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2022 EJC Promo Q5 (a) Sketch the graph of ${{y}^{2}}-{{left( x-3 right)}^{2}}=1$, labelling all essential features. [3] (b) Find the set of values of $m$ such that the line $y=mleft(
2022 VJC Promo Q3 The curve $C$ has equation $frac{9{{left( y+3 right)}^{2}}}{4}-frac{{{left( x-2 right)}^{2}}}{4}=1$. (i) Sketch $C$, stating the equations of any asymptotes and the coordinates of any turning points.
2012 AJC P1 Q9 The curve $C$ has equation $y=frac{2{{x}^{2}}-a}{x+k}$ where $a, ,k>0$. (i) Given that $2{{k}^{2}}ne a$, find the range of values of $k$ such that the curve $C$
2020 SAJC P2 Q1 (i) Sketch the graph of $y=frac{{{x}^{2}}+2}{2x+1}$, stating the equation(s) of the asymptote(s), the coordinates of the turning point(s) and intersection(s) with the axes. [4] (ii) Let
2022 HCI P1 Q4 A curve $C$ has equation ${{x}^{2}}-3{{y}^{2}}=3$. (i) Sketch $C$, giving the equations of asymptote(s) and axial intercept(s) in exact form. [3] (ii) A complex number is
2022 JPJC P2 Q1 (a) The diagram shows the derivative graph of $y=text{f}left( x right)$. Justifying your answers, find the range of values of $x$ for which the graph $y=text{f}left(
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 CJC J1 MYE Q9 The curve $C$ has equation $y=frac{3{{x}^{2}}-px-1}{x-p}$ where $p$ is a constant. (i) If $C$ has no stationary points, use an alegbraic method to find the