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###### 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.

**2015 A Level H2 Math Paper 1 Question 2**

**Suggested Handwritten and Video Solutions**

**2015 A Level H2 Math Paper 1 Question 3**

**Suggested Handwritten and Video Solutions**

**2015 A Level H2 Math Paper 1 Question 5**

**Suggested Video Solutions**

**Suggested Handwritten Solutions**

**2015 A Level H2 Math Paper 1 Question 11**

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

**Suggested Video Solutions**

**Suggested Handwritten Solutions**

**2015 A Level H2 Math Paper 2 Question 11**

**Suggested Handwritten and Video Solutions**

**Method I**

**Method II**

**Method I**

**Method II**

Paper 1

Paper 2

- Q2
- Q3
- Q5
- Q11

- (i)
- (ii)

- (i)
- (ii)

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(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]

- (i)
- (ii)
- (iii)

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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.Â

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.Â

Find, in non-trigonometric form, the exact coordinates of the turning point and explain why it is a maximum.

[6]

(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]

- (i)
- (ii)
- (iii)

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- Q11

- (i)
- (ii)
- (iii)
- (iv)
- (iv)

- (i)
- (ii)
- (iii)
- (iv)
- (iv)

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