FORMULA SHELF
25 of 370
The arithmetic behind the work: what to measure, what to type in, and what the answer comes out as. Every formula says what the symbols mean and gives a worked example, so you can check it against a job you have already done.
SHELVES
Advanced maths
25 formulas
Adding evenly spaced quantities: fence posts, rows, payments and wear allowances.
First term 2, difference 3, 10 terms: S = 155.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Compound annual growth for a herd, a woodlot, a business or an investment.
100 to 161 in 5 years is 10% a year.
Expanding repeated multiplication in engineering, statistics and compound growth.
(x + 2)3 = x3 + 6x2 + 12x + 8.
Counting selections where order does not matter: feed mixes, teams, sample plots.
5C2 = 10.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Rates of change: how fast a tank empties, a crop grows or cost rises.
d/dx (x3) = 3x2.
Checking whether two equations have a unique solution; used in surveying and transformations.
[[2,3],[1,4]] has determinant 5.
When one quantity doubles, the other doubles: seed to area, feed to animals, paint to wall.
3 bags cover 60 m2, so 7 bags cover 140 m2.
Tells you whether a quadratic has two, one or no real solutions before you solve it.
For x2 - 5x + 6, D = 1, so two real roots.
Checking a diagonal in a building, a pipe run or a 3D survey.
(0,0,0) to (2,3,6) is 7 m.
Cooling, spoilage, radioactive decay, drug clearance and declining yields.
1000 kg at 10% loss for 3 years = 729 kg.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Populations, investments, fermentation and anything that grows by a percentage each period.
100 ewes at 8% growth for 5 years = 147.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Counting arrangements, combinations and probability. 0! is defined as 1.
5! = 120.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Compound growth, repeated dilution and doubling problems.
a = 1, r = 2, n = 8 gives 255.
Finding total volume, distance or energy from a rate. The reverse of a derivative.
integral x2 dx = x3/3 + C.
When one goes up and the other goes down: speed and time, men and days, pressure and volume.
Two pumps fill in 6 hours, four pumps in 3 hours.
Light, sound, radio and spray coverage fall off with the square of distance.
Twice the distance gives a quarter of the light.
Straight-line relationships: cost per hour, fuel use against load, yield against rainfall.
A machine costs 50 + 20 per hour: y = 20x + 50.
When a calculator only has log base 10 or natural log but the problem uses another base.
log2(8) = log(8)/log(2) = 3.
Growth and decay, half-life and the inverse of the exponential function.
ln(10) = 2.3026.
Solving an equation that cannot be rearranged neatly. Iterate until the answer settles.
Solving x2 - 2 = 0 from x=1 reaches 1.414 in a few steps.
Checking a scale, a meter, a yield estimate or a mixing measurement.
Measured 98 kg against 100 kg is 2% error.
Counting ordered arrangements: jobs in a sequence, routes, rotations.
5P2 = 20.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Solving projectiles, area problems, mixing equations and any relationship that curves.
x2 - 5x + 6 = 0 gives x = 2 or 3.
Feed mix problems, two unknown costs and balancing rations.
x + y = 10 and x - y = 2 give x = 6, y = 4.
Area of an irregular field or a pond from equally spaced offsets.
Offsets 0, 2, 4, 2, 0 at 10 m spacing give 700 m2.
SOURCES & PROVENANCE
1 listed
This page is an AI-organised index. The label means the grouping and cross-links were compiled with AI; the information itself comes from the public-domain books, reports and manuals listed below. Open any source to read the local copy or follow the link to the original publication.