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2022 DHS Promo Q2 (a) Given that $text{f}$ is a continuous and increasing function, explain, with an aid of a sketch, why the value of $underset{nto infty }{mathop{lim }},frac{2}{n}left[ text{f}left(
2021 RI P1 Q8 (i) The curve $G$ has equation $y=frac{1}{1+{{x}^{2}}}$. Sketch the graph of $G$, stating the equation(s) of any asymptote(s) and the coordinates of any turning point(s). [2]
2021 TMJC P1 Q3 Two curves ${{C}_{1}}$ and ${{C}_{2}}$ have equations $y=-sqrt{left( 1-frac{{{left( x-2 right)}^{2}}}{4} right)}$ and $y=-frac{1}{4}{{x}^{2}}$ respectively. (i) Sketch ${{C}_{1}}$ and ${{C}_{2}}$ on the same diagram, stating the
2021 YIJC P1 Q5 It is given that $O$ is the origin and $A$ is the point on the curve $y=x{{text{e}}^{x}}$ where $x=3$. The region bounded by the curve $y=x{{text{e}}^{x}}$and
2021 NYJC P1 Q2 (i) On the same axes, sketch the curves with equations, $y=left| frac{ax-3a+2}{3-x} right|$ and $y=frac{a}{3}x$, where $a>1$, giving the equations of the asymptotes and the coordinates
2022 EJC P1 Q1 On the same axes, sketch the graphs of $y=left| x-a right|$ and $y=left| x-b right|$, where $a$ and $b$ are constants such that $0<a<b$. You should
2022 ASRJC P1 Q6 (b) (i) Sketch the graphs of $y=left| {{x}^{2}}-7 right|$ and $y=x+5$ on the same diagram. Indicate clearly the $x$-intercepts and the values of $x$ where the
2022 RI P1 Q8 A curve $C$ is defined by $y=frac{{{left( ln x right)}^{4}}}{sqrt{x}}$ where $0<x<10$. (i) Find the exact volume generated when the area bounded by $C$, the $x$-axis
2023 SAJC BT P2 Q3 (i) Show that $int_{0}^{frac{pi }{2}}{{{e}^{2y}}cos 2y}text{ d}y=aleft( {{e}^{pi }}+1 right)$ , where $a$ is a constant to be determined. [5] (ii) A curved container has
Home 2011 MI P2 Q2 (i) Sketch the graphs of $y=frac{2}{1+{{left( x-2 right)}^{2}}}$ and $y=1$ on the same diagram, showing clearly the coordinates of the stationary point and points of