Higher June 2022 Paper 1 Q18
18
\[12x^3 + 7x^2 + 3x - 10 \equiv 2(ax^3 + x^2 + 2x - 5) + x(bx + c)\]Work out the values of \(a\), \(b\) and \(c\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(2ax^3 + 2x^2 + 4x - 10\) and \(bx^2 + cx\) or \(2ax^3 + (2 + b)x^2 + (4 + c)x - 10\) or \(2a = 12\) or \(a = 6\) | M1 | oe correct expansions allow \(2ax^3 = 12x^3\) |
| \(2 + b = 7\) or \(b = 5\) or \(4 + c = 3\) or \(c = -1\) | M1 | oe equation |
| \(a = 6\) and \(b = 5\) and \(c = -1\) | A1 | SC2 any two of \(a = 6\) and \(b = 5\) and \(c = -1\) |
Additional guidance
| One correct value without working only scores one mark eg \(a = 6\) and \(b = -5\) and \(c = 1\) with no working eg \(a = -6\) and \(b = 5\) and \(c = 1\) with no working | M1M0A0 M0M1A0 |
| Condone an incorrect \(-10\) in the expansion if A1 is awarded | M1M1A1 |