A-Level H2 Math
5 Essential Questions

Here is where we provide free online Revision materials for your H2 Math. We have compiled 5 essential questions from each topic for you and broken down the core concepts with video explanations. Please download the worksheet and try the questions yourself! Have fun learning with us, consider joining our tuition classes or online courses.

  • Q1
  • Q2
  • Q3
  • Q4
  • Q5
YI Tutorial Question 1

The parametric equations of a curve is given by

$x={{\sin }^{2}}t$, $y=3\cos t$ for $0\le t\le \pi $

(i)

Find the cartesian equation of this curve.

(i) Find the cartesian equation of this curve.

(ii)

Sketch the curve.

(ii) Sketch the curve.

(iii)

Find the value of $t$ at the point on curve whose tangent is parallel to the $y$-axis.

(iii) Find the value of $t$ at the point on curve whose tangent is parallel to the $y$-axis.

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2016 ACJC MYE Q4

The curve $C$ has parametric equation $x=3-2\cos \,t$, $y=-\tan \,t$ for $0<t<\frac{\pi }{2}$. Using differentiation, show that the curve $C$ does not have any stationary point.

[2]

(i)

A point $Q$ on $C$ has parameter $t=\frac{\pi }{6}$. Find the equation of the tangent at $Q$, leaving your answer in exact form.

[2]

(i) A point $Q$ on $C$ has parameter $t=\frac{\pi }{6}$. Find the equation of the tangent at $Q$, leaving your answer in exact form.

[2]

(ii)

Find the cartesian equation of the locus of the mid-point of $(3-2\cos \,t,\,-\tan \,t)$ and $(-3,0)$ as $t$ varies.

[3]

(ii) Find the cartesian equation of the locus of the mid-point of $(3-2\cos \,t,\,-\tan \,t)$ and $(-3,0)$ as $t$ varies.

[3]

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2018 TJC P2 Q1

A curve $C$ has parametric equations

$x=2{{e}^{t}}$, $y={{t}^{3}}-t$,

where $-1\le t\le \frac{3}{2}$.

(i)

Find $\frac{\text{d}y}{\text{d}x}$ in terms of $t$. Hence find the exact equations of the normals to the curve which are parallel to the $y$-axis.

[3]

(i) Find $\frac{\text{d}y}{\text{d}x}$ in terms of $t$. Hence find the exact equations of the normals to the curve which are parallel to the $y$-axis.

[3]

(ii)

Sketch the curve $C$.

(ii) Sketch the curve $C$.

(iii)

Find the equation of the tangent to $C$ at the point$\left( 2{{e}^{a}},{{a}^{3}}-a \right)$. Find the possible exact values of $a$ such that the tangent cuts the $y$-axis at $y=1$.

[4]

(iii) Find the equation of the tangent to $C$ at the point$\left( 2{{e}^{a}},{{a}^{3}}-a \right)$. Find the possible exact values of $a$ such that the tangent cuts the $y$-axis at $y=1$.

[4]

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2007 AJC P1 Q12 (b)

A curve is defined by the parametric equations

$x=a{{t}^{2}},\,y=2at.$

Show that the equation of the normal to the curve at the point $(a{{t}^{2}},\,2at)$ is at $y+tx=a{{t}^{3}}+2at$.
If the normal to the curve at the point $(a{{t}^{2}},\,2at)$ meets the curve again at the point $(a{{q}^{2}},\,2aq),$ show that ${{t}^{2}}+qt+2=0$.
Deduce that ${{q}^{2}}$ cannot be less than $8$.

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2018 EJC P1 Q3

The parametric equations of curve $C$, is given as $x=at$, $y=a{{t}^{3}}$, where $a$ is a positive constant.

(i)

The point $P$ on the curve has parameter $p$ and the tangent to the curve at point $P$ cuts the $y$-axis at $S$ and the $x$-axis at $T$. The point $M$ is the midpoint of $ST$. Find a Cartesian equation of the curve traced by $M$ as $p$ varies.

[5]

(i) The point $P$ on the curve has parameter $p$ and the tangent to the curve at point $P$ cuts the $y$-axis at $S$ and the $x$-axis at $T$. The point $M$ is the midpoint of $ST$. Find a Cartesian equation of the curve traced by $M$ as $p$ varies.

[5]

(ii)

Find the exact area bounded by curve $C$, the line $x=0$, $x=3$ and $x$-axis, giving your answer in terms of $a$.

[3]

(ii) Find the exact area bounded by curve $C$, the line $x=0$, $x=3$ and $x$-axis, giving your answer in terms of $a$.

[3]

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