A wrong number can look exactly like a right one on the page. Four quick checks tell you whether the answer makes physical sense: its size, its unit, its direction and its behaviour in an extreme case.
This page is for students whose marks fall on calculations they believed were correct. It sits with the other help pages for SPM Physics.
What does this sound like?
A student might say, “I used the right formula and my calculator agrees with me, but the answer is marked wrong.” Or, “I got 0.0012 s for a car to stop and did not notice.”
Both come from trusting the arithmetic and skipping the meaning. The working is tidy, so the final number goes unquestioned.
What usually causes it?
There are three academic causes.
- The question was answered one step at a time, so nothing checks the final result against the situation.
- Quantities have no felt size. Without a sense of what 10 N, 2 m s⁻² or 1000 W look like, a wrong number cannot look wrong.
- Units and signs are treated as decoration, not as part of the answer.
A worked example
A trolley of mass 2.0 kg is pulled by a force of 8.0 N on a smooth table. A student writes a = F × m = 8.0 × 2.0 = 16 m s⁻².
Run the four checks.
- Size: 16 m s⁻² is more than a falling stone gains each second (about 10 m s⁻²), far too much for a light 8.0 N pull.
- Unit: force times mass gives kg N, not m s⁻².
- Direction: acceleration should point the way the force points.
- Extreme case: doubling the mass should halve the acceleration, but the student’s formula doubles it.
The correct relation is a = F ÷ m = 8.0 ÷ 2.0 = 4.0 m s⁻². The size, unit and extreme-case checks would each have caught the error.
What can you do on your own?
Build the checks into every calculation.
| Check | Question to ask | Quick test |
|---|---|---|
| Size | Is it plausible? | Compare with a known quantity |
| Unit | Does the unit match the quantity? | Write the unit chain |
| Direction | Does the sign fit the situation? | Sketch the motion |
| Extreme case | Does it behave sensibly if a value doubles or goes to zero? | Change one input |
Keep a short list of reference sizes: a person weighs about 600 N, a kettle has a power of about 2000 W, and a car accelerates at about 3 m s⁻². Log each mistake you catch with the mistake log and paper error review so that patterns show up. The units and significant figure checker helps with the unit check, and checking a numerical result with estimation covers the estimate.
When might one-to-one tuition help?
Self-checking works when you can already see that a result looks odd. If the checks pass but the answer is still wrong, or you cannot tell what a sensible size is, the gap may be in the physics and not the habit.
In a one-to-one lesson, a teacher can ask you to predict the size before calculating, then look at where your prediction and your answer differ. This may be worth considering if the same kind of wrong answer keeps coming back. See online one-to-one Physics tuition and the one-hour trial class (from RM50) if you would like to try a lesson.
What to read next
Once the checks are in place, turn the verified number into a statement in why a physics numerical answer needs a sentence.