| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Topic | Vectors Introduction & 2D |
| Type | Vector between two points |
| Difficulty | Easy -1.3 This is a straightforward vector arithmetic question requiring only basic addition/subtraction and magnitude calculation using Pythagoras. Both parts are routine recall with no problem-solving or geometric insight needed, making it easier than average A-level content. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| (ii) \( | \mathbf{u} + \mathbf{v} | = \sqrt{1 + 64} = \sqrt{65}\) — M1 |
| \( | \mathbf{u} - \mathbf{v} | = \sqrt{49 + 16} = \sqrt{65}\) — A1 [2] |
(i) $\mathbf{u} + \mathbf{v} = \begin{pmatrix} 1 \\ 8 \end{pmatrix}$, $\mathbf{u} - \mathbf{v} = \begin{pmatrix} 7 \\ 4 \end{pmatrix}$ — B1, B1 **[2]**
(ii) $|\mathbf{u} + \mathbf{v}| = \sqrt{1 + 64} = \sqrt{65}$ — M1
$|\mathbf{u} - \mathbf{v}| = \sqrt{49 + 16} = \sqrt{65}$ — A1 **[2]**
**Total: [4]**1 Vectors $\mathbf { u }$ and $\mathbf { v }$ are given by $\mathbf { u } = \binom { 4 } { 6 }$ and $\mathbf { v } = \binom { - 3 } { 2 }$.\\
(i) Find $\mathbf { u } + \mathbf { v }$ and $\mathbf { u } - \mathbf { v }$.\\
(ii) Show that $| \mathbf { u } + \mathbf { v } | = | \mathbf { u } - \mathbf { v } |$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q1 [4]}}