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Матем

Total questions: 25

Worksheet time: 13mins

Name
Class
Date
1.

a2−b2a^2-b^2

a)

a2−2ab+b2a^2-2ab+b^2

b)

a2+2ab+b2a^2+2ab+b^2

c)

(a−b)2\left(a-b\right)^2

d)

(a−b)(a+b)\left(a-b\right)\left(a+b\right)

e)

a2−ab+b2a^2-ab+b^2

2.

(a−b)2\left(a-b\right)^2

a)

a2−2ab+b2a^2-2ab+b^2

b)

a2+2ab+b2a^2+2ab+b^2

c)

a2−ab+b2a^2-ab+b^2

d)

(a−b)(a+b)\left(a-b\right)\left(a+b\right)

e)

a2+ab+b2a^2+ab+b^2

3.

(a+b)2\left(a+b\right)^2

a)

a2−2ab+b2a^2-2ab+b^2

b)

a2+2ab+b2a^2+2ab+b^2

c)

a2−ab+b2a^2-ab+b^2

d)

(a−b)(a+b)\left(a-b\right)\left(a+b\right)

e)

a2+ab+b2a^2+ab+b^2

4.

(a+b)3\left(a+b\right)^3

a)

a3+3a2b+3ab2+b3a^3+3a^2b+3ab^2+b^3

b)

a3−3a2b+3ab2+b3a^3-3a^2b+3ab^2+b^3

c)

(a−b)(a2+ab+b2)\left(a-b\right)\left(a^2+ab+b^2\right)

d)

(a+b)(a2−ab+b2)\left(a+b\right)\left(a^2-ab+b^2\right)

e)

(a−b)3\left(a-b\right)^3

5.

(a−b)3\left(a-b\right)^3

a)

a3+3a2b+3ab2+b3a^3+3a^2b+3ab^2+b^3

b)

a3−3a2b+3ab2+b3a^3-3a^2b+3ab^2+b^3

c)

(a−b)(a2+ab+b2)\left(a-b\right)\left(a^2+ab+b^2\right)

d)

(a+b)(a2−ab+b2)\left(a+b\right)\left(a^2-ab+b^2\right)

e)

(a−b)3\left(a-b\right)^3

6.

a3−b3a^3-b^3

a)

a3+3a2b+3ab2+b3a^3+3a^2b+3ab^2+b^3

b)

a3−3a2b+3ab2+b3a^3-3a^2b+3ab^2+b^3

c)

(a−b)(a2+ab+b2)\left(a-b\right)\left(a^2+ab+b^2\right)

d)

(a+b)(a2−ab+b2)\left(a+b\right)\left(a^2-ab+b^2\right)

e)

(a−b)3\left(a-b\right)^3

7.

a3+b3a^3+b^3

a)

a3+3a2b+3ab2+b3a^3+3a^2b+3ab^2+b^3

b)

a3−3a2b+3ab2+b3a^3-3a^2b+3ab^2+b^3

c)

(a−b)(a2+ab+b2)\left(a-b\right)\left(a^2+ab+b^2\right)

d)

(a+b)(a2−ab+b2)\left(a+b\right)\left(a^2-ab+b^2\right)

e)

(a−b)3\left(a-b\right)^3

8.

sin⁡2x+cos⁡2x\sin^2x+\cos^2x

a)

1

b)

0

c)

sinx

d)

cosx

e)

-1

9.

tgx

a)

sin⁡xcos⁡x\frac{\sin x}{\cos x}

b)

cos⁡xsin⁡x\frac{\cos x}{\sin x}

c)

2sin⁡xcos⁡x2\sin x\cos x

d)

cos⁡2x−sin⁡2x\cos^2x-\sin^2x

e)

sin⁡2x+cos⁡2x\sin^2x+\cos^2x

10.

ctgx

a)

sin⁡xcos⁡x\frac{\sin x}{\cos x}

b)

cos⁡xsin⁡x\frac{\cos x}{\sin x}

c)

2sin⁡xcos⁡x2\sin x\cos x

d)

cos⁡2x−sin⁡2x\cos^2x-\sin^2x

e)

sin⁡2x+cos⁡2x\sin^2x+\cos^2x

11.

sin⁡2x\sin2x

a)

2sin⁡xcos⁡x2\sin x\cos x

b)

cos⁡2x−sin⁡2x\cos^2x-\sin^2x

c)

2cos⁡2x−12\cos^2x-1

d)

1−2sin⁡2x1-2\sin^2x

e)

1−cos⁡2x2\frac{1-\cos2x}{2}

12.

cos⁡2x\cos2x

a)

2sin⁡xcos⁡x2\sin x\cos x

b)

cos⁡2x−sin⁡2x\cos^2x-\sin^2x

c)

1−sin⁡2x1-\sin^2x

d)

1+cos⁡2x2\frac{1+\cos2x}{2}

e)

1−cos⁡2x2\frac{1-\cos2x}{2}

13.

cos⁡2x\cos2x

a)

2sin⁡xcos⁡x2\sin x\cos x

b)

2cos⁡2x−12\cos^2x-1

c)

1−sin⁡2x1-\sin^2x

d)

1+cos⁡2x2\frac{1+\cos2x}{2}

e)

1−cos⁡2x2\frac{1-\cos2x}{2}

14.

cos⁡2x\cos2x

a)

2sin⁡xcos⁡x2\sin x\cos x

b)

1−2sin⁡2x1-2\sin^2x

c)

1−sin⁡2x1-\sin^2x

d)

