Free Printable Set 1: Clash of KMSw Mathematicians

1.

Insert your full name here

(a)

2.

Find $\lim_{x\rightarrow7}\ \frac{x^2-49}{x-7}$

a)

0

b)

7

c)

14

d)

1

3.

Find $\lim_{x\rightarrow3}\frac{x-3}{\sqrt{x+6\ }-3}$

a)

0

b)

6

c)

-6

d)

3

4.

The correct reason for f(x) is discontinuous at x=3 is...

a)

$f\left(3\right)\ne\lim_{x\rightarrow3}\ f\left(x\right)$

b)

$\lim_{x\rightarrow3}\ f\left(x\right)\$ does not exist.

c)

$f\left(3\right)\$ is undefined

d)

None of the above

5.

Determine $\lim_{x\rightarrow\infty}\ \frac{\sqrt{x^2+3}}{2x-4}$

a)

1/4

b)

-1/4

c)

1/2

d)

-1/2

6.

The derivatives of $\tan\left(3\pi+2x\right)\$ is...

a)

$\sec^2\left(3\pi+2x\right)$

b)

$3\sec^2\left(3\pi+2x\right)$

c)

$2\sec^2\left(3\pi+2x\right)$

d)

$6\sec^2\left(3\pi+2x\right)$

7.

Which of the following is true for the FIRST PRINCIPLE of derivatives of $f\left(x\right)=\sqrt{8x-3\ }$ ?

a)

$f'\left(x\right)=\lim_{h\rightarrow0}\ \frac{\sqrt{8x-3\ }\ -\ \sqrt{8h-3\ }}{h}$

b)

$f'\left(x\right)=\lim_{h\rightarrow0}\ \frac{\sqrt{8\left(x+h\right)-3}+\sqrt{8x-3}}{h}$

c)

$f'\left(x\right)=\lim_{h\rightarrow0}\ \frac{\sqrt{8\left(x+h\right)-3}-\sqrt{8x-3}}{h}$

d)

$f'\left(x\right)=\lim_{h\rightarrow0}\ \frac{\sqrt{8h-3}-\sqrt{8x-3}}{h}$

8.

Differentiate $g\left(x\right)=\frac{x}{1-e^{2x}}$

a)

$g'\left(x\right)=\ \frac{1}{1-2e^{2x}}$

b)

$g'\left(x\right)=\ \frac{1-e^{2x}+2xe^{2x}}{\left(1-e^{2x}\right)^2}$

c)

$g'\left(x\right)=\ \frac{1+e^{2x}+2xe^{2x}}{\left(1-e^{2x}\right)^2}$

d)

$g'\left(x\right)=\ \frac{x}{\left(1-2e^{2x}\right)^2}$

9.

The interval in which function $f\left(x\right)=x^2-4x+5$ decreases is...

a)

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

b)

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

c)

$\left(3,\ +\infty\right)$

d)

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

10.

Let z be a complex number such that |z|= 4 and $\arg(z)=\frac{5}{6}\pi$ . Then z = ...

a)

$2\sqrt{3}+2i$

b)

$-2\sqrt{3}+2i$

c)

$2\sqrt{3}-2i$

d)

$-\sqrt{3}+i$

11.

What is the gradient of curve $f\left(x\right)=x^3-9x^2-120x+6$ at (0,0)?

a)

6

b)

-6

c)

120

d)

-120

12.

Solve the equation $2\left(2^{2x}\right)=3\left(2^x\right)-1$

a)

x=0 or x=1

b)

x=1/2 or x=1

c)

x=-1 or x=2

d)

x=-1 or x=0

13.

Given a function $g\left(x\right)=\ \frac{5}{x+4}$ . Choose which of the following statement(s) is/are true about this function.

a)

$g\left(x\right)$ is a one-to-one function

b)

$g^{-1}\left(x\right)$ does not exist

c)

The domain is $D_g=\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

The range of its inverse is $R_{g^{-1}}=\left(-\infty,0\right)\cup\left(0,\infty\right)$

14.

The derivative of $\ln y\ =\ x\ln x$ is...

a)

$\frac{\text{d}y}{\text{d}x}=y\left(1+\ln x\right)$

b)

$\frac{\text{d}y}{\text{d}x}=\ y\frac{1}{x}$

c)

$\frac{\text{d}y}{\text{d}x}=\frac{y}{x}+\ln x$

d)

$\frac{\text{d}y}{\text{d}x}=x^2\left(1-\ln x\right)$

Set 1: Clash of KMSw Mathematicians

Total questions: 14

Worksheet time: 40mins

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