Тест на тему appearance and character traits

Ниже представлен тест по теме Неопределенный интеграл для 11 класса. Тип вопросов: открытый. Всего 20 вопросов. Тест выдает ответы после каждого задания.

Важное правило: записывайте неопределенный интеграл с константой интегрирования C.

1. Вычислите ∫ x^2 dx.
2. Вычислите ∫ (3x^4 + 2x^2 − 5) dx.
3. Вычислите ∫ (2x + 1) dx.
4. Вычислите ∫ e^{2x} dx.
5. Вычислите ∫ x e^{x} dx.
6. Вычислите ∫ sin x dx.
7. Вычислите ∫ cos x dx.
8. Вычислите ∫ cos(3x) dx.
9. Вычислите ∫ sec^2 x dx.
10. Вычислите ∫ tan x dx.
11. Вычислите ∫ dx/(x^2 + 1).
12. Вычислите ∫ x^{−1/2} dx.
13. Вычислите ∫ x/(x^2 + 1) dx.
14. Вычислите ∫ (1/x) dx.
15. Вычислите ∫ (2x + 1)√(x + 1) dx.
16. Вычислите ∫ (2x + 3) e^{x} dx.
17. Вычислите ∫ x^2 e^{3x} dx.
18. Вычислите ∫ dx/((x + 2)^2 + 1).
19. Вычислите ∫ dx/(x^2 − 1).
20. Вычислите ∫ dx/((x + 1)^2 + 1).

Ответы

1. ∫ x^2 dx = (1/3) x^3 + C.
2. ∫ (3x^4 + 2x^2 − 5) dx = (3/5) x^5 + (2/3) x^3 − 5x + C.
3. ∫ (2x + 1) dx = x^2 + x + C.
4. ∫ e^{2x} dx = (1/2) e^{2x} + C.
5. ∫ x e^{x} dx = (x − 1) e^{x} + C.
6. ∫ sin x dx = −cos x + C.
7. ∫ cos x dx = sin x + C.
8. ∫ cos(3x) dx = (1/3) sin(3x) + C.
9. ∫ sec^2 x dx = tan x + C.
10. ∫ tan x dx = −ln|cos x| + C (или ln|sec x| + C).
11. ∫ dx/(x^2 + 1) = arctan x + C.
12. ∫ x^{−1/2} dx = 2√x + C.
13. ∫ x/(x^2 + 1) dx = (1/2) ln(x^2 + 1) + C.
14. ∫ (1/x) dx = ln|x| + C.
15. ∫ (2x + 1)√(x + 1) dx = (4/5)(x + 1)^{5/2} − (2/3)(x + 1)^{3/2} + C.
16. ∫ (2x + 3) e^{x} dx = (2x + 1) e^{x} + C.
17. ∫ x^2 e^{3x} dx = e^{3x} (9x^2 − 6x + 2)/27 + C.
18. ∫ dx/((x + 2)^2 + 1) = arctan(x + 2) + C.
19. ∫ dx/(x^2 − 1) = (1/2) ln| (x − 1)/(x + 1) | + C.
20. ∫ dx/((x + 1)^2 + 1) = arctan(x + 1) + C.

Если нужно, могу адаптировать уровень сложности (чуть проще или чуть сложнее), добавить подсказки по методам решения (подстановка, интегрирование по частям, частичные дроби) или оформить тест в формате для печати.

Вот тест на тему "Past Simple" для 6 класса. Включены 21 вопрос с единственным выбором, а также ответы.

Тест: Past Simple

Вопросы:

1. What is the past simple form of "go"? a) goed
   b) went
   c) gone

2. He _____ (play) football yesterday. a) play
   b) plays
   c) played

3. They _____ (not finish) their homework last night. a) not finished
   b) didn’t finish
   c) don’t finish

4. She _____ (be) at the cinema last week. a) was
   b) is
   c) were

5. I _____ (see) a movie on Saturday. a) seen
   b) saw
   c) see

6. We _____ (not visit) the museum last summer. a) didn't visit
   b) not visited
   c) don’t visit

7. What is the past simple form of "have"? a) had
   b) have
   c) haved

8. He _____ (not eat) breakfast this morning. a) didn’t eat
   b) not ate
   c) doesn’t eat

9. They _____ (go) to the party last week. a) go
   b) going
   c) went

10. I _____ (read) that book last month. a) readed
    b) read
    c) reads

11. What is the past simple form of "make"? a) maked
    b) made
    c) make

12. You _____ (drive) to school yesterday. a) drove
    b) drived
    c) drive

13. She _____ (not like) the movie we watched. a) didn’t like
    b) not liked
    c) don’t like

14. We _____ (swim) in the lake last summer. a) swum
    b) swimmed
    c) swam

15. He _____ (tell) a funny story last night. a) telled
    b) told
    c) tells

16. I _____ (write) a letter to my friend. a) writed
    b) write
    c) wrote

17. They _____ (sing) their favorite song at the concert. a) sang
    b) singed
    c) sung

18. What is the past simple form of "fly"? a) flied
    b) flew
    c) flyed

19. The cat _____ (chase) the mouse yesterday. a) chased
    b) chaced
    c) chases

20. We _____ (see) our grandparents last weekend. a) seen
    b) saw
    c) see

21. She _____ (find) her keys under the couch. a) finded
    b) found
    c) finds

Ответы:

1. b) went
2. c) played
3. b) didn’t finish
4. a) was
5. b) saw
6. a) didn't visit
7. a) had
8. a) didn’t eat
9. c) went
10. b) read
11. b) made
12. a) drove
13. a) didn’t like
14. c) swam
15. b) told
16. c) wrote
17. a) sang
18. b) flew
19. a) chased
20. b) saw
21. b) found

Надеюсь, тест будет полезен для подготовки учеников!