел IV Квадратные и более высоких степеней уравнения и неравенства с модулями | 13 | Квадратные уравнения | 3 | -
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Некоторые уравнения более высоких степеней | 3 | 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3![](data:image/png;base64,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) Указание: ![](data:image/png;base64,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) ![](data:image/png;base64,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) 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Иррациональные уравнения | 3 | -
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| | Квадратные неравенства | 3 | -
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Раздел V Показательные и логарифмические уравнения и неравенства с модулями | 16 | Показательные уравнения с модулями. | 4 | Примеры показательных уравнений с модулями: ![](data:image/png;base64,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) -
![](data:image/png;base64,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) ; ![](data:image/png;base64,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) ![](data:image/png;base64,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) -
Определить графически количество корней уравнения: ![](data:image/png;base64,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) |
Логарифмические уравнения с модулями. | 4 | Примеры логарифмических уравнений с модулями: =2; ![](data:image/png;base64,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) ![](data:image/png;base64,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) -
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Системы показательных и логарифмических уравнений с модулями | 3 | Примеры таких систем: -
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| | Показательные и логарифмические неравенства с модулями | 4 | Примеры таких неравенств: ; -
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![](data:image/png;base64,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) -
(где 0![](data:image/png;base64,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) Решить неравенство графическим способом: . | | Раздел VI Модуль в тригонометрии. | 15 | Определение тригонометрических функций угла и некоторые их свойства. | 2 | Нахождение углов x из равенств (0): -
б) | | |
