Growing plants under lights

Plants need light to grow. No duh! Specifically, plants need a certain number of photons of specific wavelengths from the blue and red end of the spectrum to take apart water and carbon dioxide molecules to make more plant. The middle bit is reflected back and so plants look green.

The Dreaded Word Problem

Word problems are the bane of most math students, and why not. This is where mathematics, language arts, logic and the real world all intersect.

  • Find a Pattern
  • Make a Table
  • Work Backwards
  • Guess and Check
  • Draw a Picture
  • Make a List
  • Write a Number Sentence
  • Use Logical Reasoning

Translate the problem into math-ese
Solve the equations

Operation words

Financial Ratios

Current Ratio
The ratio of current assets to current liabilities. This indicates the ability to pay it's current debts. You want a ratio of 1 or better.
Price to free cash flow

Benford's Law

Benford's Law (also known as the first digit law) states that the first digit from most real life data follows a logarithmic distribution. This means that the first digit will be 1 30% of the time, 2 18% of the time, and so on to 9 appearing 5% of the time. This can be used as a good check to see if the data that you are using is biased or not.

Why cross multiplying is evil

I've noticed that a lot of my tutoring students have been taught to cross multiply when dividing fractions, whereas I was taught to multiply by the reciprocal. OK, you may think, they both wind up getting you the right answer, so what? I guess it doesn't matter if your only goal is to pass the next quiz. What you are forgetting is the power of the commutative and associative properties of multiplication.


A quadratic equation is a second order (the highest power of the variable is 2) polynomial equation of 1 variable. It is typically written either as $y = ax^2 + bx +c$ or $y = a(x+k)^2 +c$ When graphed, it forms a parabola, with a single vertex (maximum or minimum point) and 0, 1, or 2 real roots (points where the graph crosses the x axis). In real life, we find this equation when dealing with ballistics, engineering, and optics. It also turns up in economics.

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