Тест на тему Деление на двузначное число

Ниже тест для 8 класса по теме рациональные выражения. Тип вопросов: открытый. Всего 5 вопросов. Для каждого вопроса дан ответ и пошаговое решение.

1. Упростите рациональное выражение: (3x^2 - 12) / (6x - 24)

• Ответ: (x-2)(x+2) / (2(x-4)), при x ≠ 4
• Пояснение:
  • 3x^2 - 12 = 3(x^2 - 4) = 3(x-2)(x+2)
  • 6x - 24 = 6(x-4)
  • После сокращения на 3 получаем (x-2)(x+2) / [2(x-4)]
  • Домен: изначально x ≠ 4 (и в упрощённой форме тоже x ≠ 4)

2. Найдите сумму рациональных выражений: (2x)/(x^2 - 4) + 3/(x - 2)

• Ответ: (5x + 6) / (x^2 - 4), при x ≠ ±2
• Пояснение:
  • x^2 - 4 = (x-2)(x+2)
  • 3/(x-2) = 3(x+2)/[(x-2)(x+2)]
  • Слагаемые: [2x + 3(x+2)] / (x^2 - 4) = (5x + 6) / (x^2 - 4)
  • Домен: x ≠ 2 и x ≠ -2

3. Упростите произведение двух рациональных выражений: (x+3)/(x-1) * (x-2)/(x+3)

• Ответ: (x-2)/(x-1), при x ≠ 1, x ≠ -3
• Пояснение:
  • Можно сократить на x+3 (при условии, что x ≠ -3)
  • Остальное: (x-2)/(x-1)
  • Домен сохраняется: x ≠ 1, x ≠ -3

4. Решите уравнение с рациональными выражениями: (3)/(x-2) - (2)/(x+1) = 1

• Ответ: x = 1 + √10 или x = 1 - √10
• Пояснение:
  • Общий знаменатель: (x-2)(x+1)
  • 3(x+1) - 2(x-2) = (x-2)(x+1)
  • Лево: 3x + 3 - 2x + 4 = x + 7
  • Правая: x^2 - x - 2
  • Получаем уравнение: x + 7 = x^2 - x - 2 → x^2 - 2x - 9 = 0
  • Решения: x = [2 ± √(4 + 36)]/2 = 1 ± √10
  • Домены: x ≠ 2, x ≠ -1 (обе корня допустимы)

5. Упростите выражение: (x^2 - 9)/(x^2 - 3x) - 2/(x-3)

• Ответ: (x^2 - 2x - 9) / [x(x-3)], при x ≠ 0, x ≠ 3
• Пояснение:
  • (x^2 - 9) = (x-3)(x+3); x^2 - 3x = x(x-3)
  • Первая дробь упрощается до (x+3)/x (при x ≠ 0, x ≠ 3)
  • Оставшееся выражение: (x+3)/x - 2/(x-3)
  • Приведём к общему знаменателю: [ (x+3)(x-3) - 2x ] / [ x(x-3) ]
  • Числ...: (x^2 - 9) - 2x = x^2 - 2x - 9
  • Итог: (x^2 - 2x - 9) / [x(x-3)], домены x ≠ 0, x ≠ 3

Если нужна версия теста без решений или с дополнительными задачами разной сложности, могу подготовить.

Тест по английскому языку: Present Simple Tense

Класс: 9

Количество вопросов: 50

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Вопрос 1:
He __________ to school every day.
a) go
b) goes
c) going
d) gone

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Вопрос 2:
They __________ breakfast at 7 am.
a) have
b) has
c) had
d) having

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Вопрос 3:
She __________ a lot of books.
a) read
b) reads
c) reading
d) reader

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Вопрос 4:
Does he __________ to play football?
a) like
b) likes
c) liking
d) liked

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Вопрос 5:
I __________ my homework after school.
a) do
b) does
c) doing
d) done

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Вопрос 6:
The train __________ at 9 o'clock every day.
a) leave
b) leaves
c) leaving
d) left

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Вопрос 7:
She __________ music in the evening.
a) listen
b) listens
c) listening
d) listened

