Hint
Use the stated units and precision. Use symmetry of the entire named solid and its stated regularity.
Worked solution
(a)
Use symmetry of the entire named solid and its stated regularity.
The complete solid has 4 distinct mirror planes.
Answer: \(4\)
(b)
Include both visible and hidden faces of the closed solid.
Counting every polygonal face gives 5.
Answer: \(5\)
(c)
Do not double-count an edge because it belongs to two faces.
Count each shared face boundary once to obtain 9.
Answer: \(9\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Use symmetry of the entire named solid and its stated regularity.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Include both visible and hidden faces of the closed solid.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Do not double-count an edge because it belongs to two faces.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.