These Ten-Year-Series (TYS) worked solutions with video explanations for 2022 A Level H2 Mathematics Paper 1 Question 10 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2022 A Level H2 Math Paper 1 Question 10
A curve $~C$ has equation $y=ax+b+\frac{a+2b}{x-1}$, where $a$ and $b$ are real constants such that $a>0$, $b\ne -\frac{1}{2}a$ and $x\ne 1$.
(a)
Given that $~C$ has no stationary points, use differentiation to find the relationship between $a$ and $b$.
[3]
(a) Given that $~C$ has no stationary points, use differentiation to find the relationship between $a$ and $b$.
[3]
It is now given that $b=-2a$.
(b)
Sketch $~C$ on the axes below stating the equations of any asymptotes and the coordinates of the points where$~C$ crosses the axes.
[4]
(b) Sketch $~C$ on the axes below stating the equations of any asymptotes and the coordinates of the points where$~C$ crosses the axes.
[4]
(c)
On the same axes, sketch the graph of $y=ax-a$.
[1]
(c) On the same axes, sketch the graph of $y=ax-a$.
[1]
(d)
Hence solve the inequality $x-2-\frac{3}{x-1}\le x-1$.
[2]
(d) Hence solve the inequality $x-2-\frac{3}{x-1}\le x-1$.
[2]
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