O-LevelAdditional MathematicsIndices and surds4037/22 · Oct/Nov 2024 · Q65 Marks
DO NOT USE A CALCULATOR IN THIS QUESTION. Write (5-√3)(√6+ √2)⁻² in the form a+b√3, where a and b are constants.
- DO NOT USE A CALCULATOR IN THIS QUESTION. Write (5-√3)(√6+ √2)⁻² in the form a+b√3, where a and b are constants.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [B1] (√6+√2)² soi
- [B1] (√6+√2)² = 6+2+2√12 or 8 + 2√12
- [M1] (5-√3)/(8+4√3) × (8-4√3)/(8-4√3) or (5-√3)/(4(2+√3)) × (2-√3)/(2-√3) oe [FT] a(5-√3)/(b+c√d) where a, b, and c are non-zero constants and d is an integer
- [A1] (40-20√3-8√3+12) / (8²-(4√3)²) or (40-20√3-8√3+12) / (64-48) or (10-5√3-2√3+3) / (4(2²-(√3)²)) or (10-5√3-2√3+3) / 4
- [A1] 13/4 - (7/4)√3 oe, nfww [dep] on all previous marks awarded
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