Тест на тему Поворот осей координат

Примечание: тест состоит из открытых вопросов и выводится без ответов.

1. Решите линейное уравнение: 3x − 7 = 2x + 5. Найдите x и покажите полное решение.

2. Решите систему линейных уравнений: 2x + 3y = 12 −4x + y = −2 Найдите все пары (x, y).

3. Решите неравенство и запишите решение в виде промежутка: −x + 4 ≤ 7 + 2x

4. Найдите корни квадратного уравнения: 2x^2 − 5x − 3 = 0 Опишите метод и приведите корни.

5. Для функции f(x) = x^2 − 4x + 3 найдите её корни и вершину параболы.

6. Разложите на множители многочёт x^2 − 5x + 6.

7. Разделите многочлен: (x^3 − 6x^2 + 11x − 6) ÷ (x − 1) Приведите результат деления.

8. Упростите выражение и укажите допустимые значения переменной: (x^2 − 9)/(x^2 − 3x) Укажите способ упрощения и область определения.

9. Решите радикальное уравнение: sqrt(2x + 3) = x − 1 Найдите все решения и условия допуска.

10. Решите неравенство с абсолютной величиной: |3x − 5| ≤ 7 Опишите множество решений.

11. Решите уравнение в степени: 3^(2x) = 9

12. Решите радикальное уравнение: sqrt(x + 4) = x − 2

13. Найдите 5-й член арифметической последовательности, если a1 = 2 и d = 3.

14. Найдите 4-й член геометрической последовательности, если a1 = 4 и q = −2.

15. Найдите композицию функций: f(x) = 2x + 1, g(x) = x^2 − 3 Найдите (f ∘ g)(x).

16. Найдите обратную функцию к f(x) = 3x − 7 и запишите f^−1(x).

17. Свойства графика квадратичной функции: y = x^2 − 4x + 3 Найдите вершину, пересечения с осями координат и опишите график.

18. Разложите на множители: x^2 + 4x − 21

19. Разложите на множители и найдите корни многочлена: x^3 − 6x^2 + 11x − 6

20. Решите систему: x + y = 7 x^2 + y^2 = 53 Найдите все пары (x, y).

Инструкция: выберите единственный правильный вариант для каждого вопроса.

1. She ___ coffee every morning. A) drink B) drinks C) is drinking D) drinking

2. They ___ in a big city. A) lives B) living C) live D) is living

3. The train ___ at 7 a.m. Every day. A) leaves B) is leaving C) leaving D) left

4. He ___ his homework every evening. A) do B) does C) doing D) did

5. We ___ already finished the project. A) have B) has C) had D) having

6. Look! The baby ___ asleep right now. A) is sleeping B) is sleep C) sleeps D) will sleep

7. They ___ dinner right now. A) eat B) are eating C) is eating D) eats

8. She ___ the piano, but she can't right now. A) plays B) is playing C) playing D) played

9. We ___ for the bus. It is late. A) wait B) are waiting C) waits D) waiting

10. He ___ to music at the moment. A) listens B) is listening C) listened D) listen

11. I ___ to France twice this year. A) go B) went C) have been D) have went

12. She ___ to the gym since 6 a.m. A) goes B) went C) has gone D) has been going

13. We ___ this book for a week. A) read B) are reading C) have read D) have been reading

14. They ___ here for many years. A) live B) lived C) have lived D) are living

15. He ___ in that company since last year. A) works B) worked C) has been working D) has worked

16. I ___ a lot lately. A) study B) have been studying C) studied D) am studying

17. She ___ in that role for six months. A) works B) has been working C) was working D) has worked

18. We ___ here since breakfast. A) wait B) have waited C) have been waiting D) are waiting

19. He ___ the same job for ten years. A) does B) did C) has done D) has been doing

20. They ___ to fix the issue all day. A) try B) are trying C) have been trying D) have tried