Easy -1.3 This is a straightforward C1 question testing basic surd manipulation: simplifying a square root by factoring out perfect squares, and expanding a binomial with a surd term. Both parts are routine textbook exercises requiring only direct application of standard techniques with no problem-solving or insight needed.
2. (a) Express \(\sqrt { } 108\) in the form \(a \sqrt { } 3\), where \(a\) is an integer.
(b) Express \(( 2 - \sqrt { 3 } ) ^ { 2 }\) in the form \(b + c \sqrt { 3 }\), where \(b\) and \(c\) are integers to be found.
(b) Expanding \((2 - \sqrt{3})^2\) to get 3 or 4 separate terms
M1
\(7, -4\sqrt{3}\)
A1, A1
(\(b = 7, c = -4\))
Total: 4 marks
Guidance:
- (a) \(\pm 6\sqrt{3}\) also scores B1
- (b) M1: The 3 or 4 terms may be wrong.
- 1st A1 for 7, 2nd A1 for \(-4\sqrt{3}\)
- Correct answer \(7 - 4\sqrt{3}\) with no working scores all 3 marks
- \(7 + 4\sqrt{3}\) with or without working scores M1 A1 A0
- Other wrong answers with no working score no marks
**(a)** $6\sqrt{3}$ | B1 | ($a = 6$)
**(b)** Expanding $(2 - \sqrt{3})^2$ to get 3 or 4 separate terms | M1 |
$7, -4\sqrt{3}$ | A1, A1 | ($b = 7, c = -4$)
**Total: 4 marks**
**Guidance:**
- (a) $\pm 6\sqrt{3}$ also scores B1
- (b) M1: The 3 or 4 terms may be wrong.
- 1st A1 for 7, 2nd A1 for $-4\sqrt{3}$
- Correct answer $7 - 4\sqrt{3}$ with no working scores all 3 marks
- $7 + 4\sqrt{3}$ with or without working scores M1 A1 A0
- Other wrong answers with no working score no marks
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2. (a) Express $\sqrt { } 108$ in the form $a \sqrt { } 3$, where $a$ is an integer.\\
(b) Express $( 2 - \sqrt { 3 } ) ^ { 2 }$ in the form $b + c \sqrt { 3 }$, where $b$ and $c$ are integers to be found.\\
\hfill \mbox{\textit{Edexcel C1 2007 Q2 [4]}}