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2023 SAJC P1 Q5 The diagram below shows the region $R$ bounded by the circle with equation ${{left( x-4 right)}^{2}}+{{y}^{2}}=9$, the line with equation $y=-sqrt{5}x+3sqrt{5}$ and the $x$-axis. The line
2009 NJC Promo Q10 (b) The diagram above shows part of the graph of a curve $C$ given by $x=frac{y}{y-1}$.The region $R$ is bounded by $C$ and the lines $y=x$
2015 NJC Promo Q6 The diagram shows the curves with equations $y={{text{e}}^{2x-5}}$ and $y={{text{e}}^{-3x}}$.The shaded region $R$ is bounded by the curves and the line $x=2$. (i) Find the $x$-coordinate
2008 AJC Promo Q7 (a) The diagram below shows (not to scale) the region $R$ which is bounded by the curve $y=frac{3}{1+4{{x}^{2}}}$, the line $y=5x-1$ and the $y$-axis. Find the
NYJC Applications of Integration Tutorial Q1 The curve $C$ is defined by the parametric equations $x=6t-1$, $y=8{{t}^{2}}+2$ where $tge frac{1}{6}$. The line $N$, with equation $3y=8x-10$, is the tangent to
2019 DHS Promo Q4 A curve $C$ is defined by the parametric equations $x=frac{t}{1+{{t}^{2}}}$, $y=frac{t}{1-{{t}^{2}}}$, where $0le t<1$. (i) Find the equation of the tangent to $C$ at the point
2022 JPJC P2 Q4 A curve $C$ is given by the parametric equations $x=2+2sin theta $, $y=2cos theta +sin 2theta $, for $-pi <theta le pi $. (i) Sketch the
2022 DHS P2 Q1 (a) Sketch the curve $C$ given by the equation $4{{x}^{2}}-9{{left( y+1 right)}^{2}}-36=0$ indicating clearly the equations of any asymptotes. [2] (b) Find the volume generated
2023 ACJC P1 Q3 Let $text{f}left( x right)=frac{x}{sqrt{x+1}}$. (i) Show that $int_{0}^{1}{text{f}left( x right),text{d}x=frac{2}{3}left( 2-sqrt{2} right)}$. [2] (ii) The diagram below shows a sketch of the curve with equation $y=text{f}left(
2023 NYJC P2 Q5 The diagram shows the curve with equation $y=frac{1}{1+x}$. (a) By considering the shaded rectangle and the area of the region bounded by the curve and the