Find the binomial expansion of \(( 1 - 2 x ) ^ { 5 }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 2 }\)
4
Find the first two non-zero terms in the expansion of
$$( 1 - 2 x ) ^ { 5 } + ( 1 + 5 x ) ^ { 2 }$$
in ascending powers of \(x\).
4
Hence, use an appropriate value of \(x\) to obtain an approximation for \(0.998 ^ { 5 } + 1.005 ^ { 2 }\) [2 marks]
\(5 A B C\) is a triangle. The point \(D\) lies on \(A C\).
\(A B = 8 \mathrm {~cm} , B C = B D = 7 \mathrm {~cm}\) and angle \(A = 60 ^ { \circ }\) as shown in the diagram.
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