| Exam Board | AQA |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Triangle and parallelogram problems |
| Difficulty | Moderate -0.8 Part (a) is trivial vector subtraction (1 mark). Part (b) requires showing opposite sides are equal vectors (parallelogram) and adjacent sides have different magnitudes (not rhombus) - this is straightforward application of standard vector techniques with no problem-solving insight needed. The 5 marks reflect routine calculations rather than conceptual difficulty. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10f Distance between points: using position vectors1.10g Problem solving with vectors: in geometry |
| Answer | Marks | Guidance |
|---|---|---|
| 14(a) | Obtains correct vector | AO1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| 14(b) | Obtains one other edge as vector | AO1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| Obtains correctly both CB and DA | AO1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| (or its square) | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| different edges | AO1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| not a rhombus | AO2.1 | R1 |
| Total | 6 | |
| Q | Marking Instructions | AO |
Question 14:
--- 14(a) ---
14(a) | Obtains correct vector | AO1.1b | B1 | 4
3
6
--- 14(b) ---
14(b) | Obtains one other edge as vector | AO1.1a | M1 | 1
(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318)
(cid:1828)(cid:1829) (cid:3404) (cid:3437) 5 (cid:3441)
(cid:3398)1
1
(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318)
(cid:1827)(cid:1830) (cid:3404) (cid:3437) 5 (cid:3441)
(cid:3398)1
(cid:3398)4
(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318)
(cid:1830)(cid:1829) (cid:3404) (cid:3437)(cid:3398)3(cid:3441)
6
AB 42 32 62
61
AD 12 52 12
3 3
(cid:1827)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1828)(cid:4652)(cid:1318) (cid:3404) (cid:4652)(cid:1830)(cid:4652)(cid:4652)(cid:4652)(cid:1829)(cid:4652)(cid:1318)
ABCD must be a parallelogram
AB AD
ABCD is not a rhombus
Obtains DC correctly
Or
Obtains correctly both BC and AD
Or
Obtains correctly both CB and DA | AO1.1b | A1
Obtains length of one edge
(or its square) | AO1.1a | M1
Obtains two correct lengths of
different edges | AO1.1b | A1
Completes rigorous argument to
show ABCD is a parallelogram and
not a rhombus | AO2.1 | R1
Total | 6
Q | Marking Instructions | AO | Marks | Typical SolutionA quadrilateral has vertices A, B, C and D with position vectors given by
$$\overrightarrow{OA} = \begin{pmatrix} 3 \\ 5 \\ 1 \end{pmatrix}, \overrightarrow{OB} = \begin{pmatrix} -1 \\ 2 \\ 7 \end{pmatrix}, \overrightarrow{OC} = \begin{pmatrix} 0 \\ 7 \\ 6 \end{pmatrix} \text{ and } \overrightarrow{OD} = \begin{pmatrix} 4 \\ 10 \\ 0 \end{pmatrix}$$
\begin{enumerate}[label=(\alph*)]
\item Write down the vector $\overrightarrow{AB}$
[1 mark]
\item Show that ABCD is a parallelogram, but not a rhombus.
[5 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 2 2018 Q14 [6]}}