Factorising: WJEC GCSE Intermediate June 2022 Unit 2 Q12

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Intermediate June 2022 Unit 2 Q12

WJECIntermediateCurrent spec5 marksFactorising

12.

(a) Factorise \(8x^2 + 6xy\). [2]

(b)

(i) Factorise \(x^2 + 13x + 40\). [2]

(ii) Explain how you can check that your answer to part (i) is correct. [1]

Mark scheme (a)

Scheme	Marks	Comments
\(2x(4x + 3y)\)	B2	Award B1 for \(2x(4x\ \pm\)……..) or \(2x(\)…….\(+\ 3y)\) Award B1 for a partial factorisation. i.e. \(2(4x^2 + 3xy)\) or \(x(8x + 6y)\). Mark final answer.

Scheme	Marks	Comments
(i) \((x + 8)(x + 5)\) ISW	B2	B1 for \((x\) … \(8)(x\) … \(5)\).
(ii) Any valid explanation e.g. “you could expand the two brackets” “expanding is the opposite of factorising” “multiply the brackets together” “solve \((x + 8)(x + 5) = 0\), and then substitute the value(s) of \(x\) into \(x^2 + 13x + 40\). It should give 0.” “replace \(x\) in the brackets and expression with the same value. You should get the same answer.”	E1	Allow “the two numbers need to add to 13, but multiply to make 40” “Use FOIL (CAMO) to check” or other names explaining the method. Allow method shown to expand brackets for example: Do not accept “\((x + 8)(x + 5) = x^2 + 13x + 40\)” without further working “taking out the brackets” “reverse the calculation”