AQA Further AS Paper 1 Specimen — Question 3 1 marks

Exam BoardAQA
ModuleFurther AS Paper 1 (Further AS Paper 1)
SessionSpecimen
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConic sections
TypeHyperbola focus-directrix properties
DifficultyModerate -0.8 This is a straightforward recall question worth only 1 mark with multiple choice format. Finding asymptotes of a hyperbola x²/a² - y²/b² = 1 using the standard formula y = ±(b/a)x requires minimal calculation (√3/1) and no problem-solving. The multiple choice format further reduces difficulty by eliminating the need to derive or verify the answer independently.
Spec4.09b Sketch polar curves: r = f(theta)

3 Find the equations of the asymptotes of the curve \(x ^ { 2 } - 3 y ^ { 2 } = 1\) Circle your answer.
[0pt] [1 mark] $$y = \pm 3 x \quad y = \pm \frac { 1 } { 3 } x \quad y = \pm \sqrt { 3 } x \quad y = \pm \frac { 1 } { \sqrt { 3 } } x$$ Turn over for the next question \(\mathbf { 4 } \quad \mathbf { A } = \left[ \begin{array} { l l } 1 & 2 \\ 1 & k \end{array} \right] \quad \mathbf { B } = \left[ \begin{array} { c c } - 1 & 0 \\ 0 & 1 \end{array} \right]\)

Question 3:
AnswerMarks Guidance
\(y = \pm \dfrac{1}{\sqrt{3}}x\)B1 Circles correct answer
## Question 3:
$y = \pm \dfrac{1}{\sqrt{3}}x$ | B1 | Circles correct answer

---
3 Find the equations of the asymptotes of the curve $x ^ { 2 } - 3 y ^ { 2 } = 1$

Circle your answer.\\[0pt]
[1 mark]

$$y = \pm 3 x \quad y = \pm \frac { 1 } { 3 } x \quad y = \pm \sqrt { 3 } x \quad y = \pm \frac { 1 } { \sqrt { 3 } } x$$

Turn over for the next question\\
$\mathbf { 4 } \quad \mathbf { A } = \left[ \begin{array} { l l } 1 & 2 \\ 1 & k \end{array} \right] \quad \mathbf { B } = \left[ \begin{array} { c c } - 1 & 0 \\ 0 & 1 \end{array} \right]$\\

\hfill \mbox{\textit{AQA Further AS Paper 1  Q3 [1]}}