Приложение 2 разноуровневые задания

Арабская наука равновесия

Базовый уровень

1)         Упростите выражения, объединяя подобные члены:

a) 6a + 2b + b – 4a =                                     b) 6c + a + b – 2c + a =

c) c + 5b + 7a – 2b – 2a =                             d) 6a + 3b – 2a – 3b =

e) 7m + n – 2m – 4m + 3n =                         f) 3a + b + 2a + c – b =

2)         Если a = 5, b = 1 и c = 10, то вычислите следующее:

a) a + b + c =                          b) 2c – a =                              c) 2c + b =

d) c – 2b + a =                        e) 2ab – 1 =                           f) 3bc – 20 =

g) 9c – 16a =                          h) abc =                                  i) 7b + ac =

3)         Решите следующие уравнения:

a) x + 2 = 6                             b) x – 30 = 20                         c) x + 12 = 32

d) 14 – x = 11                         e) 3x = 21                               f) 7q = 49

Средний уровень

1)         Упростите выражения, объединяя подобные члены:

a) xy + 3cd + 3xy – cd                                   b) 3x² + 4x³ – 2x²

c) 4x + 2y + 3y² – y                                       d) 9cd² + 4cd² – 5cd²

e) 5a + 4a⁵ + 3a² – 4a                                   f) 4x² + 2x – 2 + 3x – 2x²

2)         Если e = 9 и f = 3, то вычислите следующее:

a) 47 – ef =                                        b)  =                              c) e +  =

d) e(e – f) =                                        e) 3ef =                                   f) 3e + 3f =

3)         Решите следующие уравнения:

a) 4x + 5 = 21                                     b) 2x + 7 = 9               c) 5x + 8 = 13

            d) 2(x – 2) = 2                                    e) 4(2x + 5) = 76                    f) 3(3x + 1) = 57

Углубленный уровень

1)         Упростите выражения, объединяя подобные члены:

a) 2t² + 3 + 5t³ – t² + 2                                   b) 6a³ + 5a² – a⁴ – 2a²  

c) 6x² + 4x – 3 + 5x – 2x²                              d) 2 + k x k

e) 2 x k + k                                                     f) 2 x k x k

2)         a) Найдите выражение для периметра этого равнобедренного треугольника.

b) Найдите значение периметра, если а = 8, b = 2.

3)         Решите следующие уравнения:

a) 3y – 2 = 13                         b) m + 4 = 7                                    c) 25 – 3x = 1

d) 4n + 7 – n + 2 = 30            e) 7 = 17 – x                                   f) 2y = 56 – 6y

g) 3m – 2 = m + 8                  h) 14 – x = 2x + 2

Ответы

Базовый уровень

1)         a) 2a + 3b                   b) 2a + b + 4c            c) 5a + 3b + c             d) 4a

e) m + 4n                    f) 5a + c

2)         a) 16                           b) 15                           c) 21                           d) 13

e) 9                              f) 10                           g) 10               h) 50   

 (i) 57

3)         a) x = 4                       b) x = 50                     c) x = 20                      d) x = 3

e) x = 7                       f) q = 7

Средний уровень

1)         a) 4xy +2cd                 b) x² + 4x³                         c) 4x + y + 3y²                d) 8cd²

e) a + 3a² + 4a⁵              f) 2x² + 5x -2

2)         a) 20                            b) 2                             c) 12                            d) 54

e) 81                           f) 36

3)         a) x = 4                      b) x = 1                       c) x = 1                                   d) x = 3

e) x = 7                       f) x = 6

Углубленный уровень

1)         a) 5t³ + t² + 5              b) 6a³ – a⁴ + 3a²            c) 4x² + 9x – 3            d) 2 + k²

e) 3k                           f) 2k²

2)         a) Периметр = 10a + b                                b) Периметр = 82

3)         a) y = 5                      b) m = 6                      c) x = 8                        d) n = 7

e) x = 50                     f) y = 7                        g) m = 5                      h) x = 4