Overview
This lecture reviews core math concepts and problem-solving strategies relevant to the FE (Fundamentals of Engineering) exam, focusing on algebra, geometry, calculus, statistics, and calculator use.
FE Exam Math Topics & Focus
- FE exam math includes analytic geometry, single variable calculus, vector operations, and statistics.
- Differential equations are less emphasized; focus is on basic calculus and geometry.
- Early review covers core math and statics; topics like dynamics and engineering economics come later.
Algebra & Geometry Fundamentals
- Know formulas for a line: slope-intercept (y = mx + b) and point-slope (y - y₁ = m(x - x₁)).
- The slope is the change in y over the change in x; proportional relationships are fundamental.
- Equation of a circle: (x - h)² + (y - k)² = r², derived using Pythagoras’ theorem.
Calculator Skills
- TI-36X Pro or Casio FX-115 recommended; know how to use modes (degrees/radians), table, and solver functions.
- Efficient calculator use saves time, especially for systems of equations, definite integrals, and statistics.
Algebraic Manipulation & Functions
- For inverses: swap x and y, then solve for y.
- Logarithm and exponential function manipulations may require applying properties like logₐ(x) = y ↔ aʸ = x.
Trigonometry & Identities
- Learn basic trig identities: sine, cosine, tangent, and their reciprocals (cosecant, secant).
- Example: tan(x) = sin(x)/cos(x); sin²x + cos²x = 1; sec²x = tan²x + 1.
Solving Equations & Calculus
- Systems of equations can be solved algebraically (elimination, substitution) or using a calculator.
- Calculus tasks may include finding derivatives (product rule: d(uv)/dx = u dv/dx + v du/dx) and definite integrals (area under curves).
Similar Triangles & Geometry Applications
- Recognize and use similar triangles for ratio problems, often appearing in statics and truss analysis.
- Area formulas for composite shapes may require combining standard shapes and referencing formula tables.
Vectors & Operations
- Dot product: yields scalar; A·B = AxBx + AyBy + AzBz.
- Cross product: yields vector; use determinant or calculator function.
- Unit vectors: divide the vector by its magnitude.
Statistics Essentials
- Mean: sum of values divided by count; standard deviation: root of average squared deviation.
- For normal distributions, use Z-tables to determine probabilities: Z = (μ - x)/σ.
- Linear regression: use calculator or Excel to best fit a line to data points.
- Binomial distribution: probability for k successes in n trials; use binomial formula or reference tables.
Key Terms & Definitions
- Slope-Intercept Form — Equation of a line: y = mx + b.
- Point-Slope Form — Equation: y - y₁ = m(x - x₁).
- Circle Equation — (x - h)² + (y - k)² = r².
- Derivative — Instantaneous rate of change; use rules like product rule.
- Definite Integral — Calculates area under a curve between two points.
- Dot Product — Vector operation giving scalar result.
- Cross Product — Vector operation giving a vector perpendicular to both inputs.
- Binomial Distribution — Gives the probability of k successes in n independent trials.
- Z-score — Standardized value: (μ - x)/σ.
- Standard Deviation — Measures the spread of data values.
Action Items / Next Steps
- Review reference handbook for key formulas and calculator functions.
- Practice using calculator for systems, statistics, and calculus problems.
- Revisit trig and calculus identities as listed in the FE reference manual.
- Complete any assigned review problems and prepare for next week: statics.