THE COMPOUND // FIELD NOTES // WEEK 32
Age problems, rational inequalities, and statistics
Field Book
Lessons 120 to 122, then 129
Method
Paper first, every step
Escape 8 posts: the last case before the finale. The ladder jumps from 122 straight to 129 by design: the skipped block is proof geometry, and that is a different course's file.
What you have to be able to do
- Define age variables in terms of now and solve
- Solve rational inequalities and use the laws of logarithms
- Read stem and leaf plots and compute mean, median, mode, and standard deviation
The procedures
Age problemsField Book Lesson 120
- Define every age now. Future ages add, past ages subtract.
- Write one equation per time statement and solve the system.
Rational inequalitiesField Book Lesson 121
- Multiply through by the denominator squared: always positive, so the sign holds.
- Then solve the polynomial inequality with boundaries and test points.
Laws of logarithms and setsField Book Lesson 122
- Log of a product adds, log of a quotient subtracts, log of a power multiplies out front.
- Intersection keeps the overlap, union keeps everything: draw the Venn diagram.
StatisticsField Book Lesson 129
- A stem and leaf plot keeps every data point visible while sorting them.
- Mean averages, median centers, mode repeats. Standard deviation measures spread around the mean, and the normal curve puts most data within a few of them.
Worked: center of a small set
- Find the mean of 4, 7, 7, 10.
- Sum is 28, count is 4.
- Mean = 7. The mode is also 7, and so is the median.
Terms on the record
| Term | Meaning |
|---|
| rational inequality | an inequality containing a variable in a denominator |
| union | the set of everything in either of two sets |
| standard deviation | a measure of how far data spread from the mean |