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Playbook

Units and Measurement

40 q - 1.03/paper - 0% HARD. New in 2025 and held in 2026. It has never produced a HARD question, and nearly all of it is how percentage errors add through a formula.

Questions in the bank
40
q/paper (2025–26 papers)
1.03
Tagged HARD
0%
Subtopic
1

Strand: Quick-Win

When you’ll see it

Measured values with their errors (a ± b, or a percentage), a quantity built from them by a formula, a least count, or the SI unit of a combination.

How this chapter is tested

40 q at 1.03 a paper and 0% HARD. It was not set once in the 29 papers before 2025, then carried 14 questions in the 13 papers of 2025 and 26 in the 26 papers of 2026. A student prepping only from older papers has never met it.

35 of the 40 are about measurement error, and most of those are one rule: for Q = aᵖbᵍ/cʳ, the percentage error in Q is p(Δa/a) + q(Δb/b) + r(Δc/c), every term added, whatever the sign of the power. Density from mass and length, kinetic energy from mass and speed, g from a pendulum: the same three lines each time.

The rest is a sum or a difference (absolute errors add), a least count, a mean with its mean absolute error, and a unit or a dimension. None of it has been HARD; the marks are lost to the two slips below, not to difficulty.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Errors through a product, quotient or power

    Relative errors add, each multiplied by its power: for Q = aᵖbᵍ/cʳ, ΔQ/Q = pΔa/a + qΔb/b + rΔc/c. A square root contributes half its error.

  • Errors through a sum or difference

    Absolute errors add: Δ(A ± B) = ΔA + ΔB. A difference of two close values has a large percentage error.

  • Least count and the mean

    The error in one reading is the least count of the instrument. For repeated readings, take the mean and the mean absolute error.

  • Units and dimensions

    Reduce a combination to base SI units or compare dimensions: L/R is a time, PV is an energy.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.

  • Subtracting the error of a divisor

    In a quotient the percentage errors still ADD. Density = m/l³ with 2% error in m and 1% in l carries 2 + 3 × 1 = 5%, not 2 − 3.

  • Forgetting the power

    A length cubed carries three times its percentage error, and a square root half. A sphere's volume with 2% error in r has 6%.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.

Units and Measurement notes

Drill every units and measurement question

40 questions from the bank, scoped to the named subtopic.

Drill the 40 questions

Drill one subtopic at a time

The 1 subtopic this playbook covers, in catalog order.

  • Units, Dimensions, and Error AnalysisDrill

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