AQA Further Paper 2 2022 June — Question 3 1 marks

Exam BoardAQA
ModuleFurther Paper 2 (Further Paper 2)
Year2022
SessionJune
Marks1
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Mark schemeDownload PDF ↗
TopicRoots of polynomials
TypeSum of powers of roots
DifficultyModerate -0.8 This is a straightforward application of standard root formulas requiring only two steps: recall that α+β=p and αβ=-6, then use the identity α²+β²=(α+β)²-2αβ=p²-2(-6)=p²+12. It's a routine textbook exercise with a multiple-choice format that reduces difficulty further, though it's still testing genuine algebraic manipulation rather than pure recall.
Spec4.05a Roots and coefficients: symmetric functions
3 The roots of the equation \(x ^ { 2 } - p x - 6 = 0\) are \(\alpha\) and \(\beta\) Find \(\alpha ^ { 2 } + \beta ^ { 2 }\) in terms of \(p\) Circle your answer. \(p ^ { 2 } - 6\) \(p ^ { 2 } + 6\) \(p ^ { 2 } - 12\) \(p ^ { 2 } + 12\)
Question 3:
AnswerMarks Guidance
AnswerMarks Guidance
\(p^2 + 12\)B1 Circles correct answer 
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $p^2 + 12$ | B1 | Circles correct answer |
3 The roots of the equation $x ^ { 2 } - p x - 6 = 0$ are $\alpha$ and $\beta$

Find $\alpha ^ { 2 } + \beta ^ { 2 }$ in terms of $p$\\
Circle your answer.\\
$p ^ { 2 } - 6$\\
$p ^ { 2 } + 6$\\
$p ^ { 2 } - 12$\\
$p ^ { 2 } + 12$

\hfill \mbox{\textit{AQA Further Paper 2 2022 Q3 [1]}}
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Q1 1 Q2 1 Q3 1 Q4 1 Q5 4 Q6 3 Q7 8 Q8 10 Q9 14 Q10 7 Q11 9 Q12 11 Q13 16 Q14 14