When I mark my high school students’ tests, the mistakes I find are almost always the same five. They are not calculation mistakes: they are mistakes of method, and once you learn to recognise and avoid them your grades go up very quickly.
We are in the weeks of the first physics tests of the year, in every type of school: this post gathers the cross-cutting mistakes, the ones that look the same from the first two years to Year 5. If you are looking for something more specific for your year and your type of school, you will find the dedicated posts in the section below.
Where to start, depending on your year
- Year 3: first physics test in Year 3, measurements and significant figures at the art high school, resolving forces and vectors without trigonometry, work, energy and collisions in Year 3.
- Year 2 (technical track): dynamics on the inclined plane.
- Year 4: motion graphs for the human-sciences track, work and energy at the classical high school, waves and sound at the science high school, electrostatics and circuits.
- Year 5: electromagnetic induction.
1. Skipping the force diagram
Faced with a dynamics problem most students write the formula straight away. It is a mistake. Before writing any equation you have to do two things: draw the system and sketch the force diagram on each body.
It seems a waste of time, but it is the opposite: the diagram reveals which forces are involved and in what direction they act. Without a diagram you end up forgetting the friction force, getting the sign of the tension wrong or confusing the normal force with the weight. Make it a rule never to write a single formula without having made the drawing first.
The mistake I see most often, on the inclined plane: writing the normal reaction as
On the inclined plane it is not true: the normal force balances only the perpendicular component of the weight, so
Whoever has drawn the diagram and resolved the weight into its two components does not fall for it; whoever went by rote does, and carries the mistake right to the end of the problem even if the calculations afterwards are impeccable.
2. Getting the frame of reference wrong
Once the diagram is done, a frame of reference has to be chosen and stated explicitly. Which direction is positive? Where is the origin? It is the detail that makes the difference between a consistent solution and one full of sign errors.
The practical advice: write on the sheet “I choose positive to the right” or “y-axis upwards”, even if it seems trivial. The sign of an acceleration or a velocity makes no sense without a stated frame of reference.
Classic case: an object thrown upwards at . If you declare the -axis positive upwards, then and — the acceleration is negative because it points downwards, not because the object “is slowing down”. Whoever does not declare the frame tends to write both positive “because it is going up”, and from then on every result has the wrong sign. Note that stays in the descent phase too: gravity does not change direction halfway through the problem, and this is exactly the point that stands out only if the frame is written down.
3. Ignoring dimensions
Every physical quantity has a unit of measurement. Adding metres and seconds is a mathematically impossible mistake, but it happens every day in tests. The way to avoid it is the dimensional check: every time you write a formula, stop for 10 seconds and check that the same units appear on the right and left of the equals sign.
It also works the other way round: if you do not remember a formula, the dimensional check often helps you rebuild it. A velocity must have the dimensions of length/time. An energy must have the dimensions of mass times velocity squared. They are strong constraints.
How to use it in practice. You do not remember whether the period of the pendulum is
or
Check: has dimensions , whose root is a time — correct. The other would give , whose root is : a frequency, not a period. In ten seconds you have settled a doubt that by memory stays fifty-fifty.
Watch out for mixed units too: if the problem gives km/h and the formula uses metres, the dimensional check does not notice — the dimensions still match. Always convert everything to SI units before substituting the numbers, not after.
4. Not recognising conservation laws
Almost all non-trivial problems are solved by using a conservation principle: of energy, of momentum, of angular momentum. Yet many students try to integrate the equations of motion even when the problem asks only for the final speed.
Before writing , ask yourself: is something conserved? If so, writing the conservation equation is almost always the quickest and safest route. If not, then yes, you go to the equations of motion.
An example that gets the idea across: an object slides down a curved frictionless slide of height , and the speed at the bottom is asked. With the equations of motion it is a disaster, because the acceleration changes continuously along the curve. With energy it is one line:
And you discover something the problem did not say: the final speed does not depend on the mass or on the shape of the slide, only on the height difference. The two questions to ask every time are: is there friction? (if not, mechanical energy is conserved) and are there impulsive external forces? (if not, momentum is conserved in the collision).
