Moderate -0.5 This is a straightforward application of the binomial theorem requiring students to write out two terms, equate coefficients, and solve a simple equation. While it involves algebraic manipulation with the parameter 'a', it's a standard textbook-style question with a clear method and minimal problem-solving demand, making it slightly easier than average.
SOI Can be part of expansion. Condone ax2 only if followed by a2.
ALT 27 [ 1+ax/2 ]7 → 7C1a ( x ) /2=7C2a ( x ) /2 2
7×26 2
a= =
Answer
Marks
Guidance
21×25 3
B1
Ignore extra soln a = 0. Allow a = 0.667. Do not allow an extra x in the
answer
Answer
Marks
Guidance
Total:
3
Question
Answer
Marks
Question 1:
1 | 7C1 ×26×a ( x ) , 7C2 ×25× a ( x ) 2
| B1 B1 | SOI Can be part of expansion. Condone ax2 only if followed by a2.
ALT 27 [ 1+ax/2 ]7 → 7C1a ( x ) /2=7C2a ( x ) /2 2
7×26 2
a= =
21×25 3 | B1 | Ignore extra soln a = 0. Allow a = 0.667. Do not allow an extra x in the
answer
Total: | 3
Question | Answer | Marks | Guidance
The coefficients of $x$ and $x^2$ in the expansion of $(2 + ax)^7$ are equal. Find the value of the non-zero constant $a$. [3]
\hfill \mbox{\textit{CAIE P1 2017 Q1 [3]}}