| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | September |
| Marks | 6 |
| Topic | Vectors Introduction & 2D |
| Type | Parallel or perpendicular vectors condition |
| Difficulty | Easy -1.2 This is a straightforward multi-part question testing basic vector concepts: direction angle (tan 45° = 1), parallel vectors (proportional components), and unit vectors (magnitude = 1). All parts require only direct application of standard formulas with minimal algebraic manipulation, making it easier than average A-level content. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | \(a = 0.6\) | B1 |
Total: [1]
| Answer | Marks | Guidance |
|---|---|---|
| (ii) | \(3k = 0.6\), so \(k = 0.2\) | M1 |
| (ii) | \(a = 8 \times 0.2 = 1.6\) | A1 |
Total: [2]
| Answer | Marks | Guidance |
|---|---|---|
| (iii) | \(\sqrt{a^2 + 0.6^2} = 1\) | B1 |
| (iii) | \(a^2 = 0.64\) | M1 |
| (iii) | \(a = \pm 0.8\) | A1 |
Total: [3]
(i) | $a = 0.6$ | B1 | State correct value for $a$
Total: [1]
(ii) | $3k = 0.6$, so $k = 0.2$ | M1 | Attempt to find scale factor (or $0.6k = 3$, so $k = 5$)
(ii) | $a = 8 \times 0.2 = 1.6$ | A1 | Obtain $a = 1.6$
Total: [2]
(iii) | $\sqrt{a^2 + 0.6^2} = 1$ | B1 | Correct definition for unit vector seen or implied (Allow BOD for $a^2 + 0.6^2 = 1$, with no square root seen)
(iii) | $a^2 = 0.64$ | M1 | Attempt to find at least one value for $a$
(iii) | $a = \pm 0.8$ | A1 | Both correct values for $a$
Total: [3]2 Vector $\mathbf { v } = a \mathbf { i } + 0.6 \mathbf { j }$, where $a$ is a constant.\\
(i) Given that the direction of $\mathbf { v }$ is $45 ^ { \circ }$, state the value of $a$.\\
(ii) Given instead that $\mathbf { v }$ is parallel to $8 \mathbf { i } + 3 \mathbf { j }$, find the value of $a$.\\
(iii) Given instead that $\mathbf { v }$ is a unit vector, find the possible values of $a$.
\hfill \mbox{\textit{OCR H240/01 2018 Q2 [6]}}