Moderate -0.3 This is a straightforward binomial coefficient problem requiring students to expand two binomial expressions, identify the x³ terms, set their sum equal to 100, and solve for a. It's slightly easier than average because it's a direct application of the binomial theorem with no conceptual tricks, though it does require careful arithmetic with the negative coefficient in the first term.
Question 2:
2 | (+/−)20×33( x3) 0a3( x3)
, 1 soi
−540+10a3 =100 oe
a=4 | B1B1
M1
A1 | [4] | Each term can include x3
Must have 3 terms and include
a3 and 100
The coefficient of $x^3$ in the expansion of $(1 - 3x)^6 + (1 + ax)^5$ is 100. Find the value of the constant $a$. [4]
\hfill \mbox{\textit{CAIE P1 2016 Q2 [4]}}