| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Topic | Simultaneous equations |
| Type | Line intersecting general conic |
| Difficulty | Moderate -0.8 This is a straightforward simultaneous equations question requiring substitution of a linear equation into a conic (ellipse), then solving the resulting quadratic. It's a standard technique taught early in A-level with no conceptual difficulty—simpler than average since it involves routine algebraic manipulation with clean numbers and no geometric interpretation required. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution |
Obtain correctly an equation in a single variable: $(10-2y)^2 + 2y^2 = 36$ [M1]
Obtain $3y^2 - 20y + 32 (= 0)$ aef or equivalent in $x$ [A1]
Solve their 3 term quadratic $= 0$ [depM1]
Obtain any two values from $(2, 4)$ and $\left(\frac{14}{3}, \frac{8}{3}\right)$ [A1]
Obtain $(2,4)$ and $\left(\frac{14}{3}, \frac{8}{3}\right)$ [A1]
**Total: [5]**2 Solve the following simultaneous equations.
$$x ^ { 2 } + 2 y ^ { 2 } = 36 \quad x + 2 y = 10$$
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2015 Q2 [5]}}