Higher June 2025 Paper 2 Q14
14 \(a\), \(b\) and \(c\) are positive integers.
\[a(9x + 2) \equiv 45x + 3b + c\]Work out one possible set of values for \(a\), \(b\) and \(c\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(a = 5\) \(b = 2\) \(c = 4\) or \(a = 5\) \(b = 3\) \(c = 1\) or \(a = 5\) \(b = 1\) \(c = 7\) | B3 | B2 \(3b + c = 10\) oe equation or \(a = 5\) and values for \(b\) and \(c\) other than the correct values such that \(3b + c = 10\) B1 \(a = 5\) or values for \(b\) and \(c\) such that \(3b + c = 2 \times\) their \(a\) |
Additional guidance
| The value of a letter omitted on the answer line and not evaluated in working is not taken to mean the value is zero | |
| \(a = 5\) \(b = 0\) \(c = 10\) | B2 |
| \(a = 5\) \(b = 4\) \(c = -2\) | B2 |
| \(a = 5\) \(b = \dfrac{5}{3}\) \(c = 5\) | B2 |
| \(a = 50\) \(b = 40\) \(c = -20\) | B1 |
| Condone use of \(\equiv\) for \(=\) eg \(3b + c \equiv 10\) | B2 |