Additional Mathematics 4037: Equations, inequalities and graphs Topical Past Paper Questions

**(a)** > **(i)** Write $x^2 - x - 6$ in the form $(x + a)^2 + b$ where $a$ and $b$ are constants. [2] > > **(ii)** Hence write down the coordinates of the stationary point on the curve $y = x^2 - x - 6$. [2] **(b)** On the axes, draw the graph of $y = |x^2 - x - 6|$ for $-4 \leq…

Use a graphical method to solve the inequality $ \left|2x-8\right|>4 $. [5]

(a) Solve the inequality $ 3x^{2}-12x+16>3x+4 $. (b) (i) Write $3x^{2}-12x+16$ in the form $a(x+b)^{2}+c$ where $a, b$ and $c$ are integers. (ii) Hence, write down the equation of the tangent to the curve $ y = 3x^{2} - 12x + 16 $ at the minimum point of the curve. [1]