Question 4 - A-Level Maths

AQA Further AS Paper 1 2024 June — Question 4 1 marks

Exam Board	AQA
Module	Further AS Paper 1 (Further AS Paper 1)
Year	2024
Session	June
Marks	1
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Vectors: Lines & Planes
Type	Cartesian equation of a line
Difficulty	Easy -1.2 This is a straightforward conversion from vector form to Cartesian form using the standard formula (x-a)/l = (y-b)/m = (z-c)/n, where students simply read off the position vector (4,-7,0) and direction vector (-9,1,3). It's a direct application of a standard technique with no problem-solving required, and being multiple choice removes the need to write out the solution. Below average difficulty even for Further Maths.
Spec	4.04a Line equations: 2D and 3D, cartesian and vector forms

4 The line $L$ has vector equation $$\mathbf { r } = \left[ \begin{array} { c } 4 \\ - 7 \\ 0 \end{array} \right] + \lambda \left[ \begin{array} { c } - 9 \\ 1 \\ 3 \end{array} \right]$$ Give the equation of $L$ in Cartesian form.
Tick ( ✓ ) one box. $\frac { x + 4 } { - 9 } = \frac { y - 7 } { 1 } = \frac { z } { 3 }$ \includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-03_108_109_1398_993} $\frac { x - 4 } { - 9 } = \frac { y + 7 } { 1 } = \frac { z } { 3 }$ \includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-03_108_111_1567_991} $\frac { x + 9 } { 4 } = \frac { y - 1 } { - 7 } , z = 3$ □ $\frac { x - 9 } { 4 } = \frac { y + 1 } { - 7 } , z = 3$ □

Show mark scheme Show mark scheme source

Question 4:

Answer	Marks	Guidance
Answer	Marks	Guidance
$\dfrac{x-4}{-9} = \dfrac{y+7}{1} = \dfrac{z}{3}$	B1 (AO1.1b)	Ticks the 2nd box
Total	1

## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\dfrac{x-4}{-9} = \dfrac{y+7}{1} = \dfrac{z}{3}$ | B1 (AO1.1b) | Ticks the 2nd box |
| **Total** | **1** | |

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4 The line $L$ has vector equation

$$\mathbf { r } = \left[ \begin{array} { c } 
4 \\
- 7 \\
0
\end{array} \right] + \lambda \left[ \begin{array} { c } 
- 9 \\
1 \\
3
\end{array} \right]$$

Give the equation of $L$ in Cartesian form.\\
Tick ( ✓ ) one box.\\
$\frac { x + 4 } { - 9 } = \frac { y - 7 } { 1 } = \frac { z } { 3 }$\\
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-03_108_109_1398_993}\\
$\frac { x - 4 } { - 9 } = \frac { y + 7 } { 1 } = \frac { z } { 3 }$\\
\includegraphics[max width=\textwidth, alt={}, center]{47b12ae4-ca3f-472c-9d15-2ef17a2a4d87-03_108_111_1567_991}\\
$\frac { x + 9 } { 4 } = \frac { y - 1 } { - 7 } , z = 3$ □\\
$\frac { x - 9 } { 4 } = \frac { y + 1 } { - 7 } , z = 3$ □

\hfill \mbox{\textit{AQA Further AS Paper 1 2024 Q4 [1]}}

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Q1 1 Q2 1 Q3 1 Q4 1 Q5 5 Q6 4 Q7 3 Q8 7 Q9 7 Q10 6 Q11 3 Q12 4 Q13 5 Q14 10 Q15 7 Q16 6 Q17 8