HOW TO SOLVE THIS MATH PROBLEMS (1 Viewer)

[eternallyboreduser]

spam past papers really, as many questions as possible so then u can get all the easy / repeat questions out of the way, and then spend more time on the harder ones

and make sure u have a really good conceptual understanding of what’s happening, that way no matter what they give u u can still figure out the question

Wdym by conceptual understanding? Do you mean like actually knowing why you do certain steps rather than just memorising that you have to do this and then this next?

 

[liamkk112]

Wdym by conceptual understanding? Do you mean like actually knowing why you do certain steps rather than just memorising that you have to do this and then this next?

essentially. probably the most comparable thing is in physics; my teacher always told our class 1 million times that the "concept" was much more important than any formula he would write on the board, because if we could understand the concept correctly then most of the time we could just derive the formulas anyway. not to discredit memorising the formulas/constants, but the thing is that on any exam u could possibly get, u will get a question that you have never seen before, likely requiring a completly new application of the formulas/concepts, and so its much more important to actually understand the physical concepts, eg in physics when is magnetic flux a maximum, intuitively rather than just using the angle given in the formula (you might have not learnt this yet), so even if they give u a completly unseen diagram that might be drawn terribly you can use the concept intuitively rather than the formula to deduce the answer.

the key word there really is intuition, as understanding the concepts allows you to intuitively comprehend any question, and better understand what exactly the question is asking of you and what steps/ideas would get you to the correct answer. for an example in mx2, for root questions of complex numbers it is often enough to just memorise the steps, as most of the time you are just finding all the possible angles. but a conceptual question that they could ask you that could chew through your time is to not find the roots, but instead graph all the roots for the same number of marks. a student who has only memorised the steps would likely set up an equation, find all the roots, and then graph all of the roots. but a student with a deep conceptual understanding would realise that all of the roots of a complex number are always spread out evenly, find the first angle, and then the question is effectively finished in way faster time as the only thing that is needed is to add the angles evenly (2pi / nth root, from memory).

that was not the greatest example, but my key point is that an intuitive understanding of the content will often give you a leg up over students who reduce mx2 to rote learning formulas/steps. i would say that mx1 and advanced can be very effectively reduced to just spamming formulas/steps, but the reason why subjects like mx2, physics, chem etc are difficult for many students is that the content can not just be memorised, but instead you need to develop intuitive reasoning for why things are happening in the subject, and that is done through deeply understanding concepts rather than memorisation.

 

[eternallyboreduser]

essentially. probably the most comparable thing is in physics; my teacher always told our class 1 million times that the "concept" was much more important than any formula he would write on the board, because if we could understand the concept correctly then most of the time we could just derive the formulas anyway. not to discredit memorising the formulas/constants, but the thing is that on any exam u could possibly get, u will get a question that you have never seen before, likely requiring a completly new application of the formulas/concepts, and so its much more important to actually understand the physical concepts, eg in physics when is magnetic flux a maximum, intuitively rather than just using the angle given in the formula (you might have not learnt this yet), so even if they give u a completly unseen diagram that might be drawn terribly you can use the concept intuitively rather than the formula to deduce the answer.

the key word there really is intuition, as understanding the concepts allows you to intuitively comprehend any question, and better understand what exactly the question is asking of you and what steps/ideas would get you to the correct answer. for an example in mx2, for root questions of complex numbers it is often enough to just memorise the steps, as most of the time you are just finding all the possible angles. but a conceptual question that they could ask you that could chew through your time is to not find the roots, but instead graph all the roots for the same number of marks. a student who has only memorised the steps would likely set up an equation, find all the roots, and then graph all of the roots. but a student with a deep conceptual understanding would realise that all of the roots of a complex number are always spread out evenly, find the first angle, and then the question is effectively finished in way faster time as the only thing that is needed is to add the angles evenly (2pi / nth root, from memory).

that was not the greatest example, but my key point is that an intuitive understanding of the content will often give you a leg up over students who reduce mx2 to rote learning formulas/steps. i would say that mx1 and advanced can be very effectively reduced to just spamming formulas/steps, but the reason why subjects like mx2, physics, chem etc are difficult for many students is that the content can not just be memorised, but instead you need to develop intuitive reasoning for why things are happening in the subject, and that is done through deeply understanding concepts rather than memorisation.

How can we improve this? I find that in some exams (e.g. my chem module 1 exam for tutoring. there was a q which gave us the diagram of cyclopropane and propane and asked why cyclopropane was more reactive under the same conditions. I know the answer now and it makes sense but during the exam I had no clue what it was) there are qs that I havent ever seen and i just have no clue how ti approach them.

