Mathematics AA: QUADRATICS Topical Past Paper Questions

[Maximum mark:7] Consider the quadratic polynomial given by $P(x) = 2x^2 + qx + r$ where $q, r \in \mathbb{R}$. The equation $P(x) = 0$ has roots $\alpha$ and $\beta$, where $\alpha, \beta \in \mathbb{R}$. When $P(x)$ is divided by $(x+1)$, the remainder is 12. Given that $ \alph…

[Maximum mark: 17] The following diagram shows part of the graph of a quadratic function $f$. The vertex of the parabola is $ (-2, -5) $ and the y-intercept is at point P. (a) Write down the equation of the axis of symmetry. The function can be written in the form $ f(x)=\frac{1}…

[Maximum mark: 4] Consider the equation $ kx^{2} - (k + 3)x + 2k + 9 = 0 $, where $ k \in \mathbb{R} $. (a) Write down an expression for the product of the roots, in terms of k. (b) Hence or otherwise, determine the values of k such that the equation has one positive and one nega…