OCR MEI AS Paper 1 2024 June — Question 2 2 marks

Exam BoardOCR MEI
ModuleAS Paper 1 (AS Paper 1)
Year2024
SessionJune
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeResultant of three coplanar forces
DifficultyEasy -1.2 This is a straightforward vector addition problem requiring only two steps: add the components to find the resultant (-14i + 3j), then apply Pythagoras to find magnitude √(196+9) = √205. It's routine mechanics practice with no problem-solving or conceptual challenge beyond basic vector operations.
Spec1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication
2 Two forces \(\mathbf { F } _ { 1 } \mathrm {~N}\) and \(\mathbf { F } _ { 2 } \mathrm {~N}\) are given by \(\mathbf { F } _ { 1 } = - 6 \mathbf { i } + 2 \mathbf { j }\) and \(\mathbf { F } _ { 2 } = - 8 \mathbf { i } + \mathbf { j }\).
Show that the magnitude of the resultant of these two forces is \(\sqrt { 205 } \mathrm {~N}\).
Question 2:
AnswerMarks Guidance
\(\mathbf{F_1} + \mathbf{F_2} = (-6\mathbf{i} + 2\mathbf{j}) + (-8\mathbf{i} + \mathbf{j}) = -14\mathbf{i} + 3\mathbf{j}\)M1 Attempt to add vectors
\(\sqrt{(-14)^2 + 3^2} = \sqrt{205}\) [N]A1 AG Must be clearly shown; do not allow for \(\sqrt{-14^2 + 3^2}\)
[Total: 2]
**Question 2:**

$\mathbf{F_1} + \mathbf{F_2} = (-6\mathbf{i} + 2\mathbf{j}) + (-8\mathbf{i} + \mathbf{j}) = -14\mathbf{i} + 3\mathbf{j}$ | M1 | Attempt to add vectors

$\sqrt{(-14)^2 + 3^2} = \sqrt{205}$ [N] | A1 | AG Must be clearly shown; do not allow for $\sqrt{-14^2 + 3^2}$

**[Total: 2]**
2 Two forces $\mathbf { F } _ { 1 } \mathrm {~N}$ and $\mathbf { F } _ { 2 } \mathrm {~N}$ are given by $\mathbf { F } _ { 1 } = - 6 \mathbf { i } + 2 \mathbf { j }$ and $\mathbf { F } _ { 2 } = - 8 \mathbf { i } + \mathbf { j }$.\\
Show that the magnitude of the resultant of these two forces is $\sqrt { 205 } \mathrm {~N}$.

\hfill \mbox{\textit{OCR MEI AS Paper 1 2024 Q2 [2]}}
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Q1 2 Q2 2 Q3 3 Q4 4 Q5 6 Q6 6 Q7 6 Q8 10 Q9 7 Q10 8 Q11 6 Q12 10