| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 4 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Coefficient relationship between terms |
| Difficulty | Moderate -0.3 This is a straightforward binomial coefficient problem requiring students to write out two terms using the binomial theorem, equate coefficients according to the given relationship, and solve for a. While it involves two expansions and careful algebraic manipulation, it's a standard textbook exercise with no conceptual difficulty beyond applying the binomial formula correctly—slightly easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
**Question 5**
- $^5C_2 \, 2^2 \, a^3$ or equivalent seen — B1
- $^4C_2 \, \dfrac{a^2}{9}$ or equivalent seen — B1
- Attempt to solve correct relationship — M1
- $a = \dfrac{1}{6}$ — A1
**Total: 4 marks**5 The coefficient of $x ^ { 3 }$ in the expansion of $( 2 + a x ) ^ { 5 }$ is 10 times the coefficient of $x ^ { 2 }$ in $\left( 1 + \frac { a x } { 3 } \right) ^ { 4 }$. Find $a$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q5 [4]}}