[Volume of pyramid = 1/3 × base area × height] ABCDE is a rectangular-based pyramid. AC and BD intersect at F. EF is perpendicular to FC. AD = 10cm, DC = 6cm and EC = 12 cm.

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

1. [4] (a) FC² = (10/2)² + (6/2)² oe
2. [4] M2 M1 for AC² =10² +6² oe
3. [4] or EX² + (6/2)² = 12² or EX²=12²-(10/2)² or EY² = 12²-(6/2)² or EY²+(10/2)²=12²
4. [4] M1 Dep on M2 [EF² =] 12²-their FC² oe or [EF² =] theirEX² - (10/2)² or [EF² =] theirEY² - (6/2)²
5. [4] A1 10.49 or 10.488...
6. [2] (b) 210 or 209.7 to 209.8
7. [2] M1 for 1/3 × 6 × 10 × 10.5
8. [3] (c) 29.0 or 28.95 to 28.96
9. [3] M2 for [cos =] (12²+12²-6²)/(2×12×12) or 2sin⁻¹(3/12) or M1for 6²=12²+12²-2 x 12 x 12 cosE or sin = 3/12
10. [2] (d) 34.9 or 34.85 to 34.86
11. [2] FT 72sin(their (c))
12. [2] M1 for 1/2 × 12 × 12 × sin(their 29.0) or 1/2√(12²-3²) x6 oe