O-LevelMathematicsNumber4024/11 · Oct/Nov 2020 · Q245 Marks
Express 99 as the product of prime factors.
- (a)Express 99 as the product of prime factors.[1]
- (b)(i)Expressed as the product of prime factors, p = 2ⁿ⁺²×3ⁿ×5 and q = 2ⁿ×3ⁿ⁺¹×5² where n is a positive integer. The lowest common multiple (LCM) of p and q is 2ⁿ⁺²×3ⁿ⁺¹× R. Express R as the product of prime factors.[2]
- (b)(ii)Express p+q as the product of prime factors.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [1] 3² × 11 or 3 × 3 × 11
- [2] 2² × 3 × 5²
- B1 for [p =] [2ⁿ × 3ⁿ] × 2² × 5
- or for [q =] [2ⁿ × 3ⁿ] × 3 × 5²
- or for answer 300
- or M1 for [LCM =] 2ⁿ⁺² × 3ⁿ⁺¹ × 5²
- [2] 2ⁿ × 3ⁿ × 5 × 19 oe
- B1 for 2ⁿ × 3ⁿ × ... as the only powers of 2 and 3 in a product
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