Algebra II

irrational numbers

100

Which is irrational?

square root of 1, square root of 4, or square root of 3?

square root of 3

200

Solve

(sqaure root of 3)(sqaure root of 3)

3

300

simplify

1 over [2(square root of 3)]

square root of 3 over 6

400

Multiply

(1 over square root of 3)(square root of 2 over square root of 5)

square root of 30 over 30

500

square root of 3 times square root of 5 over square root of 10

2(square root of 30)

perfect quadratics

100

Is this a perfect quadratic?

x²+2x+1

Yes

200

Is this a perfect quadratic?

x²-9

No

300

Is this a perfect square?

x²+9

What are its factors?

No

(x+3i)(x-3i)

400

Turn it into a perfect square

x+2x+3=0

x²+2x+1=-2

500

Turn into perfect quadratic and solve

x²+6x-20=0

{-3+ square root of 29, -3- square root of 29}

imaginary numbers

100

i³

-i

200

i⁴⁰⁰

1

300

simplify

2i over 4i²

-i over 2

400

Solve

(2i over i)(3i over 5)

6i over 5

500

Factor and solve

x³+25x=0

{0, -5i, 5i}

Simplifying, Multiplying, and Dividing

100

Simplify and exclude values

x-10 over 10x²-100x

1 over 10x  ; {0, 10}

200

Simplify and exclude values

10a+8 over 3a

2(5a+4) over 3a  ; {0}

300

Simplify and eclude values

49a²+63 over 14a²+28a

7a+9 over 2a+4  ; {0, -2}

400

Simplify the expression

1 over 3x-9 divided x+6 over 12x-36

4 over x+6

500

Simplify the expression

(3v+5 over v²+19v+90)(v-2 over 3v+5)

v-2 over (v+9)(v+10)

Exponential and Logarithmic Functions

100

Rewrite into log statement

125=5³

log5(125)=3

200

rewrite into log statement

e^x=9

ln9=x

300

Rewrite into exponential statement

ln(x)=5

e⁵=x

400

rewrite into exponential form

ln(3)=x

e^x=3

500

Evaluate basic log statement

log2(32)=?

log2(32)=5