1MA0 Higher June 2017 Paper 1 Q21
21 \(a = \sqrt{8} + 2\)
\(b = \sqrt{8} - 2\)
\(T = a^2 - b^2\)
Work out the value of \(T\).
Give your answer in the form \(c\sqrt{2}\) where \(c\) is an integer. (4)
| Answer | Mark | Notes |
|---|---|---|
| \(16\sqrt{2}\) | 4 | M1 for method to expand \((\sqrt{8} + 2)^2\) with at least 3 correct terms out of 4 terms M1 for method to expand \((\sqrt{8} - 2)^2\) with at least 3 correct terms out of 4 terms M1 (dep on M2) for a method to subtract the two expressions and use of \(\sqrt{8} = 2\sqrt{2}\) A1 cao OR M1 for factorising \(a^2 - b^2 = (a + b)(a - b)\) M1 for substituting for \(a\) and \(b\) with simplification (at least 1 of the two terms correct) M1 (dep on M2) for multiplying the 2 terms together and use of \(\sqrt{8} = 2\sqrt{2}\) A1 cao |