| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2012 |
| Session | Specimen |
| Marks | 7 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Binomial times linear coefficient |
| Difficulty | Moderate -0.3 Part (i) is straightforward binomial expansion requiring recall of the formula and basic arithmetic. Part (ii) involves multiplying two expansions and equating coefficients, which is a standard technique. The question requires multiple steps but uses routine methods with no novel insight needed, making it slightly easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n1.04b Binomial probabilities: link to binomial expansion |
**(i)** Obtain $1 - 18x$ **B1**
Attempt binomial expansion of at least one more term with each term product of binomial coefficient and power of $-2x$ **M1**
Obtain $144x^2$ **A1**
Obtain $-672x^3$ **A1**
**(ii)** Multiply together two relevant pairs of terms **M1**
Obtain $144 - 18a = 66$ **A1ft**
Obtain $a = \dfrac{37}{3}$ **A1**
**Total: 7 marks**6 (i) Find and simplify the first four terms in the expansion of $( 1 - 2 x ) ^ { 9 }$ in ascending powers of $x$.\\
(ii) In the expansion of
$$( 2 + a x ) ( 1 - 2 x ) ^ { 9 }$$
the coefficient of $x ^ { 2 }$ is 66 . Find the value of $a$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2012 Q6 [7]}}