Higher June 2025 Paper 2 Q3
3 Here is a plan of part of Macsen’s garden.
There is a circle inside a triangle.
The circle has a diameter of 7 m.
Macsen will cover the shaded area with gravel.
Gravel is sold in bags.
Each bag of gravel covers an area of 12.5 m2
(a) Work out the number of bags of gravel Macsen will need. (4)
Macsen finds that each bag of gravel only covers an area of 11 m2
(b) How does this affect your answer to part (a)? (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 6 | P1 | for a process to find a relevant area, eg \(16 \times 14 \div 2\ (= 112)\) or \(\pi \times \left(\dfrac{7}{2}\right)^2\ (= 38.4\ldots)\) |
| P1 | for a process to find the shaded area, eg \(\text{``}112\text{''} - \text{``}38.4\ldots\text{''}\ (= 73.51\ldots)\) or \(\text{``}8.96\text{''} - \text{``}3.07\ldots\text{''}\ (= 5.88\ldots)\) | |
| P1 | for a complete process to find the number of bags required for a full or partial area, eg \(\text{``}73.51\ldots\text{''} \div 12.5\ (= 5.88\ldots)\) or \(\text{``}112\text{''} \div 12.5\ (= 8.96)\) or \(\text{``}38.4\ldots\text{''} \div 12.5\ (= 3.07\ldots)\) or [area] \(\div\, 12.5\) or uses 12.5 in a build up method to exceed [area], eg \(12.5 \times 6\ (= 75)\) oe | |
| A1 | cao |
Additional guidance
May be implied by \(\dfrac{49}{4}\pi\)
[area] can be any area but cannot be a length.
| Answer | Mark | Mark scheme |
|---|---|---|
| Statement | C1 | for a valid statement relating to effect on number of bags needed, eg Acceptable examples Will need more bags It will increase Will need an extra bag or will now need 7 bags He won’t have enough There is no change (ft their [area] but must be supported by calculation) Not acceptable examples Will cover less area Needs to change the number of bags needed There is no change (unsupported or incorrect ft their [area]) He may need more bags A calculation using 11 with no supporting statement |