Easy -1.2 This is a straightforward factorisation requiring recognition of common factor x and difference of squares pattern (1 - 4x²) = (1-2x)(1+2x). It's simpler than average A-level work as it only requires basic algebraic manipulation with no index law complications beyond recognising x = x^1, making it easier than typical C1 questions.
Takes out factor of \(x\) or \(-x\) or even \(4x\). Must be correct. B0 for \(x(1+4x^2)\)
Factorises quadratic (or initial cubic) into two brackets
M1
Factorises quadratic resulting from first factorisation using usual rules. Also allow attempts to factorise cubic such as \((x-2x^2)(1+2x)\) etc. Should not be completing the square.
\(x(1-2x)(1+2x)\) or \(-x(2x-1)(2x+1)\) or \(x(2x-1)(-2x-1)\)
A1
Accept equivalent forms. No fractions for final answer.
Total: 3 marks
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x(1-4x^2)$ | B1 | Takes out factor of $x$ or $-x$ or even $4x$. Must be correct. B0 for $x(1+4x^2)$ |
| Factorises quadratic (or initial cubic) into two brackets | M1 | Factorises quadratic resulting from first factorisation using usual rules. Also allow attempts to factorise cubic such as $(x-2x^2)(1+2x)$ etc. Should not be completing the square. |
| $x(1-2x)(1+2x)$ or $-x(2x-1)(2x+1)$ or $x(2x-1)(-2x-1)$ | A1 | Accept equivalent forms. No fractions for final answer. |
**Total: 3 marks**
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