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These Ten-Year-Series (TYS) worked solutions with video explanations for 2002 A Level H2 Mathematics Paper 1 Question 1 (FM) are suggested by Mr Gan. For any comments or suggestions please
2024 ACJC J1 WA2 Q3 (a) A sequence ${{u}_{1}}$, ${{u}_{2}}$, ${{u}_{3}}$, … is given by ${{u}_{n}}=frac{1}{4}left( 7-{{3}^{n}} right)$, for $nge 1$. (i) By expressing $4{{u}_{n+1}}$ and $12{{u}_{n}}$ in terms of
2020 NYJC P1 Q7 A sequence of numbers ${{u}_{1}}$, ${{u}_{2}}$, ${{u}_{3}}$, … has a sum ${{S}_{n}}$ where ${{S}_{n}}=sumlimits_{r=1}^{n}{{{u}_{r}}}$. It is given that ${{S}_{n}}=A{{n}^{2}}left( n+1 right)-Bn$, where $A$ and $B$ are
2018 JJC P2 Q3 (i) Using the method of differences, find $sumlimits_{r=1}^{n}{frac{1}{rleft( r+1 right)}}$. [3] Hence find $sumlimits_{r=1}^{n}{left[ {{3}^{-r}}-frac{1}{rleft( r+1 right)} right]}$. [3] (ii) Use your results in part (i)
2023 CJC Promo Q11 A curve $C$ has parametric equations $x=1-2{{t}^{2}}$, $y={{t}^{3}}+1$, for $tin mathbb{R}$. (a) Sketch $C$, indicating the coordinates of the points of intersection with the axes. [3]
2023 NYJC Promo Q7 The parametric equations of a curve are $x=frac{1}{2}{{text{e}}^{t}}-2{{text{e}}^{-t}}$ and $y={{text{e}}^{t}}+2{{text{e}}^{-t}}$. (a) Using calculus, find the exact gradient of the normal to the curve at the point
2023 YIJC Promo Q7 A curve $C$ has parametric equations $x={{t}^{2}}-4t$, $y={{t}^{3}}-6t$. (a) Using calculus, find the equation of the normal at the point $P$ where $t=1$. [4] (b) The
2007 SAJC P1 Q10 Consider the sequence defined by ${{u}_{n+1}}=frac{2}{{{u}_{n}}-2}+3$, for all positive integers of $n$, and ${{u}_{0}}=3$. (i) Find the values of ${{u}_{1}}$, ${{u}_{2}}$ and ${{u}_{3}}$. [2] (ii) Suppose
2007 RJC P1 Q3 A sequence of negative numbers is defined by ${{x}_{n,+1}}=frac{2-3{{x}_{n}}}{{{x}_{n}}-4}$, where ${{x}_{1}}=-frac{1}{7}$. (i) Write down the values of ${{x}_{2}}$ and ${{x}_{3}}$, giving your answers correct to $3$
2010 MJC P1 Q3 A sequence of positive real numbers ${{x}_{1}}$, ${{x}_{2}}$, ${{x}_{3}}$, … satisfies the recurrence relation ${{x}_{n+1}}=frac{3{{x}_{n}}}{sqrt{2+{{x}_{n}}}}$ for $nge 1$. (i) Given that $nto infty $, ${{x}_{n}}to alpha