FE Civil Mathematics and Statistics practice problems
6 free FE Civil Mathematics and Statistics practice problems with answers and full worked solutions. Mathematics and Statistics carries 8–12 of the 110 questions on the FE Civil exam (NCEES specification effective July 2020). Pick an answer to check it, then read the worked solution and why each wrong choice is wrong.
6 worked Mathematics and Statistics problems
Question 1 of 6
An ellipse has semi-axes of 2 and 10. Its area is most nearly:
Show the answer and the reasoning
Why B
Given: semi-axes a = 2, b = 10. Relation: A = pi a b, which reduces to pi r^2 when a = b. Substitute: A = pi(2)(10). Result: A = 62.83.
Why A is tempting
Halved the area, which is the area of a half ellipse rather than the whole figure.
Why C is tempting
Treated the ellipse as a circle of the average radius.
Why D is tempting
Squared the product of the semi-axes.
Source NCEES FE Reference Handbook 10.6 — Mathematics; Engineering Probability and Statistics
Question 2 of 6
The limit of sin(3x)/(4x) as x approaches zero is most nearly:
Show the answer and the reasoning
Why B
Given: sin(3x)/(4x) as x approaches 0; both parts vanish, an indeterminate 0/0. Relation: L'Hopital's rule, the limit of f/g equals the limit of f'/g'. Substitute: f'/g' = 3cos(3x)/4, and cos(0) = 1, giving 3/4. Result: limit = 0.7500.
Why A is tempting
Substituted zero directly. Both numerator and denominator vanish, so the form is indeterminate and requires more work.
Why C is tempting
Inverted the ratio of the coefficients.
Why D is tempting
Multiplied the coefficients.
Source NCEES FE Reference Handbook 10.6 — Mathematics; Engineering Probability and Statistics
Question 3 of 6
The magnitude of the vector 5i + 2j + 10k is most nearly:
Show the answer and the reasoning
Why C
Given: A = 5i + 2j + 10k. Relation: |A| = sqrt(a1^2 + a2^2 + a3^2), Pythagoras in three dimensions. Substitute: |A| = sqrt(5^2 + 2^2 + 10^2) = sqrt(129). Result: |A| = 11.36.
Why A is tempting
Took a geometric mean of the components.
Why B is tempting
Left the k component out.
Why D is tempting
Summed the absolute components. Magnitude is the root of the sum of squares.
Source NCEES FE Reference Handbook 10.6 — Mathematics; Engineering Probability and Statistics
Question 4 of 6
A sample contains 16, 26, 57, 62, 100 and 195. The median is most nearly:
Show the answer and the reasoning
Why A
Given: six values; in order, 16, 26, 57, 62, 100, 195. Relation: with an even count, the median is the average of the two central values. Substitute: median = (57 + 62)/2. Result: median = 59.50.
Why B is tempting
Took a single middle value. With an even count the median is the average of the two central values.
Why C is tempting
Computed the mean. With a long right tail the mean sits well above the median.
Why D is tempting
Reported the range, which measures spread rather than central tendency.
Source NCEES FE Reference Handbook 10.6 — Mathematics; Engineering Probability and Statistics
Question 5 of 6
A line passes through (-7, 7) and (14, -7). Its slope is most nearly:
Line through the points (-7, 7) and (14, -7); its slope is the rise between them over the run. Show the answer and the reasoning
Why A
Given: (-7, 7) and (14, -7). Relation: m = (y2 - y1)/(x2 - x1), rise over run. Substitute: m = (-7 - 7)/(14 - (-7)) = -14/21. Result: m = -0.667.
Why B is tempting
Added the coordinates rather than differencing them.
Why C is tempting
Reversed the sign, which describes a line falling where this one rises.
Why D is tempting
Gave the slope of the perpendicular line.
Source NCEES FE Reference Handbook 10.6 — Mathematics; Engineering Probability and Statistics
Question 6 of 6
For f(x) = 3x^3 - 3x^2 - 2x, the value of f'(3) is most nearly:
Show the answer and the reasoning
Why C
Given: f(x) = 3x^3 - 3x^2 - 2x, evaluated at x = 3. Relation: d/dx(x^n) = n x^(n - 1), term by term. Substitute: f'(x) = 9x^2 - 6x - 2, so f'(3) = 9(3)^2 - 6(3) - 2. Result: f'(3) = 61.00.
Why A is tempting
Reduced each exponent without bringing down the coefficient.
Why B is tempting
Differentiated twice, giving the second derivative.
Why D is tempting
Forgot the factor of two when differentiating the squared term.
Source NCEES FE Reference Handbook 10.6 — Mathematics; Engineering Probability and Statistics
Going further
Frequently asked questions
How many Mathematics and Statistics questions are on the FE Civil exam?
Between 8 and 12 of the 110 questions, according to the NCEES FE Civil specification effective July 2020.
Are these real NCEES exam questions?
No. NCEES does not release its exam questions. These are original FE-style problems written to the NCEES specification and the FE Reference Handbook; every calculated key is checked by two independent solution methods.
Are these Mathematics and Statistics practice problems free?
Yes. All 6 problems on this page, with answers and full worked solutions, are free and need no account.
Check where you stand, free
The quick diagnostic is eight FE Civil questions in about ten minutes, with no account. The free mock is a full 110-question, 5 hour 20 minute FE Civil paper with a worked solution for every question.