| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2012 |
| Session | Specimen |
| Marks | 5 |
| Topic | Sine and Cosine Rules |
| Type | Given area find angle/side |
| Difficulty | Moderate -0.8 This is a straightforward application of the area formula (1/2)ab sin C with one equation to solve. Substituting gives (1/2)(x)(x+2)sin(30°) = 12, which simplifies to a simple quadratic x² + 2x - 48 = 0. The question requires only direct formula recall and basic algebraic manipulation, making it easier than average. |
| Spec | 1.05c Area of triangle: using 1/2 ab sin(C) |
- $\frac{1}{2}x(x+2)\sin 30° = 12$ or simplified expression [B1]
- Rearrange to get a quadratic equation including putting $\sin 30° = \frac{1}{2}$ [M1]
- Obtain $x^2 + 2x - 48 = 0$ [A1]
- Solve their quadratic equation [M1]
- Obtain $x = 6$ only [A1]
**Total: 5 marks**2
The diagram shows a triangle $A B C$ in which angle $C = 30 ^ { \circ } , B C = x \mathrm {~cm}$ and $A C = ( x + 2 ) \mathrm { cm }$. Given that the area of triangle $A B C$ is $12 \mathrm {~cm} ^ { 2 }$, calculate the value of $x$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q2 [5]}}