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

2009 A Level H2 Math

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2009 A Level H2 Math Paper 1 Question 1

(i)

The first three terms of a sequence are given by ${{u}_{1}}=10$, ${{u}_{2}}=6$, ${{u}_{3}}=5$. Given that ${{u}_{n}}$ is a quadratic polynomial in $n$, find ${{u}_{n}}$ in terms of $n$.

[4]

(i) The first three terms of a sequence are given by ${{u}_{1}}=10$, ${{u}_{2}}=6$, ${{u}_{3}}=5$. Given that ${{u}_{n}}$ is a quadratic polynomial in $n$, find ${{u}_{n}}$ in terms of $n$.

[4]

(ii)

Find the set of values of $n$ for which ${{u}_{n}}$ is greater than $100$.

[2]

(ii) Find the set of values of $n$ for which ${{u}_{n}}$ is greater than $100$.

[2]

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2009 A Level H2 Math Paper 1 Question 4
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2009 A Level H2 Math Paper 1 Question 8

Two musical instruments, $A$ and $B$, consist of metal bars of decreasing lengths.

(i)

The first bar of instrument $A$ has length $20$ cm and the lenghts of the bars form a geometric progression. The $25$th bar has length $5$ cm. Show that the length of all the bars must be less than $357$ cm, no matter how many bars there are.

(i) The first bar of instrument $A$ has length $20$ cm and the lenghts of the bars form a geometric progression. The $25$th bar has length $5$ cm. Show that the length of all the bars must be less than $357$ cm, no matter how many bars there are.

Instrument $B$ consists of only $25$ bars which are identical to the first $25$ bars of instrument $A$. 

(ii)

Find the total length, $L$ cm, of all the bars of instrument $B$ and the length of the $13$ th bar.

(ii) Find the total length, $L$ cm, of all the bars of instrument $B$ and the length of the $13$ th bar.

(iii)

Unfortunately the manufacturer misunderstands the instructions and constructs instrument $B$ wrongly, so that the lengths of the bars are in arithmetic progression with common difference $d$ cm. If the total length of the $25$ bars is still $L$ cm and the length of the $25$th bar is still $5$ cm, find the value of $d$ and the length of the longest bar.

(iii) Unfortunately the manufacturer misunderstands the instructions and constructs instrument $B$ wrongly, so that the lengths of the bars are in arithmetic progression with common difference $d$ cm. If the total length of the $25$ bars is still $L$ cm and the length of the $25$th bar is still $5$ cm, find the value of $d$ and the length of the longest bar.

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2009 A Level H2 Math Paper 1 Question 10
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2009 A Level H2 Math Paper 2 Question 1

The curve $C$ has parametric equations

$x={{t}^{2}}+4t$, $y={{t}^{3}}+{{t}^{2}}$.

(i)

Sketch the curve for $-2\le t\le 1$.

[1]

(i) Sketch the curve for $-2\le t\le 1$.

[1]

The tangent to the curve at point $P$ where $t=2$ is denoted by $l$.

(ii)

Find the cartesian equation of $l$.

[3]

(ii) Find the cartesian equation of $l$.

[3]

(iii)

The tangent $l$ meets $C$ again at the point $Q$. Use a non-calculator method to find the coordinates of $Q$.

[4]

(iii) The tangent $l$ meets $C$ again at the point $Q$. Use a non-calculator method to find the coordinates of $Q$.

[4]

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