4MA0 Higher January 2015 Paper 4 Q22
22
(a) Write \(\dfrac{1}{32}\) as a power of 2 (2)
(b) Show that \((4 + \sqrt{12})(5 - \sqrt{3}) = 14 + 6\sqrt{3}\)
Show each stage of your working clearly. (3)
Show each stage of your working clearly. (3)
| Scheme | Marks |
|---|---|
| \(2^{-5}\) | B2 |
| (2) |
Notes
B2: B1 for \(\dfrac{1}{2^5}\) or \(\left(\dfrac{1}{2}\right)^5\) or \(2^5\)
| Scheme | Marks |
|---|---|
\(20 - 4\sqrt{3} + 5\sqrt{12} - \sqrt{3}\sqrt{12}\) or \(20 - 4\sqrt{3} + 5\sqrt{12} - \sqrt{36}\) or \(20 - 4\sqrt{3} + 5\sqrt{12} - 6\) | M1 |
\(\sqrt{12} = \sqrt{4 \times 3}\) or \(\sqrt{12} = 2\sqrt{3}\) or \(5\sqrt{12} = 5\sqrt{4 \times 3}\) or \(5\sqrt{12} = 10\sqrt{3}\) | M1 |
| show | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for at least 3 correct terms with correct signs or all 4 terms correct without signs
M1: NB. This may be seen before the expansion of the brackets
A1: dep on both method marks for deriving the given answer