Factoring
Types of Sequences
Exponential decay/growth
Systems of equations
Laws of exponents
100

x2 +11x

x(x+11)

100

Common difference of -6

Arithmetic

100

formula for exponential growth

 a (1 + r)x 

  • a (or) P00 = Initial value
  • r = Rate of growth
  • k = constant of proportionality
  • x (or) t = time (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).
100

x+y=5

2x−y=7

x=4

y=1 

100

53

125

200

x2-4x-45

(x+5)(x-9)
200

9, 13, 19, 27..

Quadratic
200

formula for exponential decay


f(x) = a (1 - r)x

a = initial amount

1-r = decay factor

x= time period


200

4x+5y=11

x−y=5

x=4

y=-1

200

x4+x4

2x4

300

x2+17x+72

(x+8)(x+9)

300

an= an-1+d


Recursive Formula

300

does 1,000,000(1.05)8 represent exponential growth or decay?

exponential growth

300

2x−y=−5

y=1−3x

a=3

b=0

300

2x3y+x2y3

2x3y+x2 y3

400

 x2+10x+24

(x+4)(x+6)

400

√9, √18, √27, √36, √45...

Geometric

400

Does 10(0.92)5 represent exponential growth or decay?

exponential decay 

400

2y + 3x = 38

y − 2x = 12

x=2

y=16

400

21y7/7y4

3y3

500

18x3 +3x2 - 6x.

3x(2x - 1)(3x + 2)

500

Does this form an arithmetic sequence?

-3√7, 6√7, 15√7, 24√7, 33√7

500

What is the initial value in y=50(1.15)x

50

500

3x – 5y = -23 

5x + 3y = 7

x=-1

y=4

500

(x3a4y6)(y6a2)(x3y2)

x6a6y14