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Вопрос 8:
We __________ our friends on weekends.
a) meet
b) meets
c) meeting
d) met

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Вопрос 9:
He __________ coffee for breakfast.
a) drink
b) drinks
c) drinking
d) drank

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Вопрос 10:
What time __________ you usually go to bed?
a) do
b) does
c) doing
d) done

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Вопрос 11:
They often __________ to the cinema.
a) go
b) goes
c) going
d) gone

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Вопрос 12:
She __________ her friends every Friday.
a) visit
b) visits
c) visiting
d) visited

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Вопрос 13:
He usually __________ a shower in the morning.
a) take
b) takes
c) taking
d) took

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Вопрос 14:
We __________ our lunch at noon.
a) have
b) has
c) had
d) having

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Вопрос 15:
The cat __________ on the sofa.
a) sleep
b) sleeps
c) sleeping
d) slept

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Вопрос 16:
Do you __________ to music while studying?
a) listen
b) listens
c) listening
d) listened

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Вопрос 17:
My parents __________ to the gym every Sunday.
a) go
b) goes
c) going
d) gone

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Вопрос 18:
He __________ his teeth twice a day.
a) brush
b) brushes
c) brushing
d) brushed

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Вопрос 19:
We __________ our teacher at school.
a) respect
b) respects
c) respecting
d) respected

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Вопрос 20:
What __________ your brother do in his free time?
a) do
b) does
c) done
d) doing

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Вопрос 21:
They __________ their vacation in the summer.
a) enjoy
b) enjoys
c) enjoying
d) enjoyed

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Вопрос 22:
She __________ three languages.
a) speak
b) speaks
c) speaking
d) spoken

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Вопрос 23:
He __________ coffee every morning.
a) drink
b) drinks
c) drinking
d) drank

---

Вопрос 24:
We __________ the news every morning.
a) watch
b) watches
c) watching
d) watched

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Вопрос 25:
Does she __________ to the gym regularly?
a) go
b) goes
c) going
d) gone

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Вопрос 26:
The sun __________ in the east.
a) rise
b) rises
c) rising
d) rose

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Вопрос 27:
They __________ their car every week.
a) wash
b) washes
c) washing
d) washed

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Вопрос 28:
I usually __________ breakfast at home.
a) have
b) has
c) had
d) having

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Вопрос 29:
What __________ you like to do on weekends?
a) do
b) does
c) done
d) doing

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Вопрос 30:
He always __________ his phone at home.
a) forget
b) forgets
c) forgetting
d) forgot

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Вопрос 31:
My sister __________ the piano very well.
a) play
b) plays
c) playing
d) played

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Вопрос 32:
We __________ our lessons together.
a) study
b) studies
c) studying
d) studied

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Вопрос 33:
She __________ a lot of time reading.
a) spend
b) spends
c) spending
d) spent

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Вопрос 34:
The dog __________ every morning.
a) bark
b) barks
c) barking
d) barked

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Вопрос 35:
I __________ to the library once a week.
a) go
b) goes
c) going
d) gone

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Вопрос 36:
He __________ many friends at school.
a) have
b) has
c) had
d) having

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Вопрос 37:
They __________ soccer every Saturday.
a) play
b) plays
c) playing
d) played

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Вопрос 38:
She __________ well in her exams.
a) do
b) does
c) doing
d) done

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Вопрос 39:
I __________ my bike to school.
a) ride
b) rides
c) riding
d) rode

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Вопрос 40:
What time __________ she usually wake up?
a) do
b) does
c) doing
d) done

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Вопрос 41:
The chef __________ delicious meals.
a) cook
b) cooks
c) cooking
d) cooked

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Вопрос 42:
We __________ a lot of projects during the year.
a) complete
b) completes
c) completing
d) completed

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Вопрос 43:
He __________ his bike to the park every day.
a) ride
b) rides
c) riding
d) rode

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Вопрос 44:
They __________ the match on TV.
a) watch
b) watches
c) watching
d) watched

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Вопрос 45:
I __________ my friends in the park.
a) meet
b) meets
c) meeting
d) met

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Вопрос 46:
She __________ a lot of pictures.
a) take
b) takes
c) taking
d) took

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Вопрос 47:
What music __________ you like?
a) do
b) does
c) done
d) doing

---

Вопрос 48:
The teacher __________ us interesting facts.
a) tell
b) tells
c) telling
d) told

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Вопрос 49:
I __________ my lunch at noon.
a) eat
b) eats
c) eating
d) ate

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Вопрос 50:
He __________ the newspaper every morning.
a) read
b) reads
c) reading
d) reader

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Конец теста.

