QUIZ CHAPTER 1

Given a set of number $S=\left\{-12,-\frac{5}{8},\ 0,\ e^0,\ 2,\ \frac{1}{3},\ \sqrt{4},\ \sqrt{6}\right\}$ , which is irrational number? 

•  $\sqrt{4}$  

•  $\sqrt{6}$   

•  $\frac{1}{3}$  

•  $e^0$  

Simplify $\frac{\sqrt{x}+\sqrt{4}}{\sqrt{x}}$ . Which one is the correct answer? 

•  $\sqrt{4}$  

•  $1+\frac{4}{\sqrt{x}}$  

•  $1+\frac{4\sqrt{x}}{x}$  

•  $2$  

Sets  $A,B\ and\ C$ are given as  $A=\left(-5,5\right),\ B=\left[-2,10\right)$  and  $C=\left\{-3<x\le8,x\in Z\right\}$ . 

Find  $\left(A\cup C\right)\cap B$  

•  $\left(-2,10\right)$  

•  $\left(-5,10\right)$  

•  $\left[-2,8\right]$  

•  $\left(-5,8\right]$  

Simplify $\frac{\log_624+\log_615-\log_660}{\frac{1}{2}\log_69+\log_612}$  

• 2

•  $\frac{1}{2}$  

•  $\frac{\sqrt{2}}{2}$  

• -2

 $\sqrt{x^3y\sqrt{xy^2}}$  

Simplify

•  $x^{\frac{7}{4}}y$  

•  $x^{\frac{7}{2}}y^2$  

•  $\sqrt{x^{\frac{7}{4}}y^2}$  

•  $\sqrt{x^{\frac{7}{2}}y}$  

What is the conjugate of $\frac{\sqrt{3}+\sqrt{2}i}{\sqrt{5}-4i}$  

•  $4i-\sqrt{5}$  

•  $\sqrt{3}-\sqrt{2}i$  

•  $\sqrt{5}+4i$  

•  $\sqrt{2}i-\sqrt{3}$  

Given  $z=\frac{3-i}{i+6}$  , simplify  $z+\frac{1}{3i}$   in the form of  $x+yi$  

•  $\frac{51-64i}{111}$  

•  $\frac{17}{37}-\frac{9}{37}i$  

•  $\frac{17-9i}{37}$  

•  $\frac{17}{37}-\frac{64}{111}i$  

Given that $z=2-i$ , find  $\left|z-\frac{1}{z}\right|$   

•  $\sqrt{2}$  

• -2

• 2

•  $\frac{1}{2}$  

Express $z=\frac{\sqrt{3}-i}{i+\sqrt{3}}$ in polar form 

•  $z=2\left(\cos\left(\frac{\pi}{3}\right)+i\sin\left(\frac{\pi}{3}\right)\right)$  

•  $z=\cos\left(-\frac{\pi}{3}\right)+i\sin\left(-\frac{\pi}{3}\right)$  

•  $z=2\left(\cos\left(\frac{\pi}{6}\right)+i\sin\left(\frac{\pi}{6}\right)\right)$  

•  $z=2\left(\cos\left(-\frac{\pi}{6}\right)+\sin\left(-\frac{\pi}{6}\right)\right)$  

How was your Mathematics lesson so far? You can understand well all lessons?