| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 6 |
| Topic | Simultaneous equations |
| Type | Simultaneous with substitution elimination |
| Difficulty | Moderate -0.5 This is a straightforward simultaneous equations problem requiring recognition that x² - 2xy + y² = (x-y)² and substitution from the linear equation. The algebraic manipulation is routine and the question is shorter than average, making it slightly easier than a typical A-level question. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02f Solve quadratic equations: including in a function of unknown |
**Question 6**
- Substitute for $y$ (or $x$) — M1
- Obtain quadratic equation in $x$ (or $y$) — A1
- Solve their quadratic equation — M1
- Obtain $x = 2$ and $-1$ (or $y = -1$ and $2$) — A1
- Substitute back into linear or quadratic expression to find $y$ (or $x$) — M1
- Obtain $y = -1$ and $2$ (or $x = 2$ and $-1$) — A1ft
**Total: 6 marks**6 Solve the simultaneous equations
$$x + y = 1 , \quad x ^ { 2 } - 2 x y + y ^ { 2 } = 9$$
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q6 [6]}}