In a laboratory experiment, a tank is transported to and fro between station $A$ and station $B$. On the ${{1}^{\mathrm{st}}}$ visit to station $A$, $200$ ml of water is added into the tank and on subsequent visits, $200$ ml more water than the previous visit to station $A$ will be added. That is, $400$ ml and $600$ ml of water will be added into the tank on the ${{2}^{\mathrm{nd}}}$ and ${{3}^{\mathrm{rd}}}$ visit to station $A$ respectively. On each visit to station $B$, $b$ ml of water is removed from the tank. It is given that the tank is empty at the start of the experiment and it starts from station $A$. On the$~{{m}^{\mathrm{th}}}$ visit to station $A$, $3200$ml of water is added into the tank. Find $m$. [2] It is given that immediately after the ${{16}^{\mathrm{th}}}$ visit to station $B$, there is more than $25$ litres of water in the tank. Find the set of values that $b$ can take. [3] In another laboratory experiment, a tank is transported to and fro between station $A$ and station $C$. $10%$ of the water in the tank is removed on each visit to station $C$. It is given that the tank is empty at the start of the experiment and it starts from station $A$. Show that the amount of water in the tank immediately after the ${{3}^{\mathrm{rd}}}$ visit to station $C$ is $1009.8$ ml. [2] Show that the amount of water in the tank immediately after the ${{n}^{\mathrm{th}}}$ visit to station $C$ is $1800n-16\,200\left( 1-{{0.9}^{n}} \right)$. [4] The experiment stops when the amount of water in the tank immediately after it leaves station $C$ exceeds $10$ litres. After the ${{k}^{\mathrm{th}}}$ visit to station $C$, the experiment stopped. Find $k$. [1]

2022 VJC Promo Q11

12 marks

Promo

In a laboratory experiment, a tank is transported to and fro between station $A$ and station $B$.

On the ${{1}^{\mathrm{st}}}$ visit to station $A$, $200$ ml of water is added into the tank and on subsequent visits, $200$ ml more water than the previous visit to station $A$ will be added. That is, $400$ ml and $600$ ml of water will be added into the tank on the ${{2}^{\mathrm{nd}}}$ and ${{3}^{\mathrm{rd}}}$ visit to station $A$ respectively. On each visit to station $B$, $b$ ml of water is removed from the tank.

It is given that the tank is empty at the start of the experiment and it starts from station $A$.

On the$~{{m}^{\mathrm{th}}}$ visit to station $A$, $3200$ml of water is added into the tank. Find $m$.[2]
It is given that immediately after the ${{16}^{\mathrm{th}}}$ visit to station $B$, there is more than $25$ litres of water in the tank. Find the set of values that $b$ can take.[3]

In another laboratory experiment, a tank is transported to and fro between station $A$ and station $C$. $10%$ of the water in the tank is removed on each visit to station $C$. It is given that the tank is empty at the start of the experiment and it starts from station $A$.

Show that the amount of water in the tank immediately after the ${{3}^{\mathrm{rd}}}$ visit to station $C$ is $1009.8$ ml.[2]
Show that the amount of water in the tank immediately after the ${{n}^{\mathrm{th}}}$ visit to station $C$ is $1800n-16\,200\left( 1-{{0.9}^{n}} \right)$.[4]
The experiment stops when the amount of water in the tank immediately after it leaves station $C$ exceeds $10$ litres. After the ${{k}^{\mathrm{th}}}$ visit to station $C$, the experiment stopped. Find $k$.[1]

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