Higher June 2025 Paper 3 Q16
16 \(x\) is a positive even number.
\(y = (x - 3)(x - 5)(x + 6)\)
Without expanding brackets,
explain why there is only one value of \(x\) for which \(y\) is negative. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| When \(x = 2\), \((y =)\ 24\) or when \(x = 2\), negative (\(\times\)) negative (\(\times\)) positive = positive | B1 | oe |
| When \(x = 4\), \((y =)\ {-10}\) or when \(x = 4\), positive (\(\times\)) negative (\(\times\)) positive = negative | B1 | oe |
| When \(x = 6\), \((y =)\ 36\) or when \(x = 6\), positive (\(\times\)) positive (\(\times\)) positive = positive | B1 | oe SC1 correct value of \(y\) for any positive even value of \(x\) greater than 6 |
Additional guidance
| SC1 should only be considered when the response scores B0B0B0 | |
| Ignore any other evaluation attempts or written statements alongside correct responses | |
| A value of \(x\) may be implied by consistent substitution into the equation eg \((2 - 3)(2 - 5)(2 + 6) = 24\) implies \(x = 2\) | B1 |
| For any response using negative/positive, \(x = 2\) can be implied by stating ‘below 4’ and \(x = 6\) can be implied by stating ‘above 4’, or equivalent | |
| For any response using negative/positive, multiplication must be shown, referred to or implied, and the sign of the result must be stated |