FE Civil Mathematics and Statistics

Knowledge area 1 of the FE Civil exam: 8–12 of the 110 questions. The subtopics NCEES lists, how they are tested and worked practice problems with solutions.

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110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.

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What the specification lists

Analytic geometry
Single-variable calculus
Vector operations
Statistics (e.g., distributions, mean, mode, standard deviation, confidence interval, regression and curve fitting)

From the NCEES FE Civil CBT exam specifications, knowledge area 1.

Line drawing of graph paper with a plotted curve, a compass, a protractor and a calculator

How Mathematics and Statistics is tested

Mathematics questions are short and calculator-friendly: a slope, an intersection, a derivative or integral, a vector product. Most of the formulas sit in the Reference Handbook section on mathematics, so the skill being tested is recognizing the setup quickly and not spending ten minutes on a two-minute question. Expect a mean, a standard deviation, a normal-distribution probability with a z value, a confidence interval or a regression line. Practice reading the unit normal table in the Reference Handbook section on engineering probability and statistics, and know when to use the sample (n − 1) rather than the population standard deviation.

On exam day the relationships you need are in the Reference Handbook sections on Mathematics and Engineering Probability and Statistics. The handbook is the only reference allowed, so practice finding each formula in it rather than memorizing a separate sheet.

Start the free Mathematics and Statistics drill

FE Civil Mathematics and Statistics practice problems

Work each problem with your calculator and the handbook, then open the solution.

Problem 1 · Analytic geometry and trigonometry

Two sides of a triangular parcel measure 120 m and 85 m, and the angle between them is 72°. The length of the third side is most nearly:

A.47.2 m
B.123.8 m
C.167.1 m
D.203.4 m

Show the answer and solution

Answer: B: 123.8 m

Law of cosines: c² = 120² + 85² − 2(120)(85)cos 72° = 14,400 + 7,225 − 6,304 = 15,321 m², so c = 123.8 m. Adding the 2ab cos C term gives 167.1 m, and evaluating cos 72 in radian mode gives 203.4 m.

Analytic geometry and trigonometry · Reference Handbook: Mathematics

Problem 2 · Single-variable calculus

A plate occupies the region under y = x² from x = 0 to x = 3 (x and y in cm), above the x-axis. The x-coordinate of the plate's centroid is most nearly:

A.1.50 cm
B.2.00 cm
C.2.25 cm
D.2.70 cm

Show the answer and solution

Answer: C: 2.25 cm

A = ∫₀³ x² dx = 9 cm², and ∫₀³ x·x² dx = 81/4 = 20.25 cm³, so x̄ = 20.25/9 = 2.25 cm. The value 2.70 cm is ȳ = (1/A)∫(y²/2) dx, the other centroid coordinate.

Single-variable calculus · Reference Handbook: Mathematics

Problem 3 · Measures of central tendencies and dispersions

Five mortar cubes tested at 7 days gave compressive strengths of 28.4, 31.0, 30.2, 33.5, and 29.9 MPa. Using the sample standard deviation, enter the coefficient of variation in percent, to one decimal place.

Fill in the blank: answer in %.

Show the answer and solution

Answer: 6.1 % (accepted 6 to 6.2)

Mean = 153.0/5 = 30.60 MPa. Sample standard deviation s = 1.875 MPa (dividing the sum of squared deviations, 14.06 MPa², by n − 1 = 4). CV = s/x̄ × 100 = 1.875/30.60 × 100 = 6.1%. Dividing by n instead gives 5.5%.

Measures of central tendencies and dispersions · Reference Handbook: Engineering Probability and Statistics

Problem 4 · Regression (linear, multiple), curve fitting, and goodness of fit

A least-squares line y = a + bx is fitted to 8 data points with Σx = 56, Σy = 148.0, Σxy = 1,156, and Σx² = 476. Enter the intercept a to two decimal places.

Fill in the blank: answer in .

Show the answer and solution

Answer: 8.5 (accepted 8.4 to 8.6)

b = (nΣxy − ΣxΣy)/(nΣx² − (Σx)²) = (9,248 − 8,288)/(3,808 − 3,136) = 960/672 = 1.4286. a = ȳ − b·x̄ = 18.50 − 1.4286(7.0) = 8.50. The line passes through the point of means (x̄, ȳ), which is how a follows from b.

Regression (linear, multiple), curve fitting, and goodness of fit · Reference Handbook: Engineering Probability and Statistics

More FE Civil practice problems from every knowledge area

Sit the full exam under the real clock

Take a full timed FE Civil practice exam

110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.

Or start the free Mathematics and Statistics drill

Common questions

How many Mathematics and Statistics questions are on the FE Civil exam?

The NCEES FE Civil specification lists 8–12 questions on Mathematics and Statistics, out of 110. Every examinee gets the same number per knowledge area.

What does Mathematics and Statistics cover on the FE Civil exam?

Analytic geometry; Single-variable calculus; Vector operations; Statistics (e.g., distributions, mean, mode, standard deviation, confidence interval, regression and curve fitting).

Where are the Mathematics and Statistics formulas on exam day?

In the NCEES FE Reference Handbook, which appears on screen during the exam: the Mathematics and Engineering Probability and Statistics sections. Practice with your free copy from MyNCEES so you know where each relationship sits.

Original independent practice questions written to the published NCEES exam specifications. Not affiliated with or endorsed by NCEES (National Council of Examiners for Engineering and Surveying).