Intermediate November 2024 Unit 1 Q8
8. The shape below has rotational symmetry of order 6.
Diagram not drawn to scale
Find the size of angle \(x\).
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \((6x =)\) 360 – (42 × 6) (= 108(\(^\circ\))) | M2 | Check diagram for answers. Sight of 108(\(^\circ\)) implies M2. Award M1 for sight of 42 × 6 or 252(\(^\circ\)). |
| ÷ 6 | m1 | Award m1 only if M2 awarded. |
| \((x =)\) 18(\(^\circ\)) | A1 | CAO. Mark final answer. Unsupported 18 is awarded M2m1A1. Allow an embedded answer but penalise -1 if contradicted by \(x \neq 18\) or equivalent Award SC1 for a final answer of 30(\(^\circ\)) or 9·4...(\(^\circ\)) (must be clearly using rotational symmetry of order 5 or 7). |
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| 360 ÷ 6 60(\(^\circ\)) | M1 A1 | Sight of 60(\(^\circ\)) implies M1 A1 |
| \((x =)\) 60 – 42 or 42 + \(x\) = 60 | m1 | FT ‘their derived 60’– 42, provided M1 awarded and ‘their derived 60’ > 42. Unsupported 18 is awarded M1A1m1A1. |
| 18(\(^\circ\)) | A1 | Mark final answer. Allow an embedded answer but penalise -1 if contradicted by \(x \neq 18\) or equivalent If FT leads to a whole number answer, it must be shown as a whole number. Otherwise accept a fraction. Award SC1 for a final answer of 30(\(^\circ\)) or 9·4... (\(^\circ\)) (must be clearly using rotational symmetry of order 5 or 7). |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| \(6(42 + x) = 360\) or \(42 + x = 360 \div 6\) | B2 | Award B1 for sight of \(6(42 + x)\) or 360 ÷ 6 |
| \(252 + 6x = 360\) or \(42 + x = 60\) | B1 | FT from \(6x = k\), if B2 B0 previously awarded. |
| \((x =)\) 18(\(^\circ\)) | B1 | Mark final answer. Allow an embedded answer but penalise -1 if contradicted by \(x \neq 18\) or equivalent If FT leads to a whole number answer, it must be shown as a whole number. Otherwise accept a fraction. Award SC1 for a final answer of 30(\(^\circ\)) or 9·4... (\(^\circ\)) (must be clearly using rotational symmetry of order 5 or 7). |
Both alternative methods are printed in italics in the original.
Corrected by Westie's Workshop
- The board's mark scheme printed “M1A1M1A1”. Changed to “M1A1m1A1” because the third mark in this method is a dependent method mark, written m1 (small m), as in the table.
Original: see the board's mark scheme PDF (link above).