Algebra 3 Final Review

Slope-Intercept Form

100

9x+8y=56

y=-9/8x+7

200

Through (-2,-4) and Slope = 7/2

y= 7/2x+3

300

Through: (5,-4) and (-3,2)

y=-3/4x-1/4

400

Through (-3,5) and par: y=-4/3x-5

y=-4/3x+1

500

Through: (4,5) and perp: y=-9/10x+1

y=10/9x+5/9

System of Equations

100

x-2y=-6

x+y=-3

(-4,1)

200

x+2y=4

5x+2y=-4

(-2,3)

300

y=3x-1

y=5x+1

(-1,-4)

400

y=-4/3x-3

y=2/3x+3

(-3,1)

500

x-y=-1

3x+2y=-8

(-2,-1)

Solve by Factoring or Quadratic Formula

100

p^2+3p-18=0

p=-6, 3

200

a^2+7a+10=0

a=-2,-5

300

5x^2-8x-4=0

x=-2/5, 2

400

2x^2-9x-20=-2

x=-3/2, 6

500

9p^2-15p-11=7+2p^2

p=-6/7,3

Square Roots

100

r^2=sqrt20

r=2sqrt5, -2sqrt5

200

a^2+10=26

a=4, -4

300

(3sqrt4)/(2sqrt12)

sqrt3/2

400

2sqrt8+3sqrt54+2sqrt54

4sqrt2+15sqrt6

500

(5sqrt4)/(sqrt3)

(10sqrt3)/3

Exponents

100

(4x^-4)(2x^2)

8/x^2

200

(4a^-4)^2

16/a^8

300

2x^-2(2y^4)^4

(32y^16)/x^2

400

(((v^-3)^4)/(2u^-2v^2))^-4

(16v^56)/(u^8)

500

((2yx^-4)(2x^-4))/((2x^-4y^-4)(2x^3)^2)

y^5/(2x^10)

Logarithms

100

 

Condense: 2log_6 x -5log_6 y

log_6 (x^2/y^5)

200

Exp: log_4 (x^6/y)^5

30log_4 x-5log_4 y

300

log_6 (x-6) - log_6 4=2

x=150

400

log_2 6+log_2 3x^2=1

x=1/3, -1/3

500

log_5 9 +log_5 -4x =2

x=-25/36

Solve Exponential Equations

100

3^(-3m)=3^(-2m)

m=0

200

16^p=64^(-3p+2)

p=6/11

300

216^-x=36

x=-2/3

400

(1/216)^r=36

r=-2/3

500

243^3x=1/27

x=-1/5

Imaginary Numbers

100

(-6-i)+(3+8i)

-3+7i

200

(1-6i)-(-6+3i)

7-9i

300

(-2-5i)(-7-i)

9+37i

400

(6+9i)/(5i)

(6i-9)/(-5)

500

(-2+10i)/(10i)

(i+5)/5

Simplify Expression

100

4/(x+5)+6/(x+1)

(10x+34)/((x+5)(x+1))

200

6/(v-2)-(3v)/(v-1)

(-3v^2+12v-6)/((v-2)(v-1))

300

(10/(8n-16))((8n-16)/(n+1))

10/(n+1)

400

((10x^3+80x^2)/(10x^2))((x-7)/(x+8))

x-7

500

((n^2+n-72)/(n-8))((n+2)/(n^2+4n-45))

(n+2)/(n-5)