Higher January 2021 Paper 1R Q2
2 Given that \(a \lt b \lt c\)
the four whole numbers \(a\), \(a\), \(b\) and \(c\) have
a mode of 7
a median of 8.5
a mean of 9
Work out the value of \(a\), the value of \(b\) and the value of \(c\).
(4)
| Scheme | Marks |
|---|---|
| \(a = 7\) | B1 |
| \(\dfrac{b + \text{their } a}{2} = 8.5\) oe or \(b = 10\) | M1 |
\(\dfrac{\text{their } a + \text{their } a + \text{their } b + c}{4} = 9\) oe or \((c =)\; 9 \times 4 - (2 \times \text{their } a + \text{their } b)\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 7, 10, 12 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: ft their value of \(a\) or
for setting up an equation for \(b\)
or \(b = 10\)
M1: for a calculation involving \(c\) using their values or
for a calculation leading to \(c\) using their values