Class 10 Science Numericals: Audit Units, Time and Signs

A calculation you can audit

1. 1

   Known and required

   List each given quantity with its unit; name the unknown.

2. 2

   Model and convention

   Choose the relation and state any sign convention or idealisation.

3. 3

   Convert and substitute

   Make units consistent, then substitute signed values in one visible line.

4. 4

   Interpret and check

   Give the unit and explain what the size or sign means in this situation.

An original lens-power example

A convex lens in air has focal length +40 cm. The required quantity is power in dioptres. Convert first: +40 cm = +0.40 m. Therefore P = 1/f = 1/0.40 = +2.5 D. The positive sign agrees with a converging lens.

Using 1/40 = 0.025 and attaching D at the end does not repair the omitted conversion. The unit is part of the calculation, not a decoration added to whichever number appears.

Electrical energy: choose joules or kilowatt-hours

An ideal 60 W lamp operates for 2 hours. For joules, E = Pt = 60 × (2×3600) = 432,000 J. For the commercial unit, 60 W = 0.060 kW, so E = 0.060 × 2 = 0.120 kWh. These are the same energy: 1 kWh = 3.6×10⁶ J. Multiplying 60 by 2 gives 120 Wh, not 120 J.

A 10 Ω uniform wire is 2 m long with cross-sectional area 0.50 mm². In ρ = RA/L, convert area as a squared length: 0.50 mm² = 0.50×10⁻⁶ m². Hence ρ = 10×0.50×10⁻⁶/2 = 2.5×10⁻⁶ Ω m. This is an original ideal-wire example, not an identification of its material. Confusing 0.50 mm² with 0.00050 m² makes the answer 1,000 times too large.

The electrical examples practise unit reasoning. The linked current curriculum and sample paper contain conflicting assessment wording; confirm your assessed topic list with your school. These examples do not resolve that conflict.

Keep a small conversion reference

Swipe across the table to see all columns.

Use the answer to test the setup

Ask whether the unit matches the requested quantity. An area should not end in centimetres alone, and a reciprocal metre can represent dioptres in the lens-power context. Check whether a negative sign is meaningful, rather than erasing it because physical sizes are usually positive.

Estimate the result before exact arithmetic. A focal length below one metre has power magnitude above one dioptre. This catches a factor-of-100 mistake without repeating the whole calculation.

Review the first wrong line

When marking an attempt, classify the first error as model, conversion, sign, substitution or arithmetic. Correct that line and recompute what follows. Copying only the final answer leaves the underlying error ready to recur. Use the specific official marking scheme to assess marks; this workflow is a study aid, not a marking policy.

Choose what to study next

Sources and scope

This is a focused learning resource, not a complete chapter or a prediction of board questions. Use your current syllabus and the paper-specific marking scheme for assessment requirements.

Try a short check, then return to the explanation

Optional TutorMax original practice: five questions on light, lenses and mirrors, with explanations and a fresh retest. These checks sample a few skills; they are not official paper questions or a whole-subject readiness score. Existing explanations and official paper downloads stay available on this page.