4MA0 Higher January 2018 Paper 3 Q20
20
(a) \(\sqrt{50} + \sqrt{128} - \sqrt{200} = n\sqrt{2}\) where \(n\) is an integer.
Find the value of \(n\).
Show each stage of your working. (2)
Find the value of \(n\).
Show each stage of your working. (2)
Given that \(a\) is a prime number,
(b) simplify \(\dfrac{5\sqrt{a} + a}{10\sqrt{a}}\)
Give your answer in the form \(x + y\sqrt{a}\), where \(x\) and \(y\) are fractions.
Show your working clearly. (2)
Give your answer in the form \(x + y\sqrt{a}\), where \(x\) and \(y\) are fractions.
Show your working clearly. (2)
| Scheme | Marks |
|---|---|
\(\sqrt{25 \times 2} + \sqrt{64 \times 2} - \sqrt{100 \times 2}\) or \(5\sqrt{2} + 8\sqrt{2} - 10\sqrt{2}\) or \(3\sqrt{2}\) | M1 |
| 3 | A1 |
| (2) |
Notes
M1: for at least 2 out of 3 correct products from those shown or for \(3\sqrt{2}\)
| Scheme | Marks |
|---|---|
E.g. \(\dfrac{5\sqrt{a} + a}{10\sqrt{a}} \times \dfrac{\sqrt{a}}{\sqrt{a}}\) or \(\dfrac{5\sqrt{a}}{10\sqrt{a}} + \dfrac{a}{10\sqrt{a}}\) or \(\dfrac{\sqrt{a}(5 + \sqrt{a})}{10\sqrt{a}}\) | M1 |
| \(\dfrac{1}{2} + \dfrac{1}{10}\sqrt{a}\) | A1 |
| (2) |
Notes
M1: \(\sqrt{a}\) for multiplying numerator and denominator by \(\sqrt{a}\) (or a multiple of \(\sqrt{a}\)) or splitting fraction into 2 parts or
taking out \(\sqrt{a}\) as a common factor
A1: from correct working
NB. individual fractions need not be in their simplest form