Free Printable math review (part 3)

1.

Simplify $\left(3-i\right)\left(2i+1\right)-3i$

a)

$7+i$

b)

$5+2i$

c)

$5+5i$

d)

$1+7i$

2.

if $\overrightarrow{u}=<5,-3>,\ \overrightarrow{v}=<2,6>$ , find the value of $3\overrightarrow{v}+2\overrightarrow{u}$

a)

<16,12>

b)

<19,3>

c)

<12,16>

d)

<3,19>

3.

if $u=\left(3,-4\right),\ v=\left(-2,1\right)$ , and $w=<-2,4>$ , find $\overrightarrow{uv}-2\overrightarrow{w}$

a)

$<-1,-3>$

b)

$<-3,1>$

c)

$<9,-13>$

d)

$<-13,9>$

4.

Given that $\frac{i-3}{z\left(2i+1\right)}=3i$ , find the value of $30z$

a)

$\frac{7}{15}+\frac{i}{15}$

b)

$7+i$

c)

$14+i$

d)

$14+2i$

5.

Given that $z_1=-5-3i,\ z_2=6-i$ , find the value of $z_1-z_2$
(Write in the form $<a,b>$ or $\left(a,b\right)$ )

(a)

6.

Given that $z_1=6+2i,\ z_2=-4+5i$ , find the value of $z_2+z_1$

(Write in the form

<a,b>

or

\left(a,b\right)

)

(a)

7.

Find the modulus and argument of $z$ when $z=-3i+4$

a)

$\left|z\right|=5,\ \arg\left(z\right)=-36.87\degree$

b)

$\left|z\right|=5,\ \arg\left(z\right)=-53.13\degree$

c)

$\left|z\right|=5,\ \arg\left(z\right)=36.87\degree$

d)

$\left|z\right|=5,\ \arg\left(z\right)=53.13\degree$

8.

express $-6-2\sqrt{3}i$ in the form $z=r\left(\cos\theta-i\sin\theta\right)$ where $-\pi<\theta<\pi$

a)

$z=4\sqrt{3}\left(\cos\left(\frac{5\pi}{6}\right)+i\sin\left(\frac{5\pi}{6}\right)\right)$

b)

$z=4\sqrt{3}\left(\cos\left(\frac{7\pi}{6}\right)+i\sin\left(\frac{7\pi}{6}\right)\right)$

c)

$z=4\sqrt{3}\left(\cos\left(-\frac{7\pi}{6}\right)+i\sin\left(-\frac{7\pi}{6}\right)\right)$

d)

$z=4\sqrt{3}\left(\cos\left(-\frac{5\pi}{6}\right)+i\sin\left(-\frac{5\pi}{6}\right)\right)$

9.

express $5\sqrt{2}\left(\cos\left(-\frac{\pi}{4}\right)+i\sin\left(-\frac{\pi}{4}\right)\right)$
in the form $z=a+bi$ where $a,b\in R$ $\left(\sqrt{2}=1.414,\ \sqrt{3}=1.732\right)$

(a)

10.

The complex number $z$ is such that $\left|z\right|=4$ and $\arg\left(z\right)=-\frac{5\pi}{6}$ , find $z$ in the form $z=a+bi$ , where $a,b\in R$

a)

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

b)

$2-2\sqrt{3}i$

c)

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

d)

$2+2\sqrt{3}i$

11.

Solve the equation:
$3x^2+6x+30=-3$

a)

$-1+i\sqrt{10}$

b)

$-1-i\sqrt{10}$

c)

$1-i\sqrt{10}$

d)

$1+i\sqrt{10}$

12.

Given that $z=4-3i$ is one of the root of the equation $2z^2-bz+c=0$ , where a,b, and c are real constant, find the value of a,b, and c

a)

$b=-8,\ c=25$

b)

$b=16,\ c=50$

c)

$b=-16,\ c=50$

d)

$b=8,\ c=25$

13.

Given the function

$f\left(x\right)=2x^3+15x^2+Qx-18$ , if $f\left(\frac{1}{2}\right)=0$ , solve for x when $f\left(x\right)=0$

a)

$-4\pm i\sqrt{2}$

b)

$-\frac{1}{2}$

c)

$\frac{1}{2}$

d)

$4\pm i\sqrt{2}$

e)

no answer is correct

14.

Given the equation

x^3-3x^2+12x-10=0

,
Solve for x

a)

$1\pm3i$

b)

$-1\pm3i$

c)

$-1\pm\sqrt{3}i$

d)

$1$

e)

$-1$

15.

Given the function $f\left(x\right)=x^3+ax^2+ax+b$ , if $f\left(2\right)=0$ and $b=-8a$ ,

solve for x when

f\left(x\right)=0

and

x\in C

(C is complex number)

a)

$-3\pm i\sqrt{7}$

b)

$3\pm i\sqrt{7}$

c)

2

d)

$3\pm7i$

e)

no answer is correct

16.

Please rate the test difficulty

4 lines

math review (part 3)

Total questions: 16

Worksheet time: 1hrs 29mins

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