# Question 2: Section A (36 marks)

**1** Find, in the form $y = ax + b$, the equation of the line through $(3, 10)$ which is parallel to $y = 2x + 7$. [3]

**2** Sketch the graph of $y = 9 - x^2$. [3]

**3** Make $a$ the subject of the equation $2a + 5c = af + 7c$. [3]

**4** When $x^3 + kx + 5$ is divided by $x - 2$, the remainder is 3. Use the remainder theorem to find the value of $k$. [3]

**5** Calculate the coefficient of $x^4$ in the expansion of $(x + 5)^6$. [3]

**6** Find the value of each of the following, giving each answer as an integer or fraction as appropriate.

(i) $25^{3/2}$ [2]

(ii) $\left(\frac{7}{3}\right)^{-2}$ [2]

**7** You are given that $a = \frac{3}{2}$, $b = \frac{9 - \sqrt{17}}{4}$ and $c = \frac{9 + \sqrt{17}}{4}$. Show that $a + b + c = abc$. [4]

**8** Find the set of values of $k$ for which the equation $2x^2 + kx + 2 = 0$ has no real roots. [4]

**9** (i) Simplify $3a^3b \times 4(ab)^2$. [2]

(ii) Factorise $x^2 - 4$ and $x^2 - 5x + 6$. Hence express $\frac{x^2 - 4}{x^2 - 5x + 6}$ as a fraction in its simplest form. [3]