| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2020 |
| Session | Specimen |
| Marks | 6 |
| Topic | Simultaneous equations |
| Type | Linear simultaneous equations |
| Difficulty | Moderate -0.5 This is a straightforward simultaneous equations problem requiring substitution of y = 1-x into the second equation, which simplifies to (x-y)² = 9, giving x-y = ±3. Combined with x+y = 1, this yields two solution pairs through simple linear algebra. While it involves a quadratic expression, the algebraic manipulation is routine and the problem-solving path is clear, making it slightly easier than average. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution |
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 $-1$) — **A1** (A1ft)
**Total: 6**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 2020 Q6 [6]}}