Free Mathematics Online Lesson and Q&A Session

60 Replies to “Free Mathematics Online Lesson and Q&A Session”

1. Well can you tell me by what the definition of “cross- sectional area” ??
   Also can you explain and breakdown Differentiation and the finding of the minimum and the maximum by Differentiation ??

   • Hello Anushia,

     Thanks for writing to us!

     A cross section means simply, view into the inside of something after cutting through it. It is the shape made, when a solid is cut through parallel to the base.

     And the cross-sectional area is, the area of a two-dimensional shape that is obtained when a three-dimensional object (can be a cylinder) is sliced perpendicular to a particular axis at a point.

     And for the second question, let us take an example.

     Ex: f(x) = x^3-3x^2 + 1

     When you differentiate with respect to x,
     f'(x) = 3x^2-6x
     f'(x) = 3x(x-2)

     To find the stationary points,
     3x(x-2) = 0
     Then,
     3x = 0 and (x-2) = 0
     x = 0 and x = 2

     Now it is important to know whether you have found a maximum point or a minimum point .
     So that, the gradient at both sides of the stationary point needs to be considered (we can use the second derivative as another option).

     At the local maxima, the gradient becomes positive just before the maxima, it is zero at the maxima and it is negative just after the maxima.

     At the local minima, the gradient becomes negative just before the minima, zero at the minima, and then positive.
     

     Here in this sum,
     when x = 0,
     Consider two x values just before 0 and, after 0.

     When x = -0.1, f'(x) = 3x(x-2)
     = + (positive)

     x = 0 f'(x) = 0 (already found)

     When x = +0.1, f'(x) = 3x(x-2)
     = – (negative)

     So that, it is a maximum point as per the above explanation.

     when x = 2,
     Consider two x values just before 2 and, after 2.

     When x = 1.9, f'(x) = 3x(x-2)
     = – (negative)

     x = 2, f'(x) = 0 (already found)

     x = 2.1 f'(x) = 3x(x-2)
     = + (positive)

     So that, it is a minimum point as per the above explanation.

     Hope this helps! We are here for you!

     Best Regards,
     Mathematics Department

     • Thank you !!
       Really helped a lot…

       • Hi Anushia,

         It is our pleasure to help you!

         Best Regards,
         Mathematics Department

2. Hi,
   Just wanted to know if you could share some tips for preparing for the exam 0607 international maths and some tips specifically to improve in the paper 6 of 0607 investigations and modelling

   • Hi Saanvi,

     We appreciate your enthusiasm.

     To prepare for the exam 0607 International Mathematics,

     1. Practice latest past papers and get familiar with the paper structure.
     2. Identify the short answer questions, structured questions and investigation and modelling questions when you practice the past papers (paper 1 to paper 6)
     3. Refer to these command words when you are writing answers to the past papers

     Calculate – workout from given facts, figures or information, generally from using the calculator

     Compare – Write about similarities and differences

     Describe – Write down the general type and the main characteristics

     Explain – Give purposes and reasons. Make clear the relationships between things
     Answer why and/or how and support with relevant evidence.

     Give – Provide an answer from memory or from a given source.

     Investigate – Use available information to search systematically for results

     Plot – Mark point(s) on a graph

     Revise – Change to take account of further information

     Show that – Provide structured evidence that leads to a given result

     Sketch – Make a simple freehand drawing showing the key features

     Work out – Calculate from given facts, figures or information with or without the use of a calculator

     Write – Give an answer in a particular form

     Write down – Give an answer without doing significant working

     To prepare for the paper 6 in 0607 International Mathematics,

     1. You can refer to the tips we have mentioned in the answer for your first question
     2. You should have the right mindset when answering, as you have to apply what you know to real-life scenarios (real world problems)
     3. They can not ask anything that you do not know, so make sure you understand every concept in the syllabus.
     4. Practice creative thinking – best way is to answer the past papers.

     Hope this helps! Best of luck!

     Best regards,
     Mathematics Department

     • Thank youu so muchhh!!this is so helpful!!

       • Hi Saanvi,

         It is our pleasure to help you!

         Best Regards,
         Mathematics Department

3. hi,
   I have my igcses this april and there are hardly three months left.I’ve finished solving most of the topics from the 0607 textbook and have finished past papers till 2018.What do you think would be best for me to do the next three months in order to get a*.

   • Hi Saanvi,

     The best method is to practice the past papers from latest years (starting from 2020). We recommend you to practice these under exam conditions. It will help you to manage time well in the exam and tackle every question in the paper during the exam. Understand every concept well and write answers to many practice questions throughout this time period you have got.

     Best of luck!

     Hope this helps! We are here for you!