| | | | Найти Упростить выражения: а) б) ; в) 2 при 4. Вычислить ![](data:image/png;base64,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) при ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAAApCAIAAADMGe7nAAAEuUlEQVR4nO2abSh7bRzHsY01yUYeMk8reUteuG/yEJIXlChRlOWFUFoRmudobjJNkafaUkokb6RWJG88LFGYh5S8kIm0STNTk92/zmr7x/3ffzvnOsdZ9/V5de20/X7f3/a9znX9zi6u3W73w2AIuD8tAMMisBswLrAbMC6wG3yGx8dHmUy2ubkpFAqVSmVZWRnyFNgNPkNPT09bW9vCwsLAwEB1dbXJZOLz+WhTYDf4BgaDQS6XSyQSGLe3tw8NDVmtVuyG/ylisdg5Pjs7q62tFYlEyLNgN/gYx8fHjY2Ns7OzdATHbvAldDod+MBisWRkZGg0GqlUijb+VzdsbW0VFhb+51s5HI7NZkObHuMVfxPAr1BcXKxQKGh3Q0FBwefnJ9ocGLTweDzYUZaXlyOPjFcKn4TL5aanp6MPizwihg6MRuPGxkZpaalAIICbt1qtVqlUyLNgN/gG4Ibh4eGWlpaGhobIyMjBwcG4uDjkWbAbfIPk5OSTkxO6s/yMG66url5eXqisfNQj0I0v1sioG+x2+/r6+sTEBPSx4+PjJOqkHsER5Pb21mw2x8TEhIWF+RFP9yIJSERDrhBJjeRgyA0mkwk2PtPT0w8PDxUVFbu7u9A3MxzBib+//93dXXZ29uHhIbjBMf+0Wi1FN7CqRnLQ7gar1drc3Ly4uCgWi5uamurq6hzTkckI37m/vw8NDU1NTYXx8vKyH/Fgh3Q0dtZIgq9ugHmDNoHBYNBoNAkJCVNTU797yume5+dn9xG80uw4B7qzs5OTkxMQEAAvZ2ZmsrKygoKCSAf8o8I/grZG97g5CUv7vQHW5v39fVgFS0pKJBIJNEhSqVQoFDIZ4TvghpqaGhgcHBzAvMzPz6cSjZ01kuCrG+g4Qv0XwdjYGKyIIyMjXV1dVVVVcrk8KSkJSQRvNb+/v5+enubl5cF6weVyr6+vwQ02m43H4zneQOJLYFuN5GCup4iKiurv74ciYZ2GSbC6utrR0cFwBAd6vT4wMDA6Onp7ezsxMRHGAoEALqalpZGIhlYhqhrds7e3Nzk5OT8/D7X/ep3p5w0w/2oILBbLD0bg8/l9fX3Qv0FbIRKJzs/PKysryUWjSSHFCO65ubmBhuX19fXLXtULN8Ba29raenl5mZmZOTc3Fx8fT0VQcHAwlY//LoInIqGVMBqNjjH0mdBtuslCpWqaavwVcvIcVvt+3VM3XFxcqFQqpVIJay0sZjCTYNfj4WcZA7lIlleNXJ6nblhaWlKr1Y5dLmyAc3Nzn56eIiIiqORGDnKRLK8auTxP3VBfX+9seFJSUmD3ERISQjorTSAXyfKqkcvz1A2xsbHOMey8oBdCfnybOshFsrxq5PLI9BRarRYaYipZGQC5SJZXjUSe1244OjqC2xHD/6Z4C3KRLK8alTzv3PD29raysqJQKChmpRXkIlleNUJ5Xrjh4+NjdHS0t7eXw+H4EWezwsPDqStAC3KRLK8arTxP3WC322UyWVFRkV6vh5dms1mn03V3d5NOTAfIRbK8auTyPHVDZ2fnNIHzytraGumsNIFcJMurRi7PUzf8Q0AlEwMgF8nyqpHLw2emMS6wGzAusBswLrAbMC7+Ba4ucQHKVjY7AAAAAElFTkSuQmCC) Упростить выражение: . Показать на единичной окружности дуги α, для которых: |
Основные тригонометрические тождества. Формулы приведения. | 3 | Формулы: ![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAATCAIAAAAifNuEAAAAF0lEQVR4nGP5//8/AzbAglV0VGLoSAAA0dMDSjyUZ3wAAAAASUVORK5CYII=) Упростите: |
| | | | Доказать тождества: а) б) в) г) д) е) ж) |
Теоремы сложения и их следствия | 2 | Упростить: а) б) , ![](data:image/png;base64,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) в) ; г) |
| | Тригонометрические уравнения с модулями. | 3 | Уравнения, эквивалентные совокупности двух уравнений: а) б) в) г) е) Уравнения, которые сводятся к равносильной совокупности смешанных систем уравнений и неравенств: Решение:
Отсюда имеем совокупность таких 4х систем: (1) (2) |
| | | | (3) (4) и т.д. |
Примеры тригонометрических неравенств с модулями. | 2 | 2. -
