Pre-U Pre-U 9794/1 2015 June — Question 3 3 marks

Exam BoardPre-U
ModulePre-U 9794/1 (Pre-U Mathematics Paper 1)
Year2015
SessionJune
Marks3
TopicSine and Cosine Rules
TypeAlgebraic side lengths
DifficultyStandard +0.3 This is a straightforward application of the sine rule to find an unknown side length. Students must recognize that angle A = 180° - 39° - 28° = 113°, then apply sine rule: x/sin(28°) = (2x-1)/sin(39°), and solve the resulting linear equation. It's slightly above average difficulty due to the algebraic manipulation required, but remains a standard textbook exercise with no novel insight needed.
Spec1.05b Sine and cosine rules: including ambiguous case

3 \includegraphics[max width=\textwidth, alt={}, center]{816a16df-e3a5-48ae-84c6-7f6f5bbba9ca-2_305_825_630_660} The diagram shows a triangle \(A B C\) in which angle \(B = 39 ^ { \circ }\), angle \(C = 28 ^ { \circ } , A B = x \mathrm {~cm}\) and \(A C = ( 2 x - 1 ) \mathrm { cm }\). Find the value of \(x\).

Substitute into correct sine rule \(\left(\dfrac{x}{\sin 28} = \dfrac{2x-1}{\sin 39}\right)\) [B1]
Simplify to obtain a value for \(x\) [M1]
Obtain \(x\) rounding to \(1.52\) (\(1.51626967\)) (exact answer gets A0) [A1]
Total: [3]
Substitute into correct sine rule $\left(\dfrac{x}{\sin 28} = \dfrac{2x-1}{\sin 39}\right)$ [B1]
Simplify to obtain a value for $x$ [M1]
Obtain $x$ rounding to $1.52$ ($1.51626967$) (exact answer gets A0) [A1]
**Total: [3]**
3\\
\includegraphics[max width=\textwidth, alt={}, center]{816a16df-e3a5-48ae-84c6-7f6f5bbba9ca-2_305_825_630_660}

The diagram shows a triangle $A B C$ in which angle $B = 39 ^ { \circ }$, angle $C = 28 ^ { \circ } , A B = x \mathrm {~cm}$ and $A C = ( 2 x - 1 ) \mathrm { cm }$. Find the value of $x$.

\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2015 Q3 [3]}}