Тест на тему Входной

Ниже тест из 5 открытых вопросов по теме «Дроби углублённый уровень» для 7 класса. В конце — ответы с краткими решениями.

1. Упростите сложную дробь: (3/4) ÷ (5/6). Запишите ответ в виде несократимой дроби.

2. Вычислите: (7/12) + (5/8) - (1/3). Ответ запишите в виде несократимой дроби.

3. Решите уравнение с дробями: (2x - 3)/4 = (x + 5)/6. Найдите значение x.

4. В рецепте на одну порцию нужны 3/4 чашки сахара и 2/3 чашки муки. Если приготовить три порции, сколько нужно сахара и муки? Ответ запишите в дробях и укажите единицы измерения.

5. Разложите на простейшие дроби выражение (2x+3)/(x^2 - 9). Укажите ограничения на x (домейн).

Ответы

1. (3/4) ÷ (5/6) = (3/4) × (6/5) = 18/20 = 9/10. Ответ: 9/10.

2. Сначала приводим к общему знаменателю 12, 8, 3 -> 24: 7/12 = 14/24, 5/8 = 15/24, 1/3 = 8/24. 14/24 + 15/24 - 8/24 = 21/24 = 7/8. Ответ: 7/8.

3. (2x - 3)/4 = (x + 5)/6. Перемножаем кросс: 6(2x - 3) = 4(x + 5) → 12x - 18 = 4x + 20 → 8x = 38 → x = 38/8 = 19/4. Ответ: x = 19/4.

4. На одну порцию: сахар 3/4 чашки, мука 2/3 чашки. Значит для трёх порций: сахар: 3 × (3/4) = 9/4 чашки = 2 1/4 чашки; мука: 3 × (2/3) = 6/3 = 2 чашки. Ответ: сахар — 9/4 чашки, мука — 2 чашки.

5. (2x+3)/(x^2 - 9) = (2x+3)/[(x-3)(x+3)]. Разложим: (2x+3)/[(x-3)(x+3)] = A/(x-3) + B/(x+3). 2x+3 = A(x+3) + B(x-3) → (A+B)x + (3A - 3B) = 2x + 3. Система: A + B = 2; 3A - 3B = 3 → A - B = 1. Решения: A = 3/2, B = 1/2. Значит разложение: (2x+3)/(x^2 - 9) = (3/2)/(x-3) + (1/2)/(x+3) = 3/[2(x-3)] + 1/[2(x+3)]. Ограничения на x: x ≠ 3, x ≠ -3.

Инструкция: Выберите один правильный ответ для каждого предложения. Вставляйте либо some, либо a, либо an в пустое место.

1. I would like ___ cookies. A) some B) a C) an D) the

2. There is ___ apple in the bag. A) some B) a C) an D) the

3. She has ___ sisters. A) some B) a C) an D) the

4. I need ___ pencil. A) some B) a C) an D) the

5. We bought ___ oranges. A) some B) a C) an D) the

6. He can't find ___ umbrella. A) some B) a C) an D) the

7. There are ___ students in class. A) some B) a C) an D) the

8. I saw ___ dog in the park. A) some B) a C) an D) the

9. She wants ___ eggs. A) some B) a C) an D) the

10. He has ___ idea. A) some B) a C) an D) the

11. We need ___ notebooks. A) some B) a C) an D) the

12. There is ___ hour to finish. A) some B) a C) an D) the

13. I would like ___ cup of tea. A) some B) a C) an D) the

14. They bought ___ bananas. A) some B) a C) an D) the

15. She has ___ money. A) some B) a C) an D) the

16. I need ___ spoon. A) some B) a C) an D) the

17. They want ___ new toys. A) some B) a C) an D) the

18. There is ___ problem. A) some B) a C) an D) the

19. We drank ___ juice. A) some B) a C) an D) the

20. We bought ___ apples and bananas. A) some B) a C) an D) the

21. I have ___ brother. A) some B) a C) an D) the

22. She needs ___ new dress. A) some B) a C) an D) the

23. There are ___ chairs in the room. A) some B) a C) an D) the

24. He wants ___ ice cream. A) some B) a C) an D) the

25. I saw ___ elephant at the zoo. A) some B) a C) an D) the

26. I need ___ paper. A) some B) a C) an D) the

27. There was ___ loud noise. A) some B) a C) an D) the

28. I would like ___ milk. A) some B) a C) an D) the

29. There is ___ student who needs help. A) some B) a C) an D) the

30. I have ___ fish. A) some B) a C) an D) the

31. We need ___ batteries. A) some B) a C) an D) the

32. She bought ___ shirt. A) some B) a C) an D) the

33. There are ___ birds in the tree. A) some B) a C) an D) the

34. He wants ___ information. A) some B) a C) an D) the

35. I found ___ old coin. A) some B) a C) an D) the

36. We need ___ chairs. A) some B) a C) an D) the

37. I saw ___ interesting book. A) some B) a C) an D) the

38. There are ___ pencils on the desk. A) some B) a C) an D) the

39. He has ___ old car. A) some B) a C) an D) the

40. We need ___ orange juice. A) some B) a C) an D) the

41. She bought ___ new shoes. A) some B) a C) an D) the

42. There is ___ map on the wall. A) some B) a C) an D) the

43. I have ___ idea. A) some B) a C) an D) the

44. They want ___ friends. A) some B) a C) an D) the

45. He picked ___ flower. A) some B) a C) an D) the

46. There are ___ chairs outside. A) some B) a C) an D) the

47. She needs ___ information. A) some B) a C) an D) the

48. I saw ___ rabbit in the garden. A) some B) a C) an D) the

49. We need ___ papers for the project. A) some B) a C) an D) the

50. There is ___ apple on the table. A) some B) a C) an D) the

Ответы: 1 A 2 C 3 A 4 B 5 A 6 C 7 A 8 B 9 A 10 C 11 A 12 C 13 B 14 A 15 A 16 B 17 A 18 B 19 A 20 A 21 B 22 B 23 A 24 A 25 C 26 A 27 B 28 A 29 B 30 A 31 A 32 B 33 A 34 A 35 C 36 A 37 C 38 A 39 C 40 A 41 A 42 B 43 C 44 A 45 B 46 A 47 A 48 B 49 A 50 C

Тест по математике для 4 класса: Задачи на расчет денежных средств

Вопрос 1:

Маша хочет купить 3 игрушки. Первая игрушка стоит 150 рублей, вторая - 200 рублей, а третья - 100 рублей. Сколько всего рублей Маша потратит на игрушки?

a) 350 рублей
b) 400 рублей
c) 450 рублей
d) 500 рублей

Правильный ответ: c) 450 рублей
Обоснование: 150 + 200 + 100 = 450 рублей.

Тест по Английскому языку: Погода

Класс: 6

Вопросы:

1. What is the opposite of "sunny"? A) Windy B) Cloudy C) Rainy D) Snowy Ответ: B) Cloudy

2. Which season is known for hot weather and long days? A) Winter B) Spring C) Summer D) Autumn Ответ: C) Summer

3. What do we call it when small drops of water fall from the sky? A) Fog B) Hail C) Storm D) Rain Ответ: D) Rain

Надеюсь, этот тест поможет вам подготовиться к урокам английского языка!