The hook
The math that shows up on the FS exam is tools you USE, not theorems to prove. Trig, analytic geometry, basic calculus, linear algebra. Knowing when to reach for which is the skill — pure memorization isn\'t.
Keep these in muscle memory
Formulas to know cold
Right triangle (SOH-CAH-TOA)
sin = opp/hyp, cos = adj/hyp, tan = opp/adjLaw of cosines
c² = a² + b² − 2ab·cos(C)Solves any triangle when 2 sides + included angle, or all 3 sides, are known.
Law of sines
a/sin(A) = b/sin(B) = c/sin(C)When 2 angles + 1 side, or 2 sides + non-included angle, are known.
Distance between points
d = √((x₂−x₁)² + (y₂−y₁)²)Slope of a line
m = (y₂−y₁) / (x₂−x₁)Quadratic formula
x = (−b ± √(b² − 4ac)) / (2a)Memorize these
Concepts that show up on the exam
Radians vs. degrees
1 radian = 180/π degrees ≈ 57.296°. Trig functions in math libraries take radians; surveyors think in degrees. Convert with care.
Vector
Magnitude + direction. Add by components: (a₁ + b₁, a₂ + b₂). Survey lat/dep are vector components.
Matrix multiplication
Used in coordinate transformations, least squares. (m × n)(n × p) = (m × p). Inner dimensions must match.
Derivative
Instantaneous rate of change. d/dx of x² = 2x. Used in error propagation: σ_y depends on (∂y/∂xᵢ).
Integral
Cumulative sum / area under a curve. Used in volume by integration of cross-section areas, area under irregular curves (Simpson's rule).
Test yourself
How well did it stick?
A quick 5-question check on College Mathematics. See where you stand and what to review.