Find constant from coefficient condition

Questions that give the coefficient of a specific term in the sum or difference of two binomial expansions and ask to find an unknown constant.

5 questions

CAIE P1 2022 November Q4

4 The coefficient of \(x ^ { 2 }\) in the expansion of \(\left( 1 + \frac { 2 } { p } x \right) ^ { 5 } + ( 1 + p x ) ^ { 6 }\) is 70 .
Find the possible values of the constant \(p\).

CAIE P1 2011 June Q1

1 The coefficient of \(x ^ { 3 }\) in the expansion of \(( a + x ) ^ { 5 } + ( 1 - 2 x ) ^ { 6 }\), where \(a\) is positive, is 90 . Find the value of \(a\).

CAIE P1 2012 June Q3

3 The coefficient of \(x ^ { 3 }\) in the expansion of \(( a + x ) ^ { 5 } + ( 2 - x ) ^ { 6 }\) is 90 . Find the value of the positive constant \(a\).

CAIE P1 2018 June Q1

1 The coefficient of \(x ^ { 2 }\) in the expansion of \(\left( 2 + \frac { x } { 2 } \right) ^ { 6 } + ( a + x ) ^ { 5 }\) is 330 . Find the value of the constant \(a\).

CAIE P1 2016 November Q2

2 The coefficient of \(x ^ { 3 }\) in the expansion of \(( 1 - 3 x ) ^ { 6 } + ( 1 + a x ) ^ { 5 }\) is 100 . Find the value of the constant \(a\).