FE Civil

Evaluate the limit lim(x→0) (sin 3x)/x.

• A0
• B1
• C3
• DUndefined

A normally distributed concrete-strength data set has mean 4,200 psi and standard deviation 350 psi. What strength is exceeded by approximately 84% of cylinders (one standard deviation below the mean)?

• A3,500 psi
• B3,850 psi
• C4,200 psi
• D4,550 psi

Solve the differential equation dy/dx = ky for y(0) = y₀.

• Ay = y₀ + kx
• By = y₀ e^(kx)
• Cy = y₀ x^k
• Dy = y₀ cos(kx)

A vector A = 3i + 4j and B = 2i − k. What is A · B?

• A6
• B8
• C10
• D−4

What is the integral of f(x) = 2x from x = 1 to x = 4?

• A6
• B9
• C15
• D20

The probability that a single soil boring encounters bedrock is 0.30. If three independent borings are drilled, what is the probability that at least one encounters bedrock?

• A0.30
• B0.49
• C0.66
• D0.90

A 2×2 matrix A = [[3, 1],[2, 4]] has determinant equal to:

• A6
• B10
• C12
• D14

Use the trapezoidal rule with two equal subintervals to estimate ∫₀² (x² + 1) dx.

• A3.0
• B4.0
• C4.67
• D5.0

Saturated water at 20°C has approximately what kinematic viscosity?

• A1.0 × 10⁻⁶ m²/s
• B1.0 × 10⁻⁴ m²/s
• C1.0 × 10⁻³ m²/s
• D1.0 × 10⁻¹ m²/s

For a concrete mix, lowering the water-cement (w/c) ratio while keeping other factors constant generally produces concrete that is:

• ALower in compressive strength and more permeable
• BHigher in compressive strength and less permeable
• CHigher in slump and easier to place
• DUnchanged in strength but lower in durability

Earthwork volume is computed between two cross-sections 100 ft apart with end areas of 250 ft^2 and 350 ft^2. Using the average-end-area method, the volume is approximately:

• A926 yd^3
• B1,111 yd^3
• C1,296 yd^3
• D30,000 yd^3

A water-treatment sedimentation basin is 30 m long, 10 m wide, and processes 6,000 m^3/day. The surface overflow rate (overflow velocity) is approximately:

• A10 m/day
• B20 m/day
• C200 m/day
• D600 m/day

On a project, the budgeted cost of work performed (earned value, EV) is $80,000 and the actual cost (AC) is $95,000. The cost variance (CV) and cost status are:

• A+$15,000; under budget
• B-$15,000; over budget
• C+$15,000; over budget
• D-$15,000; under budget

A data set of concrete cylinder strengths is {3,800; 4,000; 4,200; 4,400; 4,600} psi. The sample mean and median are:

• AMean 4,200 psi; median 4,000 psi
• BMean 4,200 psi; median 4,200 psi
• CMean 4,000 psi; median 4,200 psi
• DMean 4,400 psi; median 4,200 psi

A line has a whole-circle azimuth (measured from north) of 210 deg. Its equivalent quadrant bearing is:

• AN 30 deg E
• BS 30 deg W
• CS 30 deg E
• DN 30 deg W