Computational Thinking for the FE Exam
Success on the FE exam requires more than knowing formulas and concepts. You need strong computational thinking skills: the ability to break down complex problems, identify the right approach, execute calculations accurately, and verify your results. This guide covers the problem-solving strategies that separate successful candidates from those who struggle.
The Problem-Solving Framework
Every FE exam problem can be approached using this systematic framework:
- Step 1: Read and understand. Read the entire problem, including all given information and what is being asked. Do not start solving until you understand what the question wants.
- Step 2: Identify the concept. What engineering topic does this problem involve? What formulas or principles apply?
- Step 3: Draw a diagram. For any problem involving physical systems, draw a sketch. Label all known quantities and identify unknowns.
- Step 4: Plan your approach. Before calculating, decide which equations you will use and in what order.
- Step 5: Execute. Carry out the calculations carefully, tracking units throughout.
- Step 6: Check. Verify that your answer is reasonable and has the correct units.
Estimation and Sanity Checking
Before diving into a detailed calculation, develop a rough estimate of what the answer should be. This skill helps you:
- Eliminate obviously wrong answer choices
- Catch order-of-magnitude errors in your calculations
- Save time by confirming you are on the right track
For example, if a problem asks for the stress in a steel bar and you know the applied force is 10 kN and the cross-sectional area is about 100 mm^2, you can estimate: stress is roughly 10,000 / 100 = 100 MPa. If your detailed calculation gives 100 kPa or 100 GPa, something is wrong.
Working Backward from Answer Choices
The FE exam is multiple choice, which gives you a powerful tool: the answer choices. Use them to:
- Estimate the magnitude: If all answer choices are in the range of 100 to 500, and your calculation gives 0.5 or 50,000, check for unit conversion errors.
- Plug and check: For some problem types, it is faster to plug each answer choice into the problem conditions and see which one works.
- Eliminate wrong answers: Even if you cannot solve the problem completely, you may be able to eliminate two or three answers based on physical reasoning or dimensional analysis.
Common Calculation Errors and How to Avoid Them
Sign Errors
Sign errors are among the most common mistakes in engineering calculations. Prevent them by:
- Establishing a clear sign convention at the start of each problem
- Being consistent with your convention throughout the solution
- Double-checking signs when substituting values into equations
Order of Operations Errors
When entering complex expressions into the calculator, use parentheses to enforce the correct order of operations. Do not rely on the calculator to interpret your intent. For example, a/b*c might not give you a/(b*c) depending on how the calculator processes the input.
Transcription Errors
When copying numbers from the problem statement or from an intermediate calculation, double-check each digit. Transposing digits (writing 53 instead of 35) or dropping a zero (writing 1.5 instead of 15) can lead to completely wrong answers.
Converting Between Representations
Engineering problems often require converting between different representations:
- Graphs to equations: Read slope and intercept from a graph to write the equation of a line.
- Tables to interpolated values: Use linear interpolation to find values between table entries.
- Word problems to mathematical models: Translate verbal descriptions into equations.
- Diagrams to free body diagrams: Extract forces and constraints from physical setups.
Practice these conversions because they are required for many FE exam problems.
Dealing with Complex Multi-Step Problems
Some FE exam problems require multiple calculation steps. For these problems:
- Break the problem into smaller, manageable parts
- Solve each part independently
- Keep track of intermediate results with proper labels and units
- Combine the results at the end
- Do not round intermediate results; keep full precision until the final answer
Using the Reference Handbook Strategically
The reference handbook is a computational tool in itself. Use it to:
- Look up formulas rather than trying to derive them during the exam
- Find standard values (material properties, conversion factors, statistical tables)
- Verify the correct form of an equation when you are unsure
- Find beam deflection formulas, interest tables, and other pre-calculated results
Building Speed Through Practice
Computational speed comes from repetition. The more problems you solve, the faster you recognize patterns and execute solutions. Aim to:
- Solve at least 500 practice problems before the exam
- Time yourself regularly to track your speed improvement
- Focus on understanding, not just getting the right answer; understand why the approach works
- Review mistakes thoroughly; understanding an error teaches more than solving a problem you already knew
Mental Math Shortcuts
Quick mental math saves time on the exam:
- Know powers of 2 up to 2^10 = 1,024
- Know common square roots: sqrt(2) is approximately 1.414, sqrt(3) is approximately 1.732
- Know pi is approximately 3.14159 and e is approximately 2.71828
- Use scientific notation to manage large and small numbers
Computational thinking is a skill that improves with deliberate practice. Approach every practice problem with the same systematic framework, and by exam day, your problem-solving process will be efficient, accurate, and automatic.