Ten-Year-Series (TYS) Solutions | Past Year Exam Questions

2015 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 2015 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.

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2015 A Level H2 Math Paper 1 Question 2
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2015 A Level H2 Math Paper 1 Question 3
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2015 A Level H2 Math Paper 1 Question 5

(i)

State a sequence of transformations that will transform the curve with equation $y={{x}^{2}}$on to the curve with equation $y=\frac{1}{4}{{\left( x-3 \right)}^{2}}$.

[2]

(i) State a sequence of transformations that will transform the curve with equation $y={{x}^{2}}$on to the curve with equation $y=\frac{1}{4}{{\left( x-3 \right)}^{2}}$.

[2]

A curve has equation $y=\text{f}\left( x \right)$, where

$\text{f}\left( x \right)=\left\{ \begin{matrix}
1\text{ for }0\le x\le 1, \\
\frac{1}{4}{{\left( x-3 \right)}^{2}}\text{ for }1<x\le 3, \\
0\text{ otherwise}\text{.} \\
\end{matrix} \right.$

(ii)

Sketch the curve for $-1\le x\le 4$.

[3]

(ii) Sketch the curve for $-1\le x\le 4$.

[3]

(iii)

On a separate diagram, sketch the curve with equation $y=1+\text{f}\left( \frac{1}{2}x \right)$, for $-1\le x\le 4$.

[2]

(iii) On a separate diagram, sketch the curve with equation $y=1+\text{f}\left( \frac{1}{2}x \right)$, for $-1\le x\le 4$.

[2]

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2015 A Level H2 Math Paper 1 Question 11

A curve $C$ has parametric equations

$x={{\sin }^{3}}\theta $, $y=3{{\sin }^{2}}\theta \cos \theta $, $0\le \theta \le \frac{\pi }{2}$.

(i)

Show that $\frac{\text{d}y}{\text{d}x}=2\cot \theta -\tan \theta $.

[3]

(i) Show that $\frac{\text{d}y}{\text{d}x}=2\cot \theta -\tan \theta $.

[3]

(ii)

Show that $C$ has a turning point when $\tan \theta =\sqrt{k}$, where $k$ is an integer to be determined. 
Find, in non-trigonometric form, the exact coordinates of the turning point and explain why it is a maximum.

[6]

(ii) Show that $C$ has a turning point when $\tan \theta =\sqrt{k}$, where $k$ is an integer to be determined. 
Find, in non-trigonometric form, the exact coordinates of the turning point and explain why it is a maximum.

[6]

The line with equation $y=ax$, where $a$ is a positive constant, meets $C$ at the origin and at the point $P$.

(iii)

Show that $\tan \theta =\frac{3}{a}$ at $P$. Find the exact value of $a$ such that the line passes through the maximum point of $C$.

[3]

(iii) Show that $\tan \theta =\frac{3}{a}$ at $P$. Find the exact value of $a$ such that the line passes through the maximum point of $C$.

[3]

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2015 A Level H2 Math Paper 2 Question 11
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Method I


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Method II


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2015 TYS 2015

Method I


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Method II


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