1. 1
   Consider the expansion of $(2+x)^5$ in ascending powers of $x$.

   (a)

   Find the coefficient of $x^2$.

   [1 mark]

   • A$40$
   • B$80$
   • C$10$
   • D$160$

   (b)

   Find the coefficient of $x^4$.

   [1 mark]

   • A$5$
   • B$2$
   • C$80$
   • D$10$

   (c)

   Hence find the coefficient of $x^2$ in the expansion of $(1-x)(2+x)^5$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Row 6 of Pascal's triangle is $1, 6, 15, 20, 15, 6, 1$. Consider the expansion of $\left(x - \dfrac{2}{x}\right)^6$, where $x \ne 0$.

   (a)

   Use the given row to find the value of $\binom{7}{3}$.

   [1 mark]

   • A$21$
   • B$20$
   • C$35$
   • D$210$

   (b)

   Find the term independent of $x$ in the expansion.

   [1 mark]

   • A$-160$
   • B$160$
   • C$-20$
   • D$60$

   (c)

   Find the coefficient of $x^{-4}$ in the expansion.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Maya deposits 5000 dollars in a savings account that pays compound interest of 2% per year, with no further deposits or withdrawals. After 8 years the amount in the account, in dollars, is $5000\times1.02^8$. She wants to estimate this without a calculator using the expansion of $(1+x)^8$.

   (a)

   Find the first four terms of the expansion of $(1+x)^8$ in ascending powers of $x$.

   [3 marks]

   (b)

   Use your answer to (a) to estimate the amount in the account after 8 years, to the nearest dollar. Explain why your estimate is slightly less than the true amount.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In the expansion of $(1+kx)^n$, where $n\in\mathbb{N}$, $n\ge2$ and $k$ is a non-zero constant, the coefficient of $x$ is 12 and the coefficient of $x^2$ is 60.

   (a)

   Show that $n = 6$, and find the value of $k$.

   [6 marks]

   (b)

   Using the values of $n$ and $k$ from (a):
   (i) find the coefficient of $x^3$ in the expansion of $(1+kx)^n$;
   (ii) hence find the coefficient of $x^3$ in the expansion of $(3-x)(1+kx)^n$.

   [6 marks]

   Total for question 4: 12 marks

End of questions