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Ниже представлен тест по алгебре для 9 класса в формате открытых вопросов. Все задания сопровождаются решениями и ответами.
Вопрос 1 Решите уравнение: 3x - 7 = 2x + 5. Решение (кратко): перенесём 2x, получим x - 7 = 5; x = 12. Ответ: x = 12
Вопрос 2 Решите систему уравнений: x + y = 7 2x − y = 1 Решение: сложим уравнения: 3x = 8 → x = 8/3. Подставляем в первое: 8/3 + y = 7 → y = 13/3. Ответ: x = 8/3, y = 13/3
Вопрос 3 Решите квадратное уравнение: x^2 − 5x + 6 = 0. Решение: дискриминант D = 25 − 24 = 1; корни x = (5 ± 1)/2 → x = 2 и x = 3. Ответ: x = 2 или x = 3
Вопрос 4 Решите неравенство: x^2 − 4x − 5 < 0. Решение: разложим на множители: (x − 5)(x + 1) < 0. Промежуток решения: x ∈ (−1, 5). Ответ: −1 < x < 5
Вопрос 5 Решите уравнение с модулем: |2x − 3| = 7. Решение: 2x − 3 = 7 или 2x − 3 = −7 → x = 5 или x = −2. Ответ: x = 5 или x = −2
Вопрос 6 Рациональное уравнение: 1/(x − 1) − 1/(x + 2) = 3. Решение: приведём к общему знаменателю: [ (x+2) − (x−1) ] / [(x−1)(x+2)] = 3 → 3 / [(x−1)(x+2)] = 3 → (x−1)(x+2) = 1. Преобразование: x^2 + x − 2 = 1 → x^2 + x − 3 = 0. Решения: x = [−1 ± √13]/2 (поскольку знаменатели не обращаются к нулю). Ответ: x = [−1 + √13]/2 или x = [−1 − √13]/2
Вопрос 7 Функция линейная: f(x) = ax + b, известно f(0) = 4 и f(3) = 10. Найдите a и b. Решение: b = 4; 3a + b = 10 → 3a + 4 = 10 → a = 2. Ответ: a = 2, b = 4
Вопрос 8 Найдите вершину параболы y = −x^2 + 4x − 3. Решение: вершина параболы с коэффициентом a = −1, b = 4 имеет координату x_v = −b/(2a) = −4/(−2) = 2. Значение y_v = −(2)^2 + 4·2 − 3 = −4 + 8 − 3 = 1. Ответ: вершина (2, 1)
Вопрос 9 Словесная задача: два числа A и B такие, что A + B = 15 и A на 3 больше B (A = B + 3). Найдите числа. Решение: подставим A = B + 3: (B + 3) + B = 15 → 2B + 3 = 15 → B = 6; A = 9. Ответ: A = 9, B = 6
Вопрос 10 Решите систему и окружность: x^2 + y^2 = 25 и x − y = 1. Решение: y = x − 1. Подставим в окружность: x^2 + (x − 1)^2 = 25 → 2x^2 − 2x + 1 = 25 → 2x^2 − 2x − 24 = 0 → x^2 − x − 12 = 0 → (x − 4)(x + 3) = 0 → x = 4 или x = −3. Соответственно y = 3 или y = −4. Ответ: (4, 3) и (−3, −4)
Ниже представлен тест по английскому языку на тему Present Simple и Present Perfect для 10 класса. Тип вопросов: единичный выбор. Всего 20 вопросов. Ответы приведены после теста.
Тест
They ... in that company for five years. A) work B) works C) have worked D) have works
My sister ... to bed early every night. A) go B) goes C) going D) has gone
I ... never seen such a thing before. A) am B) is C) have D) has
They ... the project yet. A) finish B) finishes C) finished D) haven't finished
She ... in that school since 2010. A) works B) worked C) has worked D) having worked
On Sundays, he ... to the gym. A) go B) goes C) going D) went
I have known him ... ten years. A) since B) for C) during D) from
Which sentence is in the Present Perfect tense? A) Do you ever go to Japan? B) Have you ever been to Japan? C) Are you ever been to Japan? D) Do you been to Japan?
What time ... your classes start on Mondays? A) do B) does C) are D) will
She ... meat. A) eat B) eats C) eating D) eaten
They ... here since 2012. A) live B) lives C) lived D) have lived
On weekdays, he ... to work by bus. A) go B) goes C) going D) went
We ... already finished the task. A) have B) has C) had D) having
Which sentence is correct in Present Simple to ask about origin? A) Where are you from? B) Where is you from? C) Where you from are? D) From where you are?
He has lived in London since he was a child. A) has lived B) have lived C) lived D) living
Do you work on weekends? A) do B) does C) did D) doing
She has never seen snow before. A) have B) has C) had D) having
I ... to the cinema twice this week. A) go B) goes C) went D) have been
He always helps his mother. A) help B) helps C) helping D) helped
They haven't seen each other since graduation. A) haven't seen B) haven't saw C) didn't see D) not have seen
Ответы
1 C 2 B 3 C 4 D 5 C 6 B 7 B 8 B 9 A 10 B 11 D 12 B 13 A 14 A 15 A 16 A 17 B 18 D 19 B 20 A
Тест по английскому языку на тему "Present Simple" для 6 класса
Инструкция: Выберите правильный вариант ответа из предложенных.
She ____ to school every day.
a) go
b) goes
c) going
They ____ TV in the evenings.
a) watch
b) watches
c) watching
I ____ my homework on weekdays.
a) do
b) does
c) doing
He ____ to play football on Saturdays.
a) like
b) likes
c) liking
We ____ breakfast at 7 a.m.
a) have
b) has
c) having
The sun ____ in the east.
a) rise
b) rises
c) rising
My brother ____ to the gym after school.
a) go
b) goes
c) going
You ____ like chocolate ice cream.
a) doesn't
b) don't
c) do
She ____ her guitar every morning.
a) practice
b) practices
c) practicing
We ____ in a big house.
a) live
b) lives
c) living
It ____ rain a lot in spring.
a) do
b) does
c) doing
They ____ lunch at noon.
a) eat
b) eats
c) eating
He usually ____ to bed at 10 p.m.
a) go
b) goes
c) going
I ____ coffee in the morning.
a) drink
b) drinks
c) drinking
The children ____ in the park after school.
a) play
b) plays
c) playing
She often ____ books before sleep.
a) read
b) reads
c) reading
My parents ____ to the cinema on Fridays.
a) go
b) goes
c) going
The teacher ____ us new words every lesson.
a) teach
b) teaches
c) teaching
He ____ a very good student.
a) am
b) is
c) are
We ____ our friends every weekend.
a) meet
b) meets
c) meeting
Удачи!
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