Edexcel C1 — Question 5

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting general conic
DifficultyModerate -0.5 This is a straightforward simultaneous equations problem requiring substitution of a linear equation into a circle equation, then solving a quadratic. It's slightly easier than average because the linear equation is simple to rearrange (x = 2y + 1), the resulting quadratic is clean, and it's a standard C1 technique with no conceptual challenges.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.03d Circles: equation (x-a)^2+(y-b)^2=r^2
5. Solve the simultaneous equations $$\begin{gathered} x - 2 y = 1 \\ x ^ { 2 } + y ^ { 2 } = 29 \end{gathered}$$
Question 5:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
(a) \(7=5a_1-3 \Rightarrow a_1=2\)M1 Writes \(7=5a_1-3\) and attempts to solve for \(a_1\). If rearranged wrongly before substitution: M0
\(a_1=2\)A1 Cao
(b) \(a_3=32\), \(a_4=157\)M1 Attempts to find \(a_3\) or \(a_4\) using \(a_{n+1}=5a_n-3\), \(a_2=7\)
\(\sum_{r=1}^{4}a_r = a_1+a_2+a_3+a_4 = 2+7+32+157\)dM1 Depends on previous M. Sum of their four adjacent terms from the given sequence
\(= 198\)A1 Cao 
## Question 5:

| Answer/Working | Marks | Guidance |
|---|---|---|
| (a) $7=5a_1-3 \Rightarrow a_1=2$ | M1 | Writes $7=5a_1-3$ and attempts to solve for $a_1$. If rearranged wrongly before substitution: M0 |
| $a_1=2$ | A1 | Cao |
| (b) $a_3=32$, $a_4=157$ | M1 | Attempts to find $a_3$ or $a_4$ using $a_{n+1}=5a_n-3$, $a_2=7$ |
| $\sum_{r=1}^{4}a_r = a_1+a_2+a_3+a_4 = 2+7+32+157$ | dM1 | Depends on previous M. Sum of their four adjacent terms from the given sequence |
| $= 198$ | A1 | Cao |
5. Solve the simultaneous equations

$$\begin{gathered}
x - 2 y = 1 \\
x ^ { 2 } + y ^ { 2 } = 29
\end{gathered}$$

\hfill \mbox{\textit{Edexcel C1  Q5}}
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