| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2012 |
| Session | Specimen |
| Marks | 6 |
| Topic | Simultaneous equations |
| Type | Simultaneous with substitution elimination |
| Difficulty | Standard +0.3 This is a straightforward simultaneous equations problem requiring substitution of y = 1 - x into the quadratic equation, leading to a standard quadratic to solve. While it involves algebraic manipulation across multiple steps, the technique is routine and commonly practiced, making it slightly easier than average for A-level. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution |
- Substitute for $y$ [M1]
- Obtain quadratic equation in $x$ [A1]
- Solve their quadratic equation [M1]
- Obtain $x = 2$ and $-1$ [A1]
- Substitute back to find $y$ or $x$, into linear or quadratic equation [M1]
- Obtain $y = -1$ and $2$ [A1ft]
**Total: 6 marks**3 Solve the simultaneous equations
$$x + y = 1 , \quad x ^ { 2 } - x y + y ^ { 2 } = 7 .$$
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q3 [6]}}