Bac STI2D - independent subject practice cheat sheet

State the system boundary and assumptions before calculation.

Units, sign conventions and uncertainty are part of the answer.

Verification against a specification differs from validation for an intended use.

Drawings need a declared convention and controlled revision.

Classroom models do not authorize physical operation or structural approval.

Engineering stress σ = F/S₀ uses original area; E = σ/ε applies to the linear elastic region. Engineering stress itself is not confined to that region.

Toughness = whole curve area; resilience = elastic area

Hardness is not fundamental but correlates with strength

Grain refinement commonly increases yield strength in conventional metallic microstructures, subject to material and scale limits.

Selection needs specific indices (σ/ρ, E/ρ) plus cost and durability

R=d/λ uses thickness in metres; total resistance includes the model’s surfaces and layers.

U=1/R_total is a steady-state element model, not the complete building energy demand.

Permanent, occupancy, wind and snow actions require the stated design framework.

Moisture, airtightness and intended ventilation must be considered together.

Example tie spacing is supplied data, not a code rule.

1 kWh = 3.6 MJ; 1 tep ≈ 41.86 GJ

Conversion efficiency must use a consistent useful output and input; it differs from a heat pump coefficient of performance, which can exceed one.

Carnot heat-engine efficiency is1−T_cold/T_hot using kelvin and the stated hot/cold reservoirs.

Hydro: P = η·ρ·g·Q·H

Wind power grows with v³; Betz limit C_p = 0.593

Sustainability is assessed per kWh: CO₂, life cycle, energy mix

For a sinusoid V_rms = V_peak/√2; the stated impedance magnitude is for a series RLC model.

Q_C = P(tan φ₁ − tan φ₂) for power-factor correction

Transformer: V₁/V₂ = N₁/N₂ = I₂/I₁

Induction motor: n = (1 − s)·60f/p

Thévenin voltage is open-circuit voltage; deactivate independent sources to obtain resistance while preserving dependent-source behavior.

Karnaugh: give the minimum sum of products

Sensitivity = Δoutput/Δinput; resolution = smallest detectable change

Closed-loop error compares reference and measurement; integral action can remove appropriate steady-state error only under suitable stability and operating assumptions.

PLC scan: read inputs → run program → update outputs

4–20 mA live zero: (I − 4)/16 of the span

Repeatability ≠ accuracy, resolution ≠ sensitivity

Robot DOF come from its joints; workspace is the reachable volume

Fetch-decode-execute uses the PC, IR, ALU, and registers.

Memory hierarchy: registers, cache, RAM, storage, offline.

RAM is volatile; SSDs retain data without power.

A process has its own address space; threads share one.

Authentication verifies identity; authorization grants permissions.

TCP is reliable and connection-oriented; UDP is connectionless and lower overhead.

IP addresses route between networks; MAC addresses work on the local link.

A /26 subnet has 64 addresses and 62 usable hosts.

DNS resolves names; DHCP assigns addresses.

Security protects data; privacy governs collection and use.

Chain rule: never drop the inner derivative g'(x).

Integration by parts: choose u so du is simpler than u.

Change limits immediately when substituting in a definite integral.

Improper integrals require an explicit limit, not direct substitution.

Implicit differentiation collects dy/dx terms after differentiating both sides.

State domain restrictions before simplifying; cancelled factors still exclude values.

Composition f(g(x)) is evaluated inside-out and is generally not commutative.

Inverses require one-to-one functions; domain and range swap.

Horizontal transformations act opposite to the sign or factor shown.

Log laws convert sums to products, enabling solution of log equations.

Always check candidate solutions against original domain restrictions.

n = m/M, n = cV (V in dm3) and n = V/24.0 for gases at RTP are the three key conversions.

The limiting reagent is the one with the smallest moles ÷ coefficient; product amount depends on it.

Percentage yield measures practical success; atom economy measures how much reactant mass is useful.

Dilution uses c1V1 = c2V2 because the moles of solute do not change.

Always balance the equation before applying any molar ratio.

ΔH is negative for exothermic reactions; standard enthalpy of formation of an element in its standard state is zero.

q = mcΔT uses the total mass of solution, and ΔH per mole = −q/n.

Hess's law lets you combine any route; combustion data are used in the reverse order to formation data.

ΔH = Σ bonds broken − Σ bonds formed, and mean bond enthalpies are averages.

Feasibility is determined by ΔG = ΔH − TΔS, not by ΔH alone.

Orders are determined experimentally, not from stoichiometric coefficients.

Rate constant units depend on overall order: for second order overall, dm3 mol−1 s−1; for third order overall, dm6 mol−2 s−1.