Higher June 2022 Paper 2 Q4
4 Festival A will be in a rectangular field with an area of 80 000 m2
The greatest number of people allowed to attend Festival A is 425
Festival B will be in a rectangular field 700 m by 2000 m.
The greatest number of people allowed to attend Festival B is 6750
The area per person allowed for Festival B is greater than the area per person allowed for Festival A.
(a) How much greater?
Give your answer correct to the nearest whole number. (4)
Give your answer correct to the nearest whole number. (4)
Callum says,
“300 cm2 is the same as 3 m2 because there are 100 cm in 1 m so you divide by 100”
Callum’s method is wrong.
(b) Explain why. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 19 | P1 | for process to find area available at festival B, eg \(700 \times 2000\ (= 1\,400\,000)\) |
| P1 | for process to find the area available per person at one festival, eg \(80\,000 \div 425\ (= 188.23\ldots)\) or [area] \(\div\, 6750\ (= 207.40\ldots)\) | |
| P1 | for process to find the area available per person at both festivals, eg \(80\,000 \div 425\ (= 188.23\ldots)\) and [area] \(\div\, 6750\ (= 207.40\ldots)\) | |
| A1 | for an answer in the range 18.7 to 19.5 |
Additional guidance
Accept either number rounded eg 207 or 188
| Answer | Mark | Mark scheme |
|---|---|---|
| explanation | C1 | for a valid statement relating to scale factor for area, Acceptable examples There are 10000 (cm2) in 1 (m2) Because 1 m2 is the same as \(100 \times 100 = 10000\) cm2 There are 2 side lengths that change from 1 m to 100 cm \(300 \div 3\) is 100 should use \(100^2\) \(300 \div 100 \div 100 = 0.03\) \(3 \times 100 \times 100 = 30000\) Because it’s area not length. Because it’s in m2 not just metres He hasn’t taken the squared sign into account Not acceptable examples There are 1000 cm in 1 m Callum is correct because ……. \(300 \div 3\) is 100 \(3^2 = 9\) \(300 \times 300 = 90000\) You have to square the number |