Properties of Numbers: WJEC GCSE Higher November 2023 Unit 1 Q4

Higher November 2023 Unit 1 Q4

WJECHigherCurrent spec6 marksProperties of Numbers

(a) Express 495 as a product of its prime factors in index form. [3]

(b) Explain how your answer to part (a) tells you that 495 is not a square number. [1]

Mark scheme (a)

Scheme	Marks	Comments
For a correct method that produces 2 prime factors from the set {3,3,5,11} before 2^nd error.	M1	Must be a method that involves only division. Check for errors in the method before checking the 2 prime factors from the set. (Note: 495 = 3 × 165 495 = 5 × 99 495 = 11 × 45)
3, 3, 5, 11	A1	CAO For sight of the four correct factors (Ignore 1s).
3² × 5 × 11	B1	Do not FT non-primes. FT ‘their primes’ provided at least one index form used with at least a square. Allow (3²)(5)(11) and 3².5.11 Do not allow 3²,5,11 Inclusion of 1 as a factor gets B0.

Mark scheme (b)

Scheme	Marks	Comments
Any valid reason referring to not all the indices being even e.g “the powers are not (all) even” “only one index is even”	E1	Allow reference to 22² = 484 and 23² = 529 Do not accept “they are not (all) even” “all factors are not (all) even” “the 5 and 11 are not squared” “the prime factors are all odd” “the little numbers are not even”.

Mark scheme (c)

Scheme	Marks	Comments
60 = 2 × 2 × 3 × 5 or equivalent correct strategy	M1	M1 for sight of 2,2,3,5 ‘together’ Allow M1 for selection of 2 × 2 × 15 or 4 × 15 (Not for other products e.g. 2 × 30, 3 × 20, 5 × 12, 6 × 10) (Not for just listing all the factors 1,2,3,4,5,6,10,12,15,20,30,60)
(HCF = ) 15	A1	Mark final answer. M1A0 for 3 × 5 FT ‘their answer to 4(a)’ only if equivalent difficulty (at least two common prime factors). Unsupported 15 gains M1 A1. If no marks awarded, award SC1 for sight of all common factors (1, 3, 5 and 15) and no other factors.