Algebra 1 Re-cap

Exponential

100

dn x 5d³n⁵

^x=multiply

5d⁴n⁶

200

7n⁵ x 4n^-5g³

^x=multiply

24 n g³

300

5 x 5^-4

x=multiply

1/5³

400

4z^-6s⁵/6z⁴s^-5

2s¹⁰/3z¹⁰

500

gs/3g³s⁴

1/3g³s⁴

Quadratics

100

Completing the square

s²+16s+s

64

200

Square root

2x²+8=48

*Round to the nearest tenth*

(4.47,-4.47)

300

Solve by Factoring

n²-5n-2=22

n=(-3,8)

400

Square Root

8k²-5=283

(6,-6)

500

Solve by Factoring g²-6g=40

g=(-4,10)

Graphing

100

-2x + y =-4 

x = 1

(1,-2)

200

y = 1/2 x + 5

 y = -5/2x - 1

(-2,4)

300

-x + 2y = -6 

3x + 2y = 2  

(2,-2)

400

y = 7/3 x + 5

 x = -3

(-3,-2)

500

-3x + 2y = 8 

5x + 2y = -8

(-2,1)

Polynomials.

100

Dividing

(- 2z² - 5z - 4) ÷ (z + 7)  

-2z + 9 - 67/z+7

200

Subtracting/adding

(4n³ + 3n² - 2n) + (9n⁴ + 8n² - n) - (5n³ + 6n⁴ - 7n²)

3n⁴ - n³ + 18n² - 3n

300

subtracting

 (3 + d⁵ - 5d) - (9d⁵ + 4 + 2d³ ) - (8 - 7d⁵ + 6d³ )

- d⁵ - 8d³ - 5d - 9

400

divide

( 3k² + 9k + 3) ÷ (k - 2)

3k + 15 + 33/k - 2

500

Special case polynomials

(q + 9)(q - 9)

q² - 81

equations

100

6[-h]=11

h={1.83,-1.83}

200

Tim spent half of his allowance going to the movies. He washed the family car and earned 7 dollars. What is his weekly allowance if he ended with 14 dollars ?

$14

300

Joan sold half of her comic books and then bought 9 more. She now has 12. How many did she begin with ?

6 comic books

400

 - 12 = 3.7 + f

f = -15.7

500

 6.6 = n + 6.1

n = 0.5