Edexcel 2024 Paper 3 Question 3 Solution

Edexcel 2024 Paper 3 Question 3 – Motion on an Inclined Plane Explained

❓ The Question

💡 Teacher Explanation

This is one of those questions where if you start in the wrong direction, it just feels awkward the whole way through.

Nothing in it is actually that complicated. It’s just about organising things properly at the start.

You’re on a slope. So don’t think vertical/horizontal. Think along the slope and into the slope. That’s it.

If that part is clear, everything else is just following through.

Part (a) is really just one line once you see it.
Part (b) is the same idea but stretched out a bit.
Part (c) — no real maths, just understanding what’s going on.

🎯 How To Recognise This Question Type

Slope → split forces. Always.

🧠 Step By Step Solution

Start with the angle.

You’re given $\tan\alpha = \frac{5}{12}$ .

So just sketch a triangle. It saves thinking later.

That gives:

$\sin\alpha = \frac{5}{13}$
$\cos\alpha = \frac{12}{13}$

Now the forces.

Weight acts straight down. But that’s not helpful yet. So split it.

One part goes into the plane. One part goes down the slope.

Perpendicular direction first.

Nothing is moving there, so it balances:

$R = mg\cos\alpha = mg \cdot \frac{12}{13}$

Done.

Now along the slope.

Downwards component:

$mg\sin\alpha = mg \cdot \frac{5}{13}$

Friction acts up the slope:

$F = \mu R = \mu mg \cdot \frac{12}{13}$

Now just write the equation.

Down the slope:

$mg \cdot \frac{5}{13} – \mu mg \cdot \frac{12}{13} = ma$

Factor it:

$\frac{mg}{13}(5 – 12\mu) = ma$

Cancel $m$ :

$a = \frac{g}{13}(5 – 12\mu)$

That’s exactly what they want.

Last part.

If friction is big enough, it cancels the force down the slope.

So no movement.

The particle just stays where it is.

✅ Final Answer

(a) $\frac{12}{13}mg$
(b) $\frac{g}{13}(5 – 12\mu)$
(c) The particle remains at rest

🎯 Mark Scheme Breakdown

(a)

M1:
$R = mg\cos\alpha$ seen (resolving perpendicular)
A1:
$\frac{12}{13}mg$ seen
(accept $0.92mg$ or better, must be positive)

(b)

M1:
Equation of motion down the plane seen
e.g. $mg\sin\alpha – F = ma$ or $mg\sin\alpha – F = -ma$
A1:
Correct equation involving $mg\sin\alpha$ , $F$ , and $ma$ seen
(terms correct, allow sign errors / sin–cos confusion)
M1:
$F = \mu R$ seen with substitution
(must show $\mu \times R$ , not just $\mu R$ written)
A1*:
$\frac{1}{13}g(5 – 12\mu)$ seen
(must show substitution of trig ratios as fractions)

(c)

B1:
Clear statement that $P$ remains at rest seen
(e.g. “does not move”, “stays at rest”, “no sliding”, “equilibrium”)

✅ Key examiner notes

“Seen” is critical throughout — equations, substitutions, and final expressions must be explicitly written.
In (a), allow decimal equivalents of $\frac{12}{13}mg$ , but it must be positive.
In (b):
- Must use $mg$ for weight, not $W$
- Allow minor sign or trig slips for method marks
- $\mu R$ alone is not enough — substitution must be shown
- Using $\mu = \frac{5}{12}$ incorrectly scores M0
Final answer requires at least one further line of working with substituted fractions.
In (c), accept any valid statement of equilibrium; ignore lack of explanation but not contradictions.

Total: 7 marks

⚠️ Examiner Insight

Most students were fine here once the setup was in place. The marks that were lost were usually small but costly.

The biggest issue was mixing up $\sin\alpha$ and $\cos\alpha$ . That tends to happen when no quick sketch is made, so the directions aren’t properly fixed. Once that goes wrong, everything that follows is affected.

Another common problem was not matching the given answer exactly. Being close isn’t enough on a “show that” — the expression has to line up fully, otherwise the final mark isn’t awarded.

In part (c), some answers were too vague. It needs a clear statement that the particle stays at rest. If that isn’t said directly, the mark isn’t secure.

A quick diagram at the start usually prevents most of this. It makes it clear that $\cos\alpha$ acts into the plane and $\sin\alpha$ acts along it. Also, with “show that”, it helps to keep an eye on the target form early so the algebra is heading in the right direction.

💬 Need help with questions like this?

Often it’s the first step. Once you’re in, it’s usually manageable. But getting started can feel a bit unclear.

Working through a few of these with a private A Level Maths tutor can help settle that. It stops that hesitation at the beginning.

🔗 Next Steps

← Question 2 Solution
→ Question 4 Solution

👨‍🏫Author Bio

S Mahandru is a maths tutor who focuses on helping A Level students make their working clearer, so they can pick up the marks that are often missed.

📊 Final Summary

✅ Do This	❌ Avoid This
Split forces early	Guessing
Use correct trig	Mixing up
Match exact form	“Close enough”
Sketch diagram	Skipping

❓ Frequently Asked Questions

📌 Why split the weight?

Because it’s not moving vertically. It’s along the slope, so you have to split it.

📌 How do I choose sin or cos?

Just match the direction. Along the slope is sin. Into the slope is cos.

📌 Why does the form matter?

It’s a “show that”, so it has to match. Close isn’t enough.

📌 What is part (c) checking?

If friction is enough to stop it moving. If it is, nothing happens.