Вот тест по теме "Present Perfect" для 8 класса:

Тест по английскому языку: Present Perfect

Вопрос 1:

Which sentence is in the Present Perfect tense?
a) I go to the store.
b) I have gone to the store.
c) I went to the store.
d) I am going to the store.

Ответ: b) I have gone to the store.

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Вопрос 2:

Choose the correct form of the verb to complete the sentence:
She ___ (never/see) a lion before.
a) never see
b) has never seen
c) never saw
d) is never seeing

Ответ: b) has never seen

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Вопрос 3:

What is the correct negative form of the Present Perfect?
They ___ (not/finish) their homework yet.
a) have not finished
b) did not finish
c) are not finishing
d) have finished not

Ответ: a) have not finished

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Вопрос 4:

Select the sentence that correctly uses the Present Perfect tense:
a) He has wrote a letter.
b) He has written a letter.
c) He wrote a letter.
d) He is writing a letter.

Ответ: b) He has written a letter.

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Вопрос 5:

Which question is correctly formed in the Present Perfect?
a) Have you saw my keys?
b) Do you have seen my keys?
c) Have you seen my keys?
d) Are you seeing my keys?

Ответ: c) Have you seen my keys?

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Вопрос 6:

Fill in the blank with the correct form:
We ___ (live) in this city for five years.
a) lived
b) have lived
c) are living
d) live

Ответ: b) have lived

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Вопрос 7:

Choose the correct option to complete the sentence:
I ___ (just/finish) reading the book.
a) just finished
b) have just finished
c) was just finishing
d) have finishing just

Ответ: b) have just finished

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Итог:

Тест состоит из 7 вопросов на тему Present Perfect для 8 класса. Ответы представлены после каждого вопроса.

Тест по предмету GMAT: Линейные уравнения

Инструкция:

Выберите правильный ответ из предложенных вариантов.

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Вопрос 1:
Какое значение x удовлетворяет уравнению 2x + 3 = 11?
a) 1
b) 3
c) 4
d) 5

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Вопрос 2:
Решите уравнение 5x - 7 = 3x + 9.
a) 2
b) 4
c) 8
d) 10

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Вопрос 3:
Какое из следующих уравнений является уравнением прямой?
a) 3x + 2y = 6
b) x^2 + y^2 = 1
c) y = 2x^2 + 3
d) x/y = 5

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Вопрос 4:
Чему равно значение y при x = 2 в уравнении y = 4x + 1?
a) 5
b) 7
c) 9
d) 11

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Вопрос 5:
Какое уравнение соответствует прямой с угловым коэффициентом 3 и y-пересечением 2?
a) y = 3x + 2
b) y = 2x + 3
c) y = 2x - 3
d) y = -3x + 2

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Вопрос 6:
Решите уравнение 3(2x - 4) = 15.
a) 5
b) 6
c) 7
d) 8

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Вопрос 7:
Решение уравнения 4x + 9 = 2x + 17. Чему равно x?
a) 1
b) 2
c) 4
d) 6

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Вопрос 8:
Если 5x - 2 = 3x + 10, то чему равно значение x?
a) 6
b) 7
c) 8
d) 9

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Вопрос 9:
Какое из следующих выражений можно привести к уравнению ax + b = 0?
a) x^2 + 1 = 0
b) 2 = 3x + 7
c) y = mx + c
d) 4x^2 - 5 = 0

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Вопрос 10:
Решите уравнение 7x + 3 = 4x + 12.
a) 2
b) 3
c) 4
d) 5

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Удачи в выполнении теста!