68 a x2 B1 3 B1 for clear explanation H For example: 1. – x2 Because each part is a square, and 12, one is subtracted from the other. Because: b B1 B1 for clear explanation 1000 × 998 = (999 + 1) × (999 1) – = 9992 1 – 2 Two that can be cancelled, for B1 2 B1 for two examples that cancel 69 example: 3 and I chose two straightforward ones, one that would cancel by a single letter and one that would cancel by an algebraic B1 B1 for a clear explanation term. Two that cannot be cancelled, for example: and B1 B1 for two examples that cancel don’t I chose two straightforward examples, one being a single term as numerator and denominator, the other one where the denominator was more than a B1 B1 for a clear explanation single term. 4 70 To get such a term on the top this must B1 2 B1 for clear explanation H be the difference of two squares, hence the two expressions both need B1 B1 for (3x 4) multiplying by (3x 4) to give: – – B1 B1 for setting up the expression This expands to: B1 B1 for showing how to find the final expression in suitable format 4
68 a b For example: x2 – 1. Because each part is a square, x2 and 12, one is subtracted from the other. Because: 1000 × 998 = (999 + 1) × (999 – 1) = 9992 – 1 B1 B1 3 B1 for clear explanation B1 for clear explanation H 2 69 Two that can be cancelled, for example: and I chose two straightforward ones, one that would cancel by a single letter and one that would cancel by an algebraic term. Two that cannot be cancelled, for example: and I chose two straightforward examples, one being a single term as numerator and denominator, the other one where the denominator was more than a single term. B1 B1 B1 B1 2 3 B1 for two examples that cancel B1 for a clear explanation B1 for two examples that don’t cancel B1 for a clear explanation 4 70 To get such a term on the top this must be the difference of two squares, hence the two expressions both need multiplying by (3x – 4) to give: This expands to: B1 B1 B1 B1 2 B1 for clear explanation B1 for (3x – 4) B1 for setting up the expression B1 for showing how to find the final expression in suitable format H 4
Higher_Skills_Algebra_MarkScheme_AQA.docx