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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.

Mentoring students to be good in Mathematics also requires us to be their confident ally and have them actively engage in our Math tutorials. Resolving doubts, fears and any variables during class helps our Math students to be calm and resolute. Power comes from the ability to control emotions, and to solve questions in a stressful examination. During class, students will get a chance to do sums that ramps up in difficulty until they get overstretched. Then we’ll pull a safety net out for them to fall softly and we’ll run through those questions. Every question gets its day, explained to full understanding, worked till no one misunderstands it. Active learning and making mistakes creates experience. Know where one can fall, get it horribly wrong in the safety of our Math tutorial emulates how one can go wrong in examinations before attempting one. 

Our Add Math classes requires the constant improvement needed to keep ahead of the pack requires us to evolve our A Math teaching skills to suit our student’s needs. Parents will be astonished at how much more work and complexity our education system has incorporated when they look at their kids textbooks. Times have changed. Schools teach at least 1 year faster now than 10 years ago. What used to be in Sec 2 is now taught in Sec 1. In fact, for A Math, some of the topics are from GCE A’ levels. Plus, it depends on the schools as well, with some advanced schools doing 2 years ahead of schedule to keep their students on their toes. 

Our Singapore Maths lessons will be engaging our students to be learning A Maths in a fun way and shall be beneficial to their school work. We don’t rest on our laurels as years roll past because we know what is taught is just going to go faster, so we adapt and we keep ourselves at the forefront with our Math classes. Teaching ahead of all schools are our priority and helps Math students to be confident and have clarity in school lessons. Knowing they have learnt the best techniques augments confidence. Having a candid mindset to what lies ahead helps us to plan and solve our Math student’s problems as we know the requirements for them to do well individually and to do Math with efficiency. 

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