Factorising: WJEC GCSE Higher November 2023 Unit 2 Q11

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Higher November 2023 Unit 2 Q11

WJECHigherCurrent spec7 marksFactorising

11.

(a) Factorise \(6x^2 + 19x + 10\). [2]

(b) Fully factorise the expression \(m^3 - 25m\). [3]

Mark scheme (a)

Scheme	Marks	Comments
\((2x + 5)(3x + 2)\) ISW	B2	B1 for one of the following: \((2x \ldots 5)(3x \ldots 2)\) A pair of brackets which leads to the expansion of \(6x^2 + bx + c\) where either \(b = 19\) or \(c = 10\) \(\dfrac{(2ax + 5a)(3bx + 2b)}{ab}\) [e.g. \((x + 2.5)(6x + 4)\)]

Mark scheme (b)

Scheme	Marks	Comments
\(m(m + 5)(m - 5)\)	B3	Mark final answer for B3. B2 for one of the following: \((m + 5)(m^2 - 5m)\) \((m - 5)(m^2 + 5m)\) \(m(m \ldots 5)(m \ldots 5)\) \((m + 5)(m - 5)\) B1 for one of the following: sight of \(m(m^2 - 25)\) sight of \((m + 5)(m - 5)\) included within an expression, e.g. \(m^2(m + 5)(m - 5)\) \((m \ldots 5)(m \ldots 5)\)

Scheme

Marks

Comments

\(m(m + 5)(m - 5)\)

Mark final answer for B3.
B2 for one of the following:

B1 for one of the following:

sight of \(m(m^2 - 25)\)
sight of \((m + 5)(m - 5)\) included within an expression, e.g. \(m^2(m + 5)(m - 5)\)
\((m \ldots 5)(m \ldots 5)\)

Mark scheme (c)

Scheme	Marks	Comments
\((p + 7)(p + 31)\) ISW	B2	B1 for \((p + 7)(p + 29 + 2)\) OR Allow B1 for \((p + 7)(p + k)\) with \(k \neq 0\) or 2 or 7 or 29.

Scheme	Marks	Comments
\((p + 7)(p + 29) + 2(p + 7) = p^2 + 38p + 217\) \(= (p + 7)(p + 31)\) ISW	B2	No mark for the expansion and collection of terms. Award B1 for a correct factorisation, if possible, on FT from ‘their derived quadratic expression’, provided no more than one error. SC1 for an answer of \((p + 7)(p + k)\) with \(k \neq 0\) or 7 or 2 or 29.