Free Printable Kiểm tra 15 phút toán 12

1.

Với a, b là các số thực dương, $\alpha,\ \beta$ là các số thực tùy ý. Khẳng định nào sau đây đúng ?

a)

$a^{\alpha}.a^{\beta}=a^{\alpha\beta}$

b)

$a^{\alpha}.a^{\beta}=a^{\alpha-\beta}$

c)

$a^{\alpha}.a^{\beta}=\left(a^{\alpha}\right)^{\beta}$

d)

$a^{\alpha}.a^{\beta}=a^{\alpha+\beta}$

2.

Cho a, b là các số thực dương khác 1, $\alpha$ là số thực tùy ý. Khẳng định nào sau đây sai ?

a)

$\log_ab=\frac{1}{\log_ba}$

b)

$\log_a\left(\frac{a}{b}\right)=-\log_ba$

c)

$\log_ab=\frac{\log_3b}{\log_3a}$

d)

$\log_b\sqrt[]{a}=\frac{1}{2}\log_ba$

3.

Cho a là số thực dương. Biểu thức $a^{\frac{1}{3}}.\sqrt[5]{a^3}$ bằng:

a)

$\frac{14}{15}$

b)

$\sqrt[14]{a^{15}}$

c)

$\sqrt[15]{a^{14}}$

d)

$a^{\frac{15}{14}}$

4.

Số nghiệm của phương trình $25^x-5^{x+1}+6=0$ là:

a)

0

b)

1

c)

2

d)

3

5.

Số nghiệm của phương trình $\log_3\left(x^2-3x-1\right)=1$ là:

a)

0

b)

1

c)

2

d)

3

6.

Với a, b là các số thực dương. Biểu thức $\log_ab^3-\log_a\sqrt[]{b}+\log_{a^3}b$ bằng:

a)

17logb

b)

$6\log_ab$

c)

$\frac{17}{6}\log_ab$

d)

$\frac{17}{6}\log_ba$

7.

Cho a và b là các số thực dương khác 1, $\alpha$ là số thực tùy ý. Khẳng định nào sau đây sai ?

a)

$\log_aa=0$

b)

$\log_aa=1$

c)

$a^{\log_ab}=b$

d)

$\log_ab^{\alpha}=\frac{1}{\alpha}\log_ab$

8.

khẳng định nào sau đây đúng ?

a)

$\sqrt[]{5}^{2019}<\sqrt[]{5}^{2018}$

b)

$\left(\frac{1}{6}\right)^{2020}>\left(\frac{1}{6}\right)^{2021}$

c)

$\left(2-\sqrt[]{7}\right)^{2021}>\left(2-\sqrt[]{7}\right)^2$

d)

$\left(\sqrt[]{5}-2\right)^{2003}>\left(\sqrt[]{5}-2\right)^{2004}$

9.

Cho a là số thực dương khác 1, thì $\log_ax\ >\ \log_ay$ khi:

a)

x > y

b)

x > y > 0

c)

x < y

d)

0 < x < y

10.

Tập xác định của hàm số $y=x^{\pi+1}$ là:

a)

$\left(0;+\infty\right)$

b)

$\left(-\infty;+\infty\right)$

c)

$R\ \backslash\left\{0\right\}$

d)

$\left(-\infty;0\right)$

11.

Tập xác định của hàm số $y=\left(x-2\right)^{-5}$ là:

a)

$\left(2;+\infty\right)$

b)

$\left(-\infty;+\infty\right)$

c)

$R\ \backslash\left\{2\right\}$

d)

$\left(-\infty;2\right)$

12.

Tập xác định của hàm số $y=\left(x^2-2x-3\right)^{\frac{1}{2}}$ là:

a)

$\left(-1;3\right)$

b)

$\left(-\infty;+\infty\right)$

c)

$R\ \backslash\left\{-1;3\right\}$

d)

$\left(-\infty;-1\right)\cup\left(3;+\infty\right)$

13.

Tập xác định của hàm số $y=\log_2\left(x+1\right)$ là:

a)

$\left(-\infty;-1\right)$

b)

R

c)

$R\ \backslash\left\{-1\right\}$

d)

$\left(-1;+\infty\right)$

14.

Tập xác định của hàm số $y=\ln\left(2-x-x^2\right)$ là:

a)

$\left(-2;1\right)$

b)

R

c)

$R\ \backslash\left\{-2;1\right\}$

d)

$\left(-\infty;-2\right)\cup\left(1;+\infty\right)$

15.

Đặt $t=\log_{ }x$ thì phương trình $\log_{ }^2x-5\log_{ }x+4=0$ trở thành phương trình nào sau đây :

a)

$t^2-5t-4=0$

b)

$t^2-5t+4=0$

c)

$t^2-5t+4=0,\ t>0$

d)

$t^2-5t-4=0,\ t>\ 0$

16.

Hàm số $y=5^x$ có đạo hàm bằng:

a)

$y'=5^{x-1}$

b)

$y'=5^x$

c)

$y'=5^x\ln5$

d)

$y'=\frac{5^x}{\ln5}$

17.

Hàm số $y=\log_2x$ có đạo hàm bằng:

a)

$y'=x\ln2$

b)

$y'=\frac{1}{x\ln2}$

c)

$y'=\frac{x}{\ln2}$

d)

$y'=\frac{1}{2\ln x}$

18.

Hàm số $y=3^{2x+1}$ có đạo hàm bằng:

a)

$y'=2\ln3^{2x}$

b)

$y'=3^{2x}$

c)

$y'=2.3^{2x+1}.\ln3$

d)

$y'=2.3^{2x}.\ln3$

19.

Hàm số nào sau đây nghịch biến trên tập xác định của nó ?

a)

$y=\log_5x$

b)

$y=\log_{\frac{\pi}{2}}x$

c)

$y=\left(\frac{\sqrt[]{5}}{4}\right)^x$

d)

$y=\left(\frac{3}{2}\right)^x$

20.

Với a, b là các số thực dương, $\alpha,\ \beta$ là số thực tùy ý. Khẳng định nào sau đây sai ?

a)

$a^{\alpha}.b^{\alpha}=\left(a.b\right)^{\alpha}$

b)

$\frac{a^{\alpha}}{a^{\beta}}=a^{\alpha-\beta}$

c)

$a^{\alpha\beta}=\left(a^{\beta}\right)^{\alpha}$

d)

$\frac{a^{\alpha}}{b^{\beta}}=\left(\frac{a}{b}\right)^{\alpha-\beta}$

Kiểm tra 15 phút toán 12

Total questions: 20

Worksheet time: 10mins

Similar Resources on Wayground