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These Ten-Year-Series (TYS) worked solutions with video explanations for 2012 A Level H2 Mathematics Paper 1 Question 10 are suggested by Mr Gan. For any comments or suggestions please contact
Proving Second Derivative Of Arcsin(x) Given that $y={{sin }^{-1}}x$, prove that $left( 1-{{x}^{2}} right)frac{{{text{d}}^{3}}y}{text{d}{{x}^{3}}}-3xfrac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}-frac{text{d}y}{text{d}x}=0$. Suggested Video and Handwritten Solutions Written by Did You Enjoy This Article? Join our community and
Home 2009 ACJC P1 Q7 A point $left( x,y right)$ lies on the curve with equation $frac{1}{x}+frac{1}{y}=frac{1}{a}$, where $a$ is a non-zero constant, $xne 0$ and $yne 0$. (i) Express
2010 HCI P1 Q4 A curve is defined by the parametric equations $x=frac{t}{1+{{t}^{2}}}$, $y=frac{t}{1-{{t}^{2}}}$, where $tne -1$, $1$. (i) Show that the tangent to the curve at any point with
2010 CJC P1 Q8 The equation of a closed curve is ${{left( x+2y right)}^{2}}+3{{left( x-y right)}^{2}}=27$. (i) Show, by differentiation, that the gradient of the curve at the point $left(
2011 CJC P2 Q1 A curve $C$ has parametric equations $x=2sin t$ and $y=3cos t$ where $0le tle 2pi $. (i) Find the equations of the tangent and normal to
2013 HCI P1 Q3 There are two particles $A$ and $B$ with particle $A$ at $left( -13, 0 right)$ and particle $B$ at $left( 0, -9 right)$ with respect to
2013 MJC P2 Q3 (a) Each side of an equilateral triangle increases from an initial length of $9$ cm at a steady rate of $0.1text{ cm }{{text{s}}^{-1}}$. Find the rate
2013 CJC P1 Q11 The curve $C$ has parametric equations $x={{t}^{2}}+2$ , $y={{t}^{3}}$ where $tin mathbb{R}$. (i) Sketch the curve $C$. [1] The tangent to the curve at point $P$
2020 TMJC Promo Q10 A manufacturer designs a cylindrical water dispenser with a fixed volume, $V$cm$^{3}$ where $V>1$. The manufacturer decides to use stainless steel, with negligible thickness, for the