Logarithms, vectors and systems of equations: the algebra behind FE Civil statics, structural analysis and hydraulics problems.
NCEES lists these Mathematics and Statistics topics for the FE Civil: analytic geometry; single-variable calculus; vector operations; statistics: distributions, mean, mode, standard deviation, confidence intervals, regression and curve fitting; probability: estimation and expected value. On Newton’s Notes this area spans 4 chapters: this one and Analytic Geometry and Trigonometry, Calculus and Probability and Statistics. 2.2 Complex Numbers and 2.6 Progressions and Series are in the chapter too, but they are not in the NCEES FE Civil specification, so they are not on this page.
Choose any section below to get a free FE Civil practice problem. Work it with the FE Reference Handbook open, tap your answer, then check the solution.
A logarithm answers one question: what power do I raise the base to?
A quantity grows as e0.05t. How long does it take to double?
e0.05t = 2, so 0.05t = ln 2 and t = 0.6931/0.05 = 13.86.
Common trap: (D) is 1/0.05 = 20, which skips the ln 2.
LogarithmsIdentitiesln xThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
To multiply matrices, take each row of the first times each column of the second.
What is the determinant of the matrix with rows (5, −2), (3, 4)?
det = (5)(4) − (−2)(3) = 20 + 6 = 26.
Common trap: (D) subtracts 6 instead of subtracting −6.
MatricesDeterminantsmatrix multiplicationThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
A system of linear equations can be written Ax = b and solved as x = A−1b.
Using Cramer’s rule, find x for 3x + 2y = 16 and x + 4y = 12.
D = (3)(4) − (2)(1) = 10. Dx replaces the x column with (16, 12): (16)(4) − (2)(12) = 40. x = 40/10 = 4. (Then y = 2.)
Common trap: (A) is y, not x.
Matrix inverseCrameradjointThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
The dot product turns two vectors into a number, A·B = |A||B| cos θ, which gives angles, projections and work.
A force F = (10, 5, 0) N moves an object through displacement d = (3, 4, 0) m. How much work is done?
W = F·d = (10)(3) + (5)(4) + 0 = 50 J.
Common trap: (C) multiplies the magnitudes (11.18 × 5) as if the force and motion were parallel.
Vectorsdot productcross productThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Newton’s Notes FE Civil has 18 chapters (11 shared with Mechanical, 7 Civil-only) with lessons, worked examples and 420+ FE-style practice problems with full solutions, 171 of them Civil-only. Pro adds a timed full-length FE Civil practice exam (110 problems), a custom test builder and Ask Newton, the AI tutor. Try it free for 3 days, no card to start.
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