Higher November 2022 Paper 3 Q24
24 On the same day, Kate buys
a car for £14 000
and
a painting for £5000
The value of the car decreases by 35% in the first year, and then by 10% each year.
The value of the painting increases by 4% each year.
Show that the painting becomes worth more than the car during the fifth year. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| 0.65 or 0.9 or 1.04 | M1 | oe |
| \(14\,000 \times 0.65\) or 9100 | M1 | |
| their \(9100 \times 0.9^3\) or 6633.9(0) or their \(9100 \times 0.9^4\) or 5970.51 | M1dep | M3 for \(14\,000 \times 0.65 \times 0.9^3\) or 6633.9(0) or \(14\,000 \times 0.65 \times 0.9^4\) or 5970.51 |
| \(5000 \times 1.04^4\) or 5849.29… or \(5000 \times 1.04^5\) or 6083.26… | M1 | oe |
| 6633.9(0) and 5970.51 and 5849.29… and 6083.26… | A1 | value of car at years 4 and 5 value of painting at years 4 and 5 |
Additional guidance
| 5970.51 and 6083.26… with no values for year 4 | M4A0 | ||||||||||||||||||
| 6083.26… or 5849.29… with no method or other correct working or evaluations | M1M0M0M1A0 | ||||||||||||||||||
| 9100 implies M2 | |||||||||||||||||||
| \(7000 + 1400 + 700 = 9100\) | M1M1 | ||||||||||||||||||
| \(7000 + 1400 + 700\) | M0M1 | ||||||||||||||||||
Values by year
|