Easy -1.2 This is a straightforward application of rationalizing the denominator by multiplying by the conjugate. It requires only one standard technique (multiply by (√3+1)/(√3+1)) and simple arithmetic to reach the form a√3+b. This is a routine C1 exercise with no problem-solving element.
Multiply top and bottom by \(\sqrt{3}+1\) or \(-\sqrt{3}-1\); evidence of multiplying out needed
\(\frac{8\sqrt{3}+8}{3-1}\)
A1
Either numerator or denominator correct
\(4\sqrt{3}+4\)
A1
Final answer cao
Alternative: M1 Correct method to solve simultaneous equations formed from equating expression to \(a\sqrt{3}+b\); A1 Either \(a\) or \(b\) correct; A1 Both correct
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{8}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}$ | M1 | Multiply top and bottom by $\sqrt{3}+1$ or $-\sqrt{3}-1$; evidence of multiplying out needed |
| $\frac{8\sqrt{3}+8}{3-1}$ | A1 | Either numerator or denominator correct |
| $4\sqrt{3}+4$ | A1 | Final answer **cao** |
**Alternative:** M1 Correct method to solve simultaneous equations formed from equating expression to $a\sqrt{3}+b$; A1 Either $a$ or $b$ correct; A1 Both correct
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