| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2014 |
| Session | June |
| Marks | 2 |
| Topic | Sine and Cosine Rules |
| Type | Sequential triangle calculations (basic) |
| Difficulty | Easy -1.2 This is a straightforward two-part question requiring direct application of the cosine rule followed by the area formula (½ab sin C). Both are standard bookwork with no problem-solving or insight required—simpler than the typical A-level question which usually involves more steps or context. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
(i) $BC^2 = 10^2 + 7^2 - 2 \times 10 \times 7 \times \cos(100)$
$BC = 13.164... = 13.2$ to 3 sf
M1 Must be correct formula attempted
A1 [2]
(ii) Area $= 0.5 \times 10 \times 7 \times \sin(100)$
$= 34.468... = 34.5$ to 3 sf
M1 Must be correct formula attempted. Allow equiv methods as long as valid use of trig throughout
A1 [2]1 The diagram shows the triangle $A B C$. $A B = 10 \mathrm {~cm} , A C = 7 \mathrm {~cm}$ and angle $B A C = 100 ^ { \circ }$.\\
(i) Find the length $B C$.\\
(ii) Find the area of the triangle $A B C$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2014 Q1 [2]}}