5. 6. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIEAAAAVCAIAAADuNRpSAAAEFElEQVR4nO2ZWSi8URjGaciF7FuWEslWlsIMSilRlii7+oukbKGUhCYSCpESSkiIbEmELBcuUGRNWRKR7cISJUn4P83UNM2Z+ZaZz3wuPBc6c5x5/d553vOe8xm97+9vHUKfn58CgYCcZyuu4mgHgy9aPXJqa2urr6+vra1Nw9BcxdEOBo+0Sjz4k5b15wH/+vOAf/0iD97f30tKSoqKitzc3Phm4UDM0/ktHpydnSUnJ29vbwOabxYOxCodRh60tLTAUo3BFHV8fPz8/CwUCjF2dnZeWVkxMjJiG+SH2EjJ09KKVTo0HuDpoaqq6v7+nkkshkLMmZkZ3AKXl5dbW1tlWRkaGrKNwzmb0r+ilJZWzNOh8uDj4yMxMXF6ehrj6+vrqamp/f39rq4uW1tbsViMyZSUlOHhYQzm5ubq6uq8vb07OjqampqwcmFhgQz4+PjY09PT2dl5d3eXlJS0uroaGBjIEFQkEi0uLhobG7NlI6UFWlai8kBfX39gYMDS0nJ3d9fT0xOPkVFRUcgzODgYeVpZWcmSjIyMPD09xWRQUFBcXFxpaalCqLe3t8LCwqGhIXt7+/z8/KysLHNzc1ag/v7+BgYGarCR0gItK9H0oqWlJXAgSYyfnp5ubm7AjUdKvFTYlbGxscXFxV9fX66urmQcvLe3t9fR0RGlFx4ergZoe3u72mykNKFFU1KVgkAgwAZlmJFMNB7Mzs6ivqRjFF11dTV28dHRUUFBQX19vfxKBwcHMzMzVQR2dnbr6+voqjExMU5OTrm5uZmZmaampmxx1WMjpQltWFgYzNOEXEE0HqB1YoPLXu7s7OAY9PX1JVeCGO1ibW0tOztbaSiRRM3NzeiwDQ0NlZWVqamp5eXlLi4u6qEzZ/sNtBSi8gCn3MPDg4eHx97eno+Pz8nJCY4vpFpTU5Oenq6rqytbOTEx4efnZ21tXVFRcXt7e3l5iQSUxrSxsUHBIqWRkRF8EHhjWVmZ9Ffo6fhJltjFxQVKPi8vTz02UpzQ0kppOtigJiYm2Knyk1Qe4D6Aswj3AWR1dXWFmzh26NjYGPbm/Pw8jiys2djYyMjIqK2tDQkJeXl5QaUgse7ubmo+nKj/JHp9fZXOnJ+fDw4O6kj6fk5OjpeXl2zxwcEBoBMSEvCpsWIjxRUtrVSls7m5aWFhobCYyoOIiAgcdNJxfHx8f3+/u7s7SiYtLS00NFQ6j9Pv8PBQOsbFETXLkFIq2SUabVcsEbkmOjoafV/eAIZspLiipZWqdCYnJ8nFTP9XgbqTbXAcgMwfVTTX6Ogo7icUC3hk40RMPRgfH29sbAwICMD1AHcP1N2PYskLXYj66y0e2TgRUw+EEv0oiirRfr/IIxsnUuKBn0Sah+YqjnYweKT9D8hW0WbbiVi2AAAAAElFTkSuQmCC) |
6. Свойства и графики тригоно- метрических функций с моду- лями. | 2 | 1. Найти область определения функции: а) б) в) г) 2. Построить график функции: а) г) ; д) |
Примечание: Содержание и объём контроля, на усмотрение пользователя этой программы.
Литература
1. Министерство образования и науки ДНР. Программа по математике для общеобразовательных организаций (5-6 классы, 7-9 классы, 10-11 классы) Донецк, 2015г.
2. Учебники: Алгебра 7, 8, 9 классы под редакцией С.А.Теляковского, М. «Просвещение», 2016 г.
Алгебра и начала математического анализа, Ш.А. Алимов, М. «Просвещение», 2016 г.
3. «ЕГЭ. Математика. Базовый уровень». Практикум по выполнению типовых заданий ЕГЭ.
Л.Д.Лаппо, М.А.Попов. М. «Экзамен» 2016.
4. ЕГЭ 2015, Математика, экзаменационные тесты, базовый уровень, практикум по выполнению типовых тестовых заданий ЕГЭ (профильный уровень), Лаппо Л.Д., Попов М.А. М. «Экзамен». 2016г.
5. Алгебраический тренажер. Пособие для школьников и абитуриентов. Мерзляк А.Г., Полонский В.Б., Якир М.С. Харьков. «Гимназия». 2009г. 6. Полный курс математики в тестах Ю.Л. Захарийченко, А.В. Школьный, Л.И. Захарийченко, Е.В. Школьная. Харьков. «Ранок». 2012г.
7. Литвиненко М. , Федченко Л.Я. , Швец В.А. Сборник задач для экзамена по математике на аттестат о среднем образовании. Часть 1. Алгебра и начала анализа . - Львов , ВНТЛ , 1997г.
8.Федченко Л.Я.Сборник заданий для тематических и итоговых аттестаций. Алгебра 7-9 кл.
Донецк, Каштан,2009.