Higher November 2023 Paper 1 Q17
17 \(x\) and \(y\) are integers.
\(8 \leqslant 4x \leqslant 20 \qquad \text{and} \qquad y - 3x \lt 12\)
Work out the largest possible value of \(y\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(2 \leqslant x \leqslant 5\) or \(6 \leqslant 3x \leqslant 15\) or \(x = 5\) or \(3x = 15\) | M1 | may be in two parts implied by \((y =)\ 27\) or \((x =)\ 2, 3, 4, 5\) or \((3x =)\ 6, 9, 12, 15\) |
| \(y - 3 \times 5 \lt 12\) or \(y \lt 12 + 3 \times 5\) or \(y \lt 27\) or \(y - 3 \times 5 \leqslant 11\) or \(y \leqslant 11 + 3 \times 5\) or \(y \leqslant 26\) | M1dep | oe may be seen in a double-sided inequality eg condone \(18 \lt y \lt 27\) using \(\leqslant\) or \(=\) |
| 26 | A1 | SC1 17 |
Additional guidance
SC1 is for the use of 2 instead of 5
All inequalities may be reversed, eg \(2 \leqslant x \leqslant 5\) may be \(5 \geqslant x \geqslant 2\)