1+cos⁡2x2\frac{1+\cos2x}{2}

e)

1−cos⁡2x2\frac{1-\cos2x}{2}

15.

cos⁡2x\cos^2x

a)

2sin⁡xcos⁡x2\sin x\cos x

b)

1−2sin⁡2x1-2\sin^2x

c)

1−sin⁡2x1-\sin^2x

d)

1+cos⁡2x2\frac{1+\cos2x}{2}

e)

1−cos⁡2x2\frac{1-\cos2x}{2}

16.

sin⁡2x\sin^2x

a)

2sin⁡xcos⁡x2\sin x\cos x

b)

1−2sin⁡2x1-2\sin^2x

c)

1−sin⁡2x1-\sin^2x

d)

1+cos⁡2x2\frac{1+\cos2x}{2}

e)

1−cos⁡2x2\frac{1-\cos2x}{2}

17.

Вектордың ұзындығы

a)

∣x→∣⋅∣y→∣⋅cos⁡α\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|\cdot\cos\alpha

b)

∣x→∣⋅∣y→∣⋅sin⁡α\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|\cdot\sin\alpha

c)

(x2−x1)2+(y2−y1)2+(z2−z1)2\sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}

d)

x→⋅y→∣x→∣⋅∣y→∣\frac{\overrightarrow{x}\cdot\overrightarrow{y}}{\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|}

e)

(x1−x2)2+(y1−y2)2+(z1−z2)2\sqrt[]{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2+\left(z_1-z_2\right)^2}

18.

Скаляр көбейтіндісі

a)

∣x→∣⋅∣y→∣⋅cos⁡α\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|\cdot\cos\alpha

b)

∣x→∣⋅∣y→∣⋅sin⁡α\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|\cdot\sin\alpha

c)

(x2−x1)2+(y2−y1)2+(z2−z1)2\sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}

d)

x→⋅y→∣x→∣⋅∣y→∣\frac{\overrightarrow{x}\cdot\overrightarrow{y}}{\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|}

e)

(x1−x2)2+(y1−y2)2+(z1−z2)2\sqrt[]{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2+\left(z_1-z_2\right)^2}

19.

Скаляр көбейтіндісі

a)

x1⋅x2+y1⋅y2+z1⋅z2x_1\cdot x_2+y_1\cdot y_2+z_1\cdot z_2

b)

∣x→∣⋅∣y→∣⋅sin⁡α\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|\cdot\sin\alpha

c)

(x2−x1)2+(y2−y1)2+(z2−z1)2\sqrt[]{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}

d)

x→⋅y→∣x→∣⋅∣y→∣\frac{\overrightarrow{x}\cdot\overrightarrow{y}}{\left|\overrightarrow{x}\right|\cdot\left|\overrightarrow{y}\right|}

e)

(x1−x2)2+(y1−y2)2+(z1−z2)2\sqrt[]{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2+\left(z_1-z_2\right)^2}

20.

Жанаманың теңдеуі

a)

y=f′(x)⋅(x−x0)+f′(x0)y=f'\left(x\right)\cdot\left(x-x_0\right)+f'\left(x_0\right)

b)

y=x2y=x^2

c)

y=f(x)(x−x0)+f(x0)y=f\left(x\right)\left(x-x_0\right)+f\left(x_0\right)

d)

y=f′(x)⋅(x−x0)−f′(x0)y=f'\left(x\right)\cdot\left(x-x_0\right)-f'\left(x_0\right)

e)

y=f(x)(x−x0)−f(x0)y=f\left(x\right)\left(x-x_0\right)-f\left(x_0\right)

21.

Төртбұрыштың ауданы

a)

a⋅b⋅sin⁡αa\cdot b\cdot\sin\alpha

b)

12⋅a⋅b\frac{1}{2}\cdot a\cdot b

c)

12⋅a⋅h\frac{1}{2}\cdot a\cdot h

d)

π⋅r2\pi\cdot r^2

e)

4⋅a4\cdot a

22.

Үшбұрыштың ауданы

a)

a⋅b⋅sin⁡αa\cdot b\cdot\sin\alpha

b)

12⋅a⋅b\frac{1}{2}\cdot a\cdot b

c)

12⋅a⋅h\frac{1}{2}\cdot a\cdot h

d)

π⋅r2\pi\cdot r^2

e)

4⋅a4\cdot a

23.

Трапецияның ауданы

a)

a⋅b⋅sin⁡αa\cdot b\cdot\sin\alpha

b)

12⋅a⋅b\frac{1}{2}\cdot a\cdot b

c)

12⋅a⋅h\frac{1}{2}\cdot a\cdot h

d)

a+b2⋅h\frac{a+b}{2}\cdot h

e)

4⋅a4\cdot a

24.

Үшбұрыштың ауданы

a)

a⋅b⋅sin⁡αa\cdot b\cdot\sin\alpha

b)

12⋅a⋅b⋅sin⁡α\frac{1}{2}\cdot a\cdot b\cdot\sin\alpha

c)

a⋅ha\cdot h

d)

π⋅r2\pi\cdot r^2

e)

4⋅a4\cdot a

25.

Шеңбердің ауданы

a)

a⋅b⋅sin⁡αa\cdot b\cdot\sin\alpha

b)

12⋅a⋅b⋅sin⁡α\frac{1}{2}\cdot a\cdot b\cdot\sin\alpha

c)

a⋅ha\cdot h

d)

π⋅r2\pi\cdot r^2

e)

4⋅a4\cdot a