Free Printable Unit 5 Review: Quadratics (Complex Solutions)

1.

Simplify $i^{523}$

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

2.

What is $i^2$ equivalent to?

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

3.

Simplify $\sqrt{-25}$ .

a)

$5$

b)

$-5$

c)

$5i$

d)

$-5i$

4.

Simplify $\left(20-3i\right)-\left(14-2i\right)$ .

a)

$7-i$

b)

$7+i$

c)

$-7+i$

d)

$274-82i$

5.

$\left(3+5i\right)\left(8-i\right)$

Simplify

a)

$29+37i$

b)

$19+37i$

c)

$24+32i$

d)

$11+4i$

6.

Solve $x^2+40=0$

a)

$\left\{\pm2i\sqrt{10}\right\}$

b)

$\left\{\pm i\sqrt{20}\right\}$

c)

$\left\{\pm2i\sqrt{5}\right\}$

d)

$\left\{\pm i\sqrt{40}\right\}$

7.

Solve $-4x^2=36$

a)

$\left\{\pm3i\right\}$

b)

$\left\{\pm9i\right\}$

c)

$\left\{-3,3\right\}$

d)

$\left\{-9,9\right\}$

8.

Is this the correct quadratic formula? $x=\frac{-b\pm\sqrt{b-4ac}}{2}$

a)

Yes - it is correct

b)

No - there is an error

9.

Solve $7x^2-8x+1=0$

a)

$\left\{1,\frac{1}{7}\right\}$

b)

$\left\{-1,7\right\}$

c)

$\left\{-1,-\frac{1}{7}\right\}$

d)

$\left\{7,-8\right\}$

10.

What is the discriminant of $4x^2+8x+6=0$ AND what type of solutions does it have?

a)

-32; 2 complex roots

b)

32; 2 irrational roots

c)

160; 2 irrational roots

d)

16; 2 rational roots

11.

$5x^2=10x-5$

What is the discriminant of the equation AND what type of solutions does it have?

a)

0; 1 rational root

b)

0; 2 irrational roots

c)

200; 2 irrational roots

d)

200; 2 complex roots

12.

What is the absolute extreme of the function $f\left(x\right)=-\left(x+1\right)^2+5$ ?

a)

5 at x = 1; absolute minimum

b)

5 at x = -1, absolue maximum

c)

5 at x = 1; absolute maximum

d)

-5 at x = 1; absolute minimum

13.

Which equation has $-2i$ as a solution?

a)

$f\left(x\right)=x^2+4$

b)

$f\left(x\right)=x^2-4$

c)

$f\left(x\right)=\pm2ix$

d)

$f\left(x\right)=x^2+2i$

14.

If $4+3i$ is a root of a quadratic function, what has to be another root?

a)

$4-3i$

b)

$-4+3i$

c)

$-4-3i$

d)

not enough information is given

15.

Write a quadratic function with real coefficients that has $4-3i$ as a root.

a)

$f\left(x\right)=x^2-8x-9$

b)

$f\left(x\right)=x^2-9i^2+16$

c)

$f\left(x\right)=x^2-8x+9$

d)

$f\left(x\right)=x^2-16x+3$

16.

If a model rocket is launched with a trajectory described by $h\left(t\right)=-16t^2+80x$ , what will be the maximum height it reaches?

a)

80 feet

b)

100 feet

c)

1280 feet

d)

cannot be determined

17.

If a bird is flying 200 feet above ground and drops a stick, how long will it take for the stick to fall to the ground?

a)

12.5 seconds

b)

7.072 seconds

c)

3.536 seconds

Unit 5 Review: Quadratics (Complex Solutions)

Total questions: 17

Worksheet time: 9mins

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