O-LevelMathematicsNumber4024/21 · May/June 2024 · Q45 Marks
Two of the factors of 50 are square numbers. One of these square numbers is 1. Find the other square number that is a factor of 50.
- (a)Two of the factors of 50 are square numbers. One of these square numbers is 1. Find the other square number that is a factor of 50.[1]
- (b)(i)A = 2ˣ⁻¹ × 3²ʸ × 7 B = 2ˣ⁺³ × 3ʸ × 5 The numbers A and B are written as the product of their prime factors, where x and y are positive integers. Find the highest common factor (HCF) of A and B in terms of x and y.[2]
- (b)(ii)Find the lowest common multiple (LCM) of A and B in terms of x and y.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [1] 25
- [2] 2ˣ⁻¹ × 3ʸ oe final answer
- [2] B1 for correct answer seen and spoilt or answer 2ˣ⁻¹×k oe or m×3ʸ
- [2] 2ˣ⁺³ × 3²ʸ × 5 × 7 oe final answer
- [2] B1 for correct answer seen and spoilt
- [2] or answer 2ˣ⁺³×3²ʸ×5×7 oe
- [2] or 2⁶×3²ʸ×5×7 oe
- [2] or 2ˣ⁺³×3²ʸ×5 oe
- [2] or 2ˣ⁺³×3²ʸ×7 oe
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