Higher November 2021 Paper 2 Q21
21 \(x\) is an integer.
Prove that \(\qquad 35 + (3x + 1)^2 - 2x(4x - 3) \qquad\) is a square number. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(9x^2 + 3x + 3x + 1\) or \(9x^2 + 6x + 1\) or \(-(8x^2 - 6x)\) or \(-8x^2 + 6x\) | M1 | |
| \(35 + 9x^2 + 3x + 3x + 1 - 8x^2 + 6x\) or \(35 + 9x^2 + 6x + 1 - 8x^2 + 6x\) | M1dep | |
| \(x^2 + 12x + 36\) | A1 | |
| \((x + 6)^2\) | A1 | allow \((x + 6)(x + 6)\) |
Additional guidance
Condone inclusion of \(= 0\) in all working
Ignore any solution attempt for \((x + 6)^2 = 0\)
Ignore substitution of values