| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 6 |
| Topic | Factor & Remainder Theorem |
| Type | Fully specified polynomial: verify factor and solve |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem requiring substitution to verify x=2 is a root, then polynomial division to find the quadratic factor, followed by solving a simple quadratic. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple standard techniques. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
**Question 4(i)**
- $\text{f}(-2) = 0$ clearly shown — B1
**Question 4(ii)**
- Method shown e.g. division — M1
- Obtain $2x^2 + 3x - 9$ — A1
- Attempt to solve quadratic $\big((2x-3)(x+3)\big)$ — M1
- $x = \frac{3}{2}$ — B1ft
- $x = 2$ and $x = -3$ — B1ft
**Total: 6 marks**4 (i) Show that $x = 2$ is a root of the equation $2 x ^ { 3 } - x ^ { 2 } - 15 x + 18 = 0$.\\
(ii) Hence solve the equation $2 x ^ { 3 } - x ^ { 2 } - 15 x + 18 = 0$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q4 [6]}}