Foundations

Distinguish part-to-part ratios, fractions of a whole and rates with units. Scale quantities together, compare unit rates, and explain when a relationship is proportional. Check zero cases, starting amounts and whether a result fits its context.

Describe a quantity as a numerical value with a unit, and distinguish its physical kind from its dimension. Build length, area, volume and rate units, check meaningful combinations, and separate exact unit relations from measurement uncertainty.

Convert quantities with exact unit ratios, track cancellation through compound units, and apply the correct powers to area and volume. Distinguish temperature readings from differences, check dimensions and context, and retain measurement uncertainty when reporting.

Distinguish exact model values, rounded approximations and estimates from measurements. Declare the rounding rule, preserve information through calculations and unit changes, and interpret resolution, precision, accuracy and the stated uncertainty type without turning a report’s digits into guaranteed bounds.

Locate a point from an ordered pair, read named axes and their scales, and connect the same values in words, tables and plots. Keep signs, fractions and units exact, distinguish an axis point from a quadrant point, and separate selected observations from a stated rule and its domain before drawing connections.

Read a straight line as a stated relationship, calculate its slope from consistent signed coordinate changes, and interpret its intersections with the axes. Keep horizontal, vertical and coincident-point cases distinct, attach units and domain conditions to context models, and use numerical scales rather than appearance alone to judge a line’s change.

Read a graph’s quantities, units, ticks and context before judging its visual impression. Calculate differences, reference-based percentages and interval rates from the represented values; distinguish legitimate zoom from distorted spacing; and keep samples, interpolation, missing information, uncertainty and causal explanations separate.

Choose the physical quantity you want to investigate, specify the point, event or location involved, and explain how a reading relates to that quantity.

Describe displacement with fixed-axis components, combine compatible vectors, and use small exact examples to introduce span, independence, basis and real vector spaces.

Build an inspectable physics record, test and revise a bounded cart model, preserve processing history, and plan findable data with appropriate sharing conditions.

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

Sine and cosine are unit-circle coordinates whose squared values sum to one.

A linear map preserves linear combinations and has a matrix once bases are chosen.

A derivative is a finite limit of local difference quotients.

A definite integral is the limiting signed accumulation of small contributions.

Continuity connects differentiation with integration.

Use dimensions to detect impossible quantity equations.

The mole is linked to a specified number of entities.

A specified frequency fixes the photometric SI reference.

A primary caesium frequency standard relates its oscillator to the defining unperturbed Cs-133 hyperfine transition by estimating and correcting design-dependent shifts, including atomic-motion Doppler and thermal blackbody effects.

With calibrated light frequency f, vacuum wavelength is λ₀=c/f.

A Kibble balance combines weighing mg=I Bℓ with velocity-mode U=vBℓ to eliminate the common geometry-field factor: mgv=IU.

An ion's equilibrium potential balances its chemical and electrical driving terms.

Scaling the system amount is different from changing its state.

Common non-SI unit names require their correct SI scale factors.

Solid, liquid and gas describe bulk behavior rather than chemical identity.