5. Applying formulas without understanding the phenomenon
This is the father of all mistakes. If you study physics by learning 50 formulas by heart and do not know when to apply them, you are lost faced with a new problem. Physics is not maths with numbers: it is the description of a real phenomenon.
The remedy is to tell the problem in words before writing it. “There is a ball falling from a height . It is accelerating because there is gravity. The speed with which it hits the ground depends only on the energy it had at the start.” Only after describing the phenomenon do you move to the equations.
Extra mistake: the free-body diagram with invented forces
A specific flaw in the force diagram of point 1 deserves a section of its own, because it is not “forgetting” a force but drawing one that does not exist. The two variants I see most often:
- the “centrifugal force” drawn as if it were a real force pushing outwards in circular motion, when the only real force is the centripetal one (tension, friction, gravity) directed towards the centre;
- friction drawn in the wrong direction, because people tend to think of it as a force that “helps” or “brakes always in the same way”, instead of remembering that it always opposes the relative motion, whatever it is.
Worked example: a block of mass is launched upwards along a rough inclined plane of , with coefficient of kinetic friction . Find the deceleration while the block is going up.
Correct diagram: while the block goes up, it moves up the plane, so friction — which opposes the motion — points down the plane, in the same direction as the component of the weight. The two braking forces add:
Wrong diagram (the mistake I see): drawing friction upwards, as if it always opposed gravity instead of the motion. With that direction the equation becomes
The wrong result is about half the correct one — not a rounding error, a mistake that changes how far the block climbs the plane before stopping. Note also that if the same block were going down instead of up, the correct direction of friction would reverse compared with this case: it is always “opposite to the motion”, never a fixed direction tied to the slope. The lesson: the direction of friction is not decided by looking at the drawing of the plane, it is decided by looking at which way the body is moving at that instant.
A practical exercise
Next time you do a physics exercise, before writing anything follow this 4-step checklist:
- Draw the system and the force diagram.
- State the frame of reference.
- Identify any conservation principles.
- Only at this point write the first equation.
For the first few days it will seem to take longer. After two weeks it becomes automatic, and your grades go up.
How to review a marked test (the part almost nobody does)
Picking up the test and looking only at the grade is wasted time. When you take it back in hand, sort every mistake into one of these three boxes:
- I didn’t know it — a gap in theory. It is cured by studying that topic.
- I knew it but got the calculations wrong — an execution error. It is cured by slowing down and redoing the step, not by rereading the theory.
- I didn’t understand what the problem was asking — a reading error. It is cured by the habit of rephrasing the text in your own words before starting.
They are three different illnesses with three different cures, and most students treat them all the same way (“I’ll study more”). After two or three tests sorted like this you will notice that your mistakes almost always fall in the same box: that is the thing to work on.
If your mistakes are concentrated in the third box and under test conditions your mind goes blank even on topics you know, the problem is probably not physics: read how to manage test anxiety in maths and physics.
In summary
Four of the five mistakes above are not about physics: they are about the order in which you tackle the problem. Drawing, frame of reference, dimensions, conservation laws — they are all steps that come before the first equation, and that is exactly why they get skipped.
The good news is that they are corrected quickly, because they are habits and not knowledge: you do not have to relearn mechanics, you have to change the first two minutes of every exercise.
If your problem is more the way you study than the mistake on a single exercise, start from the Feynman method for physics; if instead you have to make up a failed subject, the plan is in catching up on a physics failed subject. Dimensions let you down in calorimetry too, where joules and calories coexist: see specific heat and thermal equilibrium. To train against the clock there are the mock maths and physics tests for high school.
If you want a hand building this method on your real tests, write to me or take a look at physics tutoring.
