| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Angle between two vectors |
| Difficulty | Moderate -0.3 Part (a) is a straightforward application of the dot product formula to find the angle between two vectors—a standard AS-level mechanics technique. Part (b) requires using F=ma with the given acceleration to find mass, then applying it to the second particle—routine two-step calculation. Both parts are textbook exercises with no problem-solving insight required, making this slightly easier than average. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.03d Newton's second law: 2D vectors |
| Answer | Marks |
|---|---|
| 15(a) | Uses trigonometry to find angle |
| Answer | Marks | Guidance |
|---|---|---|
| PI by 51º (AWRT) or 75º (AWRT) | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| AWRT | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 15(b) | Obtains m = 0.8 | 3.1b |
| Answer | Marks | Guidance |
|---|---|---|
| ACF | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| CAO 𝑎𝑎 | 1.1b | A1 |
| Subtotal | 3 | |
| Question 15 Total | 5 | |
| Q | Marking instructions | AO |
Question 15:
--- 15(a) ---
15(a) | Uses trigonometry to find angle
above i for path of Q
PI by 51º (AWRT) or 75º (AWRT) | 1.1a | M1 | Q angle =
−1 15
tan �8�
Angle between paths =
62°
Obtains correct angle
AWRT | 1.1b | A1
62°
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 15(b) ---
15(b) | Obtains m = 0.8 | 3.1b | B1 | kg
4 = 5𝑚𝑚 ⟹ 𝑚𝑚 = 0.8
2 2
�8 +15 = 17 m s–2
17 = 0.8𝑎𝑎 ⟹ 𝑎𝑎 =21.25
Uses F = ma for Q for their m
ACF | 1.1a | M1
Obtains = 21.25
Condone missing units
CAO 𝑎𝑎 | 1.1b | A1
Subtotal | 3
Question 15 Total | 5
Q | Marking instructions | AO | Marks | Typical solutionTwo particles, $P$ and $Q$, are initially at rest at the same point on a horizontal plane.
A force of $\begin{bmatrix} 4 \\ 0 \end{bmatrix}$ N is applied to $P$.
A force of $\begin{bmatrix} 8 \\ 15 \end{bmatrix}$ N is applied to $Q$.
\begin{enumerate}[label=(\alph*)]
\item Calculate, to the nearest degree, the acute angle between the two forces.
[2 marks]
\item The particles begin to move under the action of the respective forces.
$P$ and $Q$ have the same mass.
$P$ has an acceleration of magnitude 5 m s$^{-2}$
Find the magnitude of the acceleration of $Q$.
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 2022 Q15 [5]}}