Higher January 2021 Paper 2R Q14
14 Simon bought a house at the beginning of 2018
The value of Simon’s house had decreased by 15% by the end of 2018
The house increased in value during both 2019 and 2020
The percentage increases in the value of the house during 2019 and 2020 were the same.
The value of Simon’s house at the end of 2020 was 2.85% greater than the amount he paid for his house at the beginning of 2018
Calculate the percentage increase in the value of the house during 2019
(4)
| Scheme | Marks |
|---|---|
| \(0.85 \times x^2 = 1.0285\) or \(85 \times x^2 = 102.85\) oe or \((x^2 =)\; 1.0285 \div 0.85\) or \((x^2 =)\; 102.85 \div 85\) oe or 1.21 oe | M2 |
\((x =)\; \sqrt{1.0285 \div 0.85}\) or \((x =)\; \sqrt{102.85 \div 85}\) oe or \((x =)\) 1.1(0) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 10 | A1 |
| (4) | |
| (4 marks) |
Notes
M2: for a correct equation using their chosen letter or value in place of letter,
or a correct division or 1.21 seen otherwise:
(M1 for either 0.85 or 1.0285 seen)
M1: for a correct expression or value for \(x\)
| Scheme | Marks |
|---|---|
\(\left(\dfrac{100 + y}{100}\right)^2 \times 0.85 = 1.0285\) oe or \(\left(\dfrac{100 + y}{100}\right)^2 = 1.21\) oe or \(10^4 + 200y + y^2 = 12100\) oe | M2 |
\(\dfrac{100 + y}{100} = 1.1\) or \(100 + y = 110\) oe or \((y + 210)(y - 10) = 0\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 10 | A1 |
Notes
M2: for a correct equation using their chosen letter, otherwise:
(M1 for either 0.85 or 1.0285 seen)