FE Mechanical Exam Prep: Pass the FE Exam (Step-by-Step)

Master analytic geometry basics by computing slopes from two points, understanding straight-line equations in standard and general forms, and applying perpendicular relationships and intercept concepts.

Find the tangent to a circle of radius five at (3,4); slope -3/4 and intercept 25/4. Using angle between lines formula on slopes -7 and 3 yields about 27 degrees.

Learn to solve quadratic equations with the quadratic formula and discriminant, classify conics (ellipse, hyperbola, parabola) using b^2-4ac, and derive the parabola equation (x-4)^2=12(y-8) from vertex and directrix.

Solve ellipse, hyperbola, and circle problems in analytic geometry and trigonometry. Apply centers, axes, radii, and eccentricity to derive standard equations from given points.

Compute tangent length from a point to a circle using the tangent line equation. Find the sphere radius centered at the origin from (8,1,6) with the 3d distance formula.

Compare cosine 45 and tan 45 values, explain triangle definitions, and illustrate identities from the FAA handbook to simplify expressions like cos theta times sec theta over tan theta.

Explore analytic geometry and trigonometry through solving identities like the sine double-angle and cosine sums, and apply law of sines and cosines to flagpole height problems.

Apply law of cosines to determine triangle angles from tangent circles with radii 110, 140, 220; then estimate ellipse perimeter and circle overlap area using circular segment formulas.

Compute the circular sector radius from a 3 m² area and 50° angle, convert to radians, and apply regular polygon and prismoid formulas to find radii and height.

Demonstrates calculating a sphere’s volume with radius 10 cm and deriving a cone’s base area from a cross section, using handbook-based equations in chapter one of analytic geometry and trigonometry.

Solve analytic geometry and trigonometry problems from fe mechanical practice problems, including finding river width with tan theta and using law of cosines and sines to compute bc and bd.

Explains how the sum of two vectors yields the resultant. Demonstrates solving a geometric progression problem to find the first term using the common ratio.

Evaluate derivatives and identify the not correct derivative among options, then use implicit differentiation to find dy/dx for x^2 y - e^{2x} = sin y.

Explore first- and second-order differential equations, solving y' + a y = 0 as y = C e^{-a t} and using a^2 versus 4b to decide exponential or cosine-sine solutions.

Identify Euler's method from code and compare with trapezoidal, Newton's, and Simpson's rules; apply Newton's method with two iterations to approximate a root.

Explore probability and statistics essentials, including mean, median, mode, variance, and standard deviation, with focus on sample variance and standard deviation, plus practical problems.

Explore fluid properties in fluid mechanics, including surface tension, density from specific gravity, kinematic and dynamic viscosity, and viscous stress to calculate force, with a 26 N example.

Explore fluid statics using barometer concepts to relate atmospheric and vapor pressures through gamma h, and solve barometer and manometer problems with mercury, glycerin, and water.

Explains fluid dynamics basics, distinguishing mass and volume flow rates, applying continuity, friction factor, and head loss concepts to solve pipe flow problems including minor losses.

Explore fluid measurement and similitude through aptitude tube and sharp-edge orifice problems, linking velocity, density, and stagnation pressure to static pressure and discharge.

Compute Mach number from velocity and the speed of sound using air properties gamma and R, then use isentropic relations to relate stagnation and static temperatures along a nozzle.

Compute net power for a blower from density, head, and volume flow rate with unit conversion; then evaluate turbine power from enthalpy change and kinetic energy in an adiabatic flow.

Explore the properties of substances in thermodynamics, highlighting ideal gas behavior, the pv = mr t equation, and computing specific enthalpy and internal energy from mass, volume, and pressure.

Learn the laws of thermodynamics with practical power calculations using mass flow rate, enthalpy, and pressure. Apply the first law and steam tables to FE exam problems.

Explore cycles and entropy through series Carnot engines to find intermediate temperatures and compute the auto cycle's thermal efficiency for a compression ratio of 10 with air and k 1.4.

Convert mole fractions to mass fractions in a 30% CO2 and 70% N2 gas mixture and compute heat per mass from 150°C to 50°C using the specific heats.

Apply conduction concepts to compute heat loss across composite walls using thermal resistance, thermal conductivities, and heat transfer coefficients, with example problems.

Explore convection in heat transfer with counter-flow heat exchanger and duct flow, solving for area via log mean temperature difference and Reynolds number using hydraulic diameter.

Explain radiant heat transfer concepts, including black body behavior and absorptivity, reflectivity, transmissivity, and emissivity, and compute net radiation exchange between concentric black cylinders using the Stefan–Boltzmann framework.

Resolve a 300 newton force into components along lines B and Q in a coplanar system, apply the law of sines, and note bend supports resist forces but not moments.

Apply statics to a truss by enforcing horizontal and vertical force sums and using moments to find member forces, with BC ≈ 2500 N and D ≈ 8800 N.

Determine equilibrium on a 34-degree incline with a 2 kg block and static friction 0.2, then compute tension in cable CE for a 600 N weight suspended by three cables.

Learn to compute centroids and moments of inertia for composite shapes using area, centroid locations, and d squared times area, and apply to polar moments for circles.

Analyze the stress-strain diagram from a tensile test and apply the modulus of elasticity to compute delta l for a steel rod under a compressive load, using area and length.

Analyze binary phase diagrams with the lever rule to identify beta solid, beta liquid, and alpha liquid regions; discuss peritectic compositions and cooling curves with phase changes.

Compute plane-stress stresses using sigma_x, sigma_y, and tau_xy. Derive principal stresses and maximum shear stress with standard formulas, applying to examples yielding about 92 and -8.5 MPa and ~200 MPa.

Calculate maximum shear stress in a solid circular shaft from torque using the torsion stress equation, and determine the change in area of a glass window due to thermal expansion.

Master mechanics of materials by solving beam problems, including simply supported and cantilevered beams, using bending moment, deflection, and stress relations with E and I.

explain column buckling with euler's formula, effective length factor k, and rectangular inertia, yielding 1.3 meganewtons. evaluate eccentric compression in a 10x10 cm column to 450 kPa tensile stress.

Practice electrostatics by solving problems on electric fields between charges, the force between two charges, and current from charge and time, including zero-field points and unit conversions.

Explore direct-current circuits by analyzing resistors, inductors, and capacitors in series and parallel, calculating equivalent inductances and resistances, and applying power and energy formulas for capacitors and inductors.

Explore alternating current circuits by determining phase angle and power factor from voltage, current, and power, and relate power factor to real, reactive, and complex power.

Explore how to analyze rotating machines in DC and induction motors, calculating magnetic flux, field current, and motor slip using given constants and standard equations.