Question 81 – Sequences and Series - CCEA Maths Questions

In this question you must show detailed reasoning.

A chemical reactor is being commissioned over a 12-day period. During this period, a technician performs a primary catalyst injection every morning and a secondary maintenance flush every afternoon.

On the morning of day 1, the catalyst injection is 15 liters.
On the morning of day 12, the catalyst injection is 81 liters.

The technician considers two different commissioning protocols for the morning injections.

In Protocol A, the volume of catalyst injected each morning increases by the same constant amount each day.

Calculate the volume of catalyst injected on the morning of day 8 under Protocol A. (3)

In Protocol B, the volume of catalyst injected each morning increases by a constant percentage each day.

Calculate the volume of catalyst injected on the morning of day 8 under Protocol B. Give your answer in liters to one decimal place. (3)

Additionally, a fixed volume, $v$ liters, is used for the maintenance flush every afternoon for the entire 12-day period. Given that:

$v$ is an integer
the total volume of liquid (catalyst and flush) used over the 12 days must not exceed 1100 liters.

(i) Determine the maximum possible value of $v$ if Protocol A is used. (ii) Determine the maximum possible value of $v$ if Protocol B is used. (5)

In this question you must show detailed reasoning.

A chemical reactor is being commissioned over a 12-day period. During this period, a technician performs a primary catalyst injection every morning and a secondary maintenance flush every afternoon.

On the morning of day 1, the catalyst injection is 15 liters.
On the morning of day 12, the catalyst injection is 81 liters.

The technician considers two different commissioning protocols for the morning injections.

In Protocol A, the volume of catalyst injected each morning increases by the same constant amount each day.

Calculate the volume of catalyst injected on the morning of day 8 under Protocol A. (3)

In Protocol B, the volume of catalyst injected each morning increases by a constant percentage each day.

Calculate the volume of catalyst injected on the morning of day 8 under Protocol B. Give your answer in liters to one decimal place. (3)

Additionally, a fixed volume, $v$ liters, is used for the maintenance flush every afternoon for the entire 12-day period. Given that:

$v$ is an integer
the total volume of liquid (catalyst and flush) used over the 12 days must not exceed 1100 liters.

(i) Determine the maximum possible value of $v$ if Protocol A is used. (ii) Determine the maximum possible value of $v$ if Protocol B is used. (5)

Sequences and Series

Question 65

Sequences and Series

Question 65

Sequences and Series

Question 65

Sequences and Series Questions

Sequences and Series

Question 65

Sequences and Series Questions