Edexcel C12 2014 June — Question 2 4 marks

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2014
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeSolve equations with surds
DifficultyModerate -0.8 This is a straightforward surd manipulation question requiring students to simplify √27 = 3√3, rationalize 6x/√3 = 2x√3, then solve a linear equation. It's routine algebraic manipulation with no conceptual challenges, making it easier than average but not trivial since it requires multiple standard steps.
Spec1.02b Surds: manipulation and rationalising denominators

2. Without using your calculator, solve $$x \sqrt { 27 } + 21 = \frac { 6 x } { \sqrt { 3 } }$$ Write your answer in the form \(a \sqrt { b }\) where \(a\) and \(b\) are integers. You must show all stages of your working.

Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\sqrt{27} = 3\sqrt{3}\) or \(\frac{6}{\sqrt{3}} = 2\sqrt{3}\)M1 Simplify either \(\sqrt{27}=3\sqrt{3}\) or \(\frac{6}{\sqrt{3}}=2\sqrt{3}\)
\(3\sqrt{3}x + 21 = 2\sqrt{3}x\)A1 Uses both simplifications to rewrite equation in equivalent form.
\(\sqrt{3}x = -21\)M1 Collects \(x\) terms, simplifies and divides reaching \(x=...\)
\(x = -\frac{21}{\sqrt{3}} \Rightarrow x = -7\sqrt{3}\)A1 Answer in required form \(-7\sqrt{3}\). Accept \(-1\sqrt{147}\).
# Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\sqrt{27} = 3\sqrt{3}$ or $\frac{6}{\sqrt{3}} = 2\sqrt{3}$ | M1 | Simplify either $\sqrt{27}=3\sqrt{3}$ or $\frac{6}{\sqrt{3}}=2\sqrt{3}$ |
| $3\sqrt{3}x + 21 = 2\sqrt{3}x$ | A1 | Uses both simplifications to rewrite equation in equivalent form. |
| $\sqrt{3}x = -21$ | M1 | Collects $x$ terms, simplifies and divides reaching $x=...$ |
| $x = -\frac{21}{\sqrt{3}} \Rightarrow x = -7\sqrt{3}$ | A1 | Answer in required form $-7\sqrt{3}$. Accept $-1\sqrt{147}$. |

---
2. Without using your calculator, solve

$$x \sqrt { 27 } + 21 = \frac { 6 x } { \sqrt { 3 } }$$

Write your answer in the form $a \sqrt { b }$ where $a$ and $b$ are integers.

You must show all stages of your working.\\

\hfill \mbox{\textit{Edexcel C12 2014 Q2 [4]}}