| Exam Board | AQA |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Parallel or perpendicular vectors condition |
| Difficulty | Standard +0.3 This is a straightforward mechanics question testing vector concepts. Part (a) requires calculating Q's velocity vector and showing it's a scalar multiple of P's velocity (routine). Part (b) is a simple conceptual point about velocity vs speed. Part (c) involves setting up position vectors and using the distance formula, but follows a standard approach with clear given information. The 9 total marks reflect length rather than conceptual difficulty—all techniques are standard A-level mechanics applications with no novel problem-solving required. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement1.10f Distance between points: using position vectors1.10g Problem solving with vectors: in geometry1.10h Vectors in kinematics: uniform acceleration in vector form |
| Answer | Marks |
|---|---|
| 20(a) | Subtracts the two given position |
| Answer | Marks | Guidance |
|---|---|---|
| Condone either order | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| velocity for Q is 3i + 4j | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| move along parallel lines | 2.1 | R1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 20(b) | States one of the following |
| Answer | Marks | Guidance |
|---|---|---|
| • Q could accelerate | 2.3 | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 20(c) | Obtains 12 m for distance from | |
| X to R | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| PI by XP = 5 m | 3.1a | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone t = 2 | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| and concludes that θ=90 o | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| lines | 2.1 | R1 |
| Subtotal | 5 | |
| Question 20 Total | 9 | |
| Q | Marking instructions | AO |
Question 20:
--- 20(a) ---
20(a) | Subtracts the two given position
vectors for Q
Condone either order | 3.1a | M1 | (14i + 5j) – (5i – 7j)
= 9i + 12j
= 3(3i + 4j)
P and Q move along parallel lines.
Obtains 9i + 12j for the
displacement of Q ACF
Or
Demonstrates that the average
velocity for Q is 3i + 4j | 1.1b | A1
Completes reasoned argument
to show that 9i + 12j = 3(3i + 4j)
and concludes that P and Q
move along parallel lines | 2.1 | R1
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 20(b) ---
20(b) | States one of the following
expressions
• constant velocity is not
the same as average
velocity
• Q’s speed may change
• Q could accelerate | 2.3 | E1 | Constant velocity is not the same as
average velocity
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 20(c) ---
20(c) | Obtains 12 m for distance from
X to R | 1.1b | B1 | P’s speed = 3i+4j = 5 m s–1
Distance from X to P = 5(3 – 2)
= 5 m
Distance from X to R = 12 metres
5 2 +12 2 =13 2
P and R are moving along
perpendicular lines.
Obtains 5 m s-1 for the speed of
P
PI by XP = 5 m | 3.1a | B1
Calculates the distance travelled
by P using their speed for P and
t = 1
Condone t = 2 | 1.1a | M1
Identifies 5, 12 and 13 as a
Pythagorean triple
May be seen on a diagram
Or
Correctly applies the cosine rule
132 =122 +52 −2×12×5×cosθ
and concludes that θ=90 o | 1.1b | A1
Completes a reasoned
argument that PXR is a right-
angled triangle with hypotenuse
PR and concludes that P and R
move along perpendicular lines
Or
Completes a reasoned
argument that angle PXR is a
right angle and concludes that P
and R move along perpendicular
lines | 2.1 | R1
Subtotal | 5
Question 20 Total | 9
Q | Marking instructions | AO | Marks | Typical solutionTwo particles $P$ and $Q$ are moving in separate straight lines across a smooth horizontal surface.
$P$ moves with constant velocity $(3\mathbf{i} + 4\mathbf{j})$ m s$^{-1}$
$Q$ moves from position vector $(5\mathbf{i} - 7\mathbf{j})$ metres to position vector $(14\mathbf{i} + 5\mathbf{j})$ metres during a 3 second period.
\begin{enumerate}[label=(\alph*)]
\item Show that $P$ and $Q$ move along parallel lines.
[3 marks]
\item Stevie says
Q is also moving with a constant velocity of $(3\mathbf{i} + 4\mathbf{j})$ m s$^{-1}$
Explain why Stevie may be incorrect.
[1 mark]
\item A third particle $R$ is moving with a constant speed of 4 m s$^{-1}$, in a straight line, across the same surface.
$P$ and $R$ move along lines that intersect at a fixed point $X$
It is given that:
• $P$ passes through $X$ exactly 2 seconds after $R$ passes through $X$
• $P$ and $R$ are exactly 13 metres apart 3 seconds after $R$ passes through $X$
Show that $P$ and $R$ move along perpendicular lines.
[5 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 2 2024 Q20 [9]}}