### Bite Size Practice Additional Mathematics #21 (Integration)

Another set of work from St Margaret’s 2020 Prelim Questions with Answers for Integration with Differentiation to find decreasing functions in it. This Integration/Differentiation question is an Add Math question that requires a little bit of finesse. It launches into a direct integration question where you have to know what to do to integrate that given equation. After that part, you are required to continue getting the C (constant) of the equation by the extra information of (1,5) so don’t stop till you reach the end or there will be marks lost. Then the next part (ii) will trick a few people as it asks for range of values for decreasing function. So you have to differentiate it once to find the gradient itself, and then to find the decreasing part of it, you need to differentiate again to find the gradient of the gradient. (aka second derivative) to find where it is negative. So don’t stop at the first derivative. Once that is settled, its much easier to find the range.

For this question, we tried to put in as much guidance to help answer the questions. Also, check out how the flow works in the answers given, it helps to put the workflow into perspective. Make sure you understand your Integration and Differentiation lessons before attempting this question. Enjoy!

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Another Add Math question with answers from Chung Cheng involving integration. This question is a standard question found in textbooks so it should be quite straight forward. There is a partial fraction to prepare the original equation for integration. Once that is done, the partial fractions can be integrated. Quite easy peasy as long as you are comfortable with partial fractions and integrating the functions.

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