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.

Choose what belongs to an investigation, describe its condition at a stated time, and identify interactions with what lies outside its boundary.

Choose what a model represents, make its simplifications explicit, and check whether its predictions answer the physical question you actually asked.

Identify what a scientific statement does, examine its evidence and conditions, and avoid treating its name as a score for certainty.

Build a useful estimate, compare a correction with a stated reference scale, and check what is lost when you leave out a term.

Specify a transformation, identify what stays unchanged, and distinguish symmetry of an object from invariance of a physical model.

Use a defined system and a named quantity to track transfers, distinguish changing parts from conserved totals, and check the conditions of energy and momentum balances.

Choose a descriptive level, connect collective quantities with component behavior, and check when a simpler physical description answers a specified question.

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.

Describe a point's motion on a chosen straight axis, then connect signed changes, instantaneous rates and one exact set of position, velocity and acceleration graphs.

Choose one body, identify the forces acting on it, and use their vector sum to distinguish acceleration, balanced motion and mutual interactions.

Connect force and displacement to changes in motion, follow a spring’s stored energy, and distinguish an energy transfer from its rate.

c denotes the speed of light in vacuum. Its numerical value is fixed exactly in SI units.

h denotes the Planck constant. Its numerical value is fixed exactly in SI units.

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.

An inverse-square force models attraction between point masses.