Numericals are a routine, not a talent. Five steps for Matric and FSc physics, one worked example, the mistakes that cost marks, and how to practise from past papers.
Every physics teacher knows this student. They understand the chapter and can explain it in words, but the moment a numerical appears, their mind goes blank. Or they grab the first formula they see, push numbers into the calculator, and get an answer a thousand times too big because the mass was in grams.
Numericals are not a talent. They are a routine, and a routine can be learned. Here is one that works the same way in Matric and FSc.
The five steps
1. Read twice, then list the givens with units
Write “Given:” and list each quantity as symbol, value and unit, one per line. Convert to SI units now: km/h to m/s, grams to kilograms, centimetres to metres, minutes to seconds. Then write what is asked, for example “To find: t”.
Watch for givens hidden in words. “Starts from rest” means vi = 0. “Comes to rest” means vf = 0. “Dropped” means the starting velocity is zero. At the top of its flight, a ball thrown upwards has zero velocity for an instant.
2. Choose the formula from what is asked
Don’t start from the formula you remember best. Start from the unknown, and find the equation that links it to quantities you already have. For straight-line motion with constant acceleration, each equation leaves one quantity out:
- vf = vi + at has no distance;
- S = vit + ½at² has no final velocity;
- 2aS = vf² − vi² has no time.
So if a question never mentions time and doesn’t ask for it, the third equation is probably the one.
3. Rearrange before you put numbers in
Make the unknown the subject with symbols first, a = (vf − vi) / t, and only then bring in numbers. You make fewer arithmetic slips, and the examiner can follow your method. Working that can be seen is working that can earn marks.
4. Units all the way through
Write the unit next to every number when you substitute, and let the units work out too: (m/s) ÷ s gives m/s², exactly the unit of acceleration. If the unit comes out wrong, so did the formula or the rearranging.
This is not fussiness. In 1999 NASA lost the Mars Climate Orbiter as it arrived at Mars, because software on the ground used English units while the software on board used metric. A whole spacecraft, gone over units.
5. Sanity-check the answer
Is the answer believable? A car accelerating at 300 m/s² would leave the driver on the back seat. A ball thrown upwards that takes 40 minutes to come down means a mistake somewhere. Check the sign, check the unit, and round to a sensible number of significant figures.
One worked example
A car starts from rest and reaches a speed of 72 km/h in 10 s. Find its acceleration and the distance it covers in this time.
- Given: vi = 0 (starts from rest), vf = 72 km/h = 72 × 1000 ÷ 3600 = 20 m/s, t = 10 s. To find: a and S.
- Formula: for a, use vf = vi + at, which links a with vf, vi and t. For S, use S = vit + ½at².
- Rearrange: a = (vf − vi) / t.
- Substitute with units: a = (20 m/s − 0) ÷ 10 s = 2 m/s². Then S = (0)(10 s) + ½ × 2 m/s² × (10 s)² = 100 m.
- Check: an acceleration of 2 m/s² is gentle for a car, so it is believable. Cross-check the distance with the average speed: halfway between 0 and 20 m/s is 10 m/s, and 10 m/s × 10 s = 100 m. Two methods, one answer.
The mistakes that cost marks every year
- Units: km/h left unconverted, grams used as kilograms, cm² treated like m² (1 cm² is 0.0001 m², not 0.01).
- Significant figures: copying nine digits from the calculator. Give about as many significant figures as the least precise value in the question, and round only at the end.
- The sign of g: decide which direction is positive before you start, and keep it. If up is positive, g = −9.8 m/s² for the whole problem, going up and coming down. Use the value of g that the question or your textbook gives.
- Degrees and radians: check the calculator’s mode before every paper. In degree mode sin 30 is 0.5; in radian mode it is about −0.99. Circular motion formulas such as S = rθ need radians.
- No working: if the final answer is wrong and nothing else is written, there is nothing left for the examiner to give marks for.
How to practise from past papers
Collect your board’s papers from the last five years, from the board’s website if it has them or from a past-paper book from the bazaar. List every numerical by chapter.
- While learning a chapter, do its numericals one after another until the five steps feel automatic.
- Then practise in mixed sets: three numericals a day from different chapters, about 20 minutes. Mixing forces you to decide which formula each question needs, and that is exactly what the exam asks. In a large US trial with 787 Class 7 maths students, those who practised mixed problem types scored about 62% on a test six weeks later; those who practised one type at a time scored about 38%.
- Keep a mistake notebook: the mistake, why it happened, and the correct step. Redo those questions three days later.
- In the last month, do the numerical part of past papers against the clock.
Tonight, pick three numericals from last year’s paper and solve them with the five steps written down the margin. Slow is fine. Speed comes from the routine, not from rushing.
For a weekly plan that fits numericals around your other subjects, see our post on study methods for Matric and Inter. And if you would like someone to check your working, you can find a physics teacher in five taps.
