Factorial!
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product
of all positive integers less than or equal to n. For example,
Factorials are useful. They can show how many different ways there are to order or
arrange a set of things. For example, if you have 5 books on a shelf, and want to know
how many different ways there are to order or arrange them, simply find the factorial of
5:
5! = 5 x 4 x 3 x 2 x 1 = 120
This shows that you can arrange 5 books 120 different ways.
0! is defined as 1. The mathematical proof of this is complicated. However, one
explanation is that you can arrange a set of nothing, an empty set, in just one way—as
nothing, an empty set.
The key sequence for a TI 83 or TI 84 is MATH, PRB, 4:!.
Examples:
1.
2.
5!
2!
102!
99!
Work Problems
𝑡𝑖𝑚𝑒 𝑖𝑡 𝑡𝑎𝑘𝑒𝑠 𝑡𝑜 𝑑𝑜 𝑡ℎ𝑒 𝑗𝑜𝑏 𝑡𝑜𝑔𝑒𝑡ℎ𝑒𝑟 𝑡𝑖𝑚𝑒 𝑖𝑡 𝑡𝑎𝑘𝑒𝑠 𝑡𝑜 𝑑𝑜 𝑡ℎ𝑒 𝑗𝑜𝑏 𝑡𝑜𝑔𝑒𝑡ℎ𝑒𝑟
+
=1
𝑡𝑖𝑚𝑒 𝑖𝑡 𝑡𝑎𝑘𝑒𝑠 𝑝𝑒𝑟𝑠𝑜𝑛 1 𝑡𝑜 𝑑𝑜 𝑡ℎ𝑒 𝑗𝑜𝑏 𝑡𝑖𝑚𝑒 𝑖𝑡 𝑡𝑎𝑘𝑒𝑠 𝑝𝑒𝑟𝑠𝑜𝑛 2 𝑡𝑜 𝑑𝑜 𝑡ℎ𝑒 𝑗𝑜𝑏
1. It takes Jenny 11 hours to harvest a field. Darryl can harvest the same field in 14
hours. Find how long it would take them if they worked together.
2. Working together, Jill and Jaidee can pick forty bushels of apples in 6.46 hours.
Had she done it alone it would have taken Jaidee 14 hours. How long would it
take Jill to do it alone?
Formulas
Slope of a line through two points
𝑦2 −𝑦1
𝑥2 −𝑥1
Point-Slope (𝑦 − 𝑦1 ) = 𝑚(𝑥 − 𝑥1 )


Parallel lines have the same slope.
Perpendicular lines have slopes that are opposite reciprocals.
Distance √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
𝑥1 +𝑥2 𝑦1 +𝑦2
Midpoint (
2
,
2
)
Pythagorean Theorem 𝑎2 + 𝑏 2 = 𝑐 2