14 i 56 ÷ 5-3 = 5(6 - -3) = 5 or M2 2 M1 for showing subtraction of indices M M1 for recognising 6 = 6 +3 or – –3 =59 M1 for showing each number as a product of factors 56 × 5-3 = 5(6+-3) = 53 or M1 for combining them to give all the 5s as numerators == 53 ii M2 M1 for showing the indices are added M1 for recognising 6 + = 6 3 or –3 – M1 for showing each number as a product of factors 27 × 48 = × 2c n4 M1 for combining them to give all the 5s as numerators The power represents the reciprocal of C2 C1 for showing square root Using prime factors: squaring so take the square root. C1 for clear explanation 27 = 33 M2 M1 for finding the prime factors of each number M1 for stating each number as the product of the prime factors 48 = 24 × 3 So 27 × 48 = 34 × 24 B2 B1 for 27 expressed as product of prime factors in index form B1 for 48 expressed as product of prime factors in index form So = 3 and = 4 n c A2 A1 for = 23 cao n A1 for = 4 cao c C1 C1 for clear communication of solution 11
14 i ii 56 ÷ 5-3 = 5(6 - -3) = 5 or =59 56 × 5-3 = 5(6+-3) = 53 or == 53 27 × 48 = n4 × 2c Using prime factors: 27 = 33 48 = 24 × 3 So 27 × 48 = 34 × 24 The power represents the reciprocal of squaring so take the square root. So n = 3 and c = 4 M2 M2 C2 M2 B2 A2 C1 2 M1 for showing subtraction of indices M1 for recognising 6 – –3 = 6 +3 or M1 for showing each number as a product of factors M1 for combining them to give all the 5s as numerators M1 for showing the indices are added M1 for recognising 6 + –3 = 6 – 3 or M1 for showing each number as a product of factors M1 for combining them to give all the 5s as numerators C1 for showing square root C1 for clear explanation M1 for finding the prime factors of each number M1 for stating each number as the product of the prime factors B1 for 27 expressed as product of prime factors in index form B1 for 48 expressed as product of prime factors in index form A1 for n = 23 cao A1 for c = 4 cao C1 for clear communication of solution M 11
Higher_Skills_Number_MarkScheme_Edexcel.docx