Algebra 2

Logarithms

100

Expand:

log₁₀ (x²y⁶)

2log₁₀ (x) + 6log₁₀ (y)

200

Write in exponential form:

log₈3x=2

8²=3x

300

Write in logarithmic form:

5^x=142

log₅142=x

400

log₄(x²-2x)=log₄(5x-12)

x=3 x=4

500

log₃(25-x²)=2

x=-4 x=4

Two Step Equations and Inverse

100

67=11n+1

n=6

200

3x-10=14

x=8

300

5-5x=0

x=1

400

n+3>7

n>4

500

2n<-3

n<(-3/2) or n<-1.5

Factoring and Quadratic Formula

100

x²+5x+6=0

(x+2)(x+3)=0

x=-2 x=-3

200

x²+4x+3

(x+1)(x+3)

x=1 x=3

300

Solve x2 + 3x – 4 = 0

x = –4, x = 1

400

Solve 2x2 – 4x – 3 = 0

 x = –0.58, x = 2.58

500

Solve x2 + 2x = 1

x = –2.41, x = 0.41

Permutations

100

6 P 3

120

200

8 P 6

20160

300

12 P 9

79833600

400

A password consists of four different letters of the alphabet. How many different possible passwords are there?

358,800

500

A private school has to send 2 juniors out of 50 and 2 teachers out of 20 to an award banquet. How many possibilities are there of who to send?

232,750

Combinations

100

8 C 6

28

200

12 C 8

495

300

20 C 12

125970

400

How many ways are there to create a three topping pizza from a list of seven possible toppings?

35

500

A coach wants to name two players for each game. There are twelve players on the team. How many ways can the coach choose the players to be captains for the first game?

66