Easy -1.2 This is a straightforward rationalizing the denominator question requiring only multiplication by the conjugate and simplification. It's a standard C1 exercise with a single technique and minimal steps, making it easier than average but not trivial since students must correctly handle the algebraic manipulation.
Guidance: SC If A0A0A0 scored, both parts correct but unsimplified B1. Alternative method: equates expression to \(a+b\sqrt{3}\) and forms simultaneous equations in \(a\) and \(b\) M1; correct method to solve M1; \(a=8\) found A1; \(b=3\) found A1
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{15+\sqrt{3}}{3-\sqrt{3}} \times \frac{3+\sqrt{3}}{3+\sqrt{3}}$ | M1 | Multiply top and bottom by $\pm(3+\sqrt{3})$ |
| $= \frac{48+18\sqrt{3}}{9-3}$ | A1 | Numerator correct and simplified |
| | A1 | Denominator correct and simplified to 6 |
| $= 8+3\sqrt{3}$ | A1 | cao |
**Guidance:** SC If A0A0A0 scored, both parts correct but unsimplified B1. Alternative method: equates expression to $a+b\sqrt{3}$ and forms simultaneous equations in $a$ and $b$ **M1**; correct method to solve **M1**; $a=8$ found **A1**; $b=3$ found **A1**
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