1MA0 Higher November 2012 Paper 2 Q14
14
(a) Factorise \(x^2 + 7x\) (1)
(b) Factorise \(y^2 - 10y + 16\) (2)
*(c)
(i) Factorise \(2t^2 + 5t + 2\)
(ii) \(t\) is a positive whole number.
The expression \(2t^2 + 5t + 2\) can never have a value that is a prime number.
Explain why. (3)
The expression \(2t^2 + 5t + 2\) can never have a value that is a prime number.
Explain why. (3)
| Answer | Mark | Notes |
|---|---|---|
| \(x(x + 7)\) | 1 | B1 cao |
| Answer | Mark | Notes |
|---|---|---|
| \((y - 8)(y - 2)\) | 2 | M1 \((y \pm 8)(y \pm 2)\) or \(y(y - 2) - 8(y - 2)\) or \(y(y - 8) - 2(y - 8)\) A1 cao |
| Working | Answer | Mark | Notes |
|---|---|---|---|
| (i) \(2t^2 + 5t + 2 = (2t + 1)(t + 2)\) | \((2t + 1)(t + 2)\) | 3 | M1 \((2t + 2)(t + 1)\) oe or \(2t(t + 2) + 1(t + 2)\) or \(t(2t + 1) + 2(2t + 1)\) A1 \((2t + 1)(t + 2)\) |
| (ii) This is always a product of two whole numbers each of which is greater than 1 | Correct explanation | B1 ft from (i) for a convincing explanation referring to factors found in (i) |