Mathematics and Basic Sciences
What this domain tests
Mathematics and Basic Sciences checks whether you can set up and sanity-check engineering calculations: units, algebra, calculus, statistics, chemistry, and physics fundamentals. Questions are usually embedded in an engineering context rather than pure math.
Core rules
- Carry units through every step; a dimensionally inconsistent equation is wrong regardless of arithmetic.
- Convert to consistent base units (N, m, s, Pa, K) before substituting.
- Distinguish gauge from absolute pressure: p_abs = p_gauge + p_atm.
- For a normal distribution, z = (x − μ)/σ; the table gives the area to the left.
- Use sample standard deviation (n − 1) when data are a sample, population σ when the full population is given.
Worked example
A test result is normally distributed with μ = 100 and σ = 10. Find the probability a reading exceeds 120. z = (120 − 100)/10 = 2.00. The cumulative area to the left of z = 2.00 is 0.9772, so the right-tail probability is 1 − 0.9772 = 0.0228, about 2.3%. Check: 120 is two standard deviations above the mean, and roughly 95% lies within ±2σ, so about 2.5% should lie above +2σ. The answer is plausible.
Traps
- Using a two-tailed area when the question asks “exceeds”.
- Mixing kPa and Pa, or mm and m, in the same formula.
- Treating a percentage as a fraction (2.3% = 0.023, not 2.3).
- Reporting more significant figures than the inputs support.