     Best Regards,
     Mathematics Department

4. How many years paper should i solve in order to get a* in 0607 international maths? and any advice on how to improve for the paper 6 investigations and modelling?And it would be great if you could share some other life saving tips!!

   • Hello Saanvi,

     Thank you for writing to us.

     For your first question, we recommend you to practice at least 5 years of past papers starting from 2020, as it contains the newest syllabus. Then you can practice the latest 2019, 2018.. and so on.

     For the second question we will give some tips for each section.

     For INVESTIGATION section,
     1. Read the questions carefully and make sure you highlight/underline the key information in the questions, so that you will not miss them out.
     2. And you will see that the questions get gradually harder when you go through the paper. Therefore, make sure you answer the first 2-3 pages correctly, as it will help build confidence to answer the next difficult questions better.

     For MODELLING section,
     1. You should bring a Graphical Display Calculator with you to use where appropriate.
     2. Make sure you read the instructions carefully.
     3. You will not get marks for just the final answer, you have to show your working in the paper.
     4. Keep in mind that the examiner looks for the right thinking. Therefore, showing your working step by step (clearly) is recommended.
     5. Try and attempt every question.

     And finally, in this paper you will be evaluated on your ability to provide reasoning and communicate your methods in a clear manner. So that we recommend you to practice the past papers, starting from the latest. And try your best to manage the given time well, in each of the practice you do.

     Hope this helps! We are here for you!

     Best Regards,
     Mathematics Department

5. Hi, my question is that in answers we should write answer greater than or equal to 2significant figures. If I choose three or four significant figures does it make any difference. Also in drawing graph like in latest igcse 2020 papers ,while scale is not given, what points should we calculate for general shape? In differentiation if we have a point of inflexion, how should we describe it?I
   Thank you
   Nawal

   • Hello Nawalamir,

     First let us get some basic knowledge about significant figures. To determine the significant figures of a number, we have to follow 3 rules.

     1. Non-zero digits are always significant.
     2. Any zeros between two significant digits are significant.
     3. A final zero or trailing zeros in the decimal portion only are significant.

     And now see the following example.
     Ex: 3.657
     Round to 3 significant figures: Answer = 3.66
     Round to 2 significant figures: Answer = 3.7
     Now you can see that, when they ask you to write your answer “greater than or equal to 2 significant figures”, it involves 3.7 (ex: x ≥ 3.7). But if you write it using 3 significant figures, it involves 3.66 (ex: x ≥ 3.66).
     x ≥ 3.7 and x ≥ 3.66 are not the same. So that, the best practice is to give your answer according to what they specifically ask in the paper. It will help you gain marks.

     And the second question about the graphs is a bit confusing. We appreciate if you can elaborate it further.

     For the explanation to the 3rd question, see the below description.
     In simple, a point of inflexion can be identified, when the curve changes from concave upward to concave downward (or vice versa). There are two types of inflexion points.
     1. Concave upward to concave downward.
     2. Concave downward to concave upward.
     These are the 2 types of inflexion points. You can use the first derivative of the function, to identify these inflexion points, where the first derivative changes from increasing to decreasing or vice versa.

     Hope this will help. We are here for you!

     Best Regards,
     Mathematics Department

     • Thank you for your detail reply, just one thing in maths mark scheme gives answer sometimes in 3significant figure and also accepts answer with four significant figures. So for maths paper I should write answer s.f according to how much the given values in the question allow?. Also I’ll clarify my question in reference to graph, the paper 0580/42/m/j/2020,Q no 9, part c(i), is the one I am asking about.thanks again nawalamir

       • Hello Nawalamir,

         It is our pleasure to help you.

         In the question paper, if they ask you to give your answer as an inequality (a range for x values, ex: greater than or equal to 2 significant figures) you have to follow the above mentioned method for answering. But if they ask you to give an exact value for an answer (ex: x = 3.66 ) writing x = 3.66 instead of x = 3.7 is more accurate as it (3.66) is correct to two decimal places. BUT, what we recommend is to give your answer according to their requirement in the question. Then no second thought will be needed for the examiner, as your answer is straightforward to the question.

         For the question about graphs, in this case (0580/42/m/j/2020,Q no 9, part c(i)) a specific range for x is not given. You can decide on what values for x should be taken, to figure out the general shape of the graph. In this question, to find the point where the graph intersects the y axis, x should be 0. And to find the point, where the graph meets the x axis, y should be 0 (then x = 1) . According to the marking scheme, they have taken a small range between -2 and 4 to figure out the shape of the graph. Here you do not need to plot the graph for a large range of x. You just have to decide the range which helps to figure out the shape of the graph.

         Hope this will help. We are here for you!

         Best Regards,
         Mathematics Department