Mathematics 7357: Algebra and Functions Topical Past Paper Questions

The quadratic equation $$ 4x^{2}+bx+9=0 $$ has one repeated real root. Find b Circle your answer. [1 mark] $$ \boldsymbol{b}=\boldsymbol{0}\qquad\quad\boldsymbol{b}=\pm12\qquad\quad\boldsymbol{b}=\pm13\qquad\boldsymbol{b}=\pm36 $$

(a) Sketch the curve with equation $$ y=x^{2}(2x+a) $$ where $a>0$ [3 marks] The polynomial $ p(x) $ is given by $$ p(x)=x^{2}(2x+a)+36 $$ (b) (i) It is given that $x + 3$ is a factor of $p(x)$ Use the factor theorem to show $a = 2$ [2 marks] (b) (ii) State the transformation whi…

The function f is defined by $$ \mathrm{f}(x)=\frac{x^{2}+10}{2x+5} $$ where f has its maximum possible domain. The curve $y = f(x)$ intersects the line $y = x$ at the points $P$ and $Q$ as shown below. (a) State the value of x which is not in the domain of f. [1 mark] [1 mark] )…