 

[liamkk112]

How can we improve this? I find that in some exams (e.g. my chem module 1 exam for tutoring. there was a q which gave us the diagram of cyclopropane and propane and asked why cyclopropane was more reactive under the same conditions. I know the answer now and it makes sense but during the exam I had no clue what it was) there are qs that I havent ever seen and i just have no clue how ti approach them.

1. reading/exploring widely

this is, in my opinion, probably the most underrated technique. the hsc syllabus often seems quite limiting in its scope, and to be honest it is, but looking at other sources can be super helpful. even just watching videos on other countries' high school syllabus can help a lot, as they often provide alternative perspectives that allow you to approach questions in many different ways. for example in physics, hsc teaches all of the concepts without calculus, but understanding how many formulas came to be by using calculus definetly helped me to understand what they actually meant. first year university content can also be quite useful too, such as for combinatorics in extension 1, since these ideas are universal and its not like the hsc is the only one to be teaching these topics (would recommend this video if you're struggling with combinatorics:

). having an additional layer of understanding is also great to provide some higher level information, just make sure its not too overkill, but again first year uni content is typically quite safe.

2. fundamentals first, then all else and always link back

unfortunately in year 11 i decided to pick 3 sciences, though i eventually decided to drop to only take physics. chem was literally the worst class ever for me, and in hindsight its because i really neglected to fully absorb the fundamentals, not only in year 11 content but also year 10. the fundamentals are super important, such as for chemistry: what is an atom, molecule, chemical, isotope, etc. its really easy to just gloss over these simple defintions and terms but they will ultimately screw you over later, as everything else naturally builds on top of this. for example my first chem test was on all the decays of nuclei. i recall there was one question asking for one isotope that was used in medical industries, and in my response i referred to the isotope as an atom or element or something, causing me to lose a lot of marks on a 7 marker. these terminologies are super important not only for your responses, but also your understanding, because they are so fundamental to the subject.

now i am not an expert at chemistry at all but id say that there is probably some basic notion of reactivity that was taught very early on in the syllabus. it is quite easy to be ignorant of these small details, but definetly make sure you understand why reactivity differs, what factors are at play, etc and make sure to connect everything back to the fundamentals of chemistry, such as electrons in valence shell blah blah blah. if you understand how everything connects back to the basic "axioms" of the subject, then the content will much more naturally make sense and you can better answer any question they give you. eg in physics, always keeping the super fundamental ideas of newtons laws of motion, conservation of energy and momentum, vector and scalar quantity in the back of your mind effectively answers 90% of mod 5 questions, and reduces the amount of mistakes you will make.

3. get out of your comfort zone

a common mistake i always made in year 11 is that i would be quite demotivated to spend time on the questions that i was not entirely comfortable with answering. however, this is probably the most important thing that many people neglect. while yes, it is a good idea to keep spamming out questions in the topics you're comfortable with, definetly spend a lot of time on fixing up the patches in your knowledge, even if its frustrating. for example in ext 1 i would always neglect combinatorics as i would always think that there was a new method to solve every question lol, super annoying. but then approaching the trials i spent all of the class time we had given for revision on combinatorics, just going through the textbook derivations of everything, all of the questions i could find etc and ultimately forcing myself to not just do integration questions or whatever actually made me a lot more confident in the topic, and then in the trials i didnt get any combinatorics questions wrong at all (damn q10 in hsc though).


overall id say that i was also quite similar to you in year 11, especially in the sciences i found it so frustrating that every question seemed to require a completly different approach that seems to appear out of nowhere, as if they are just wanting to you to "use a trick" that doesn't properly test your knowledge. i would say the best thing to do is just to practice as much as you can, expose yourself to as many questions as possible, but before you do that really make sure all of your baseline knowledge is there first, draw mind maps, flowcharts, whatever lets you connect up all of the information in the subject in an intuitive manner and lets you understand how different concepts intertwine and come to be. do not just ignorantly spam out questions, at least in the beginning write down everything you think that could be relevant to a question, what techniques do you think that you could use, also possibly if theres two different methods to answer the question to double check the answer, take your time and make sure you can analyse the question as deeply as possible. also know that memorisation of some things is important, especially in chem, but never ever EVER make the mistake of just looking at a question and going "oh, that looks like a question ive seen before" because that is a big trap that you think will save you time but might end up with you losing all your marks. so always try to look at every question as if you've never seen it before, consider everything before jumping in and answering the question, this way your response will be more calculated.

uhh sorry for the end bit its a bit unclear but hopefully the numbered parts are clear : ) good luck

 

[Luukas.2]

2. fundamentals first, then all else and always link back

unfortunately in year 11 i decided to pick 3 sciences, though i eventually decided to drop to only take physics. chem was literally the worst class ever for me, and in hindsight its because i really neglected to fully absorb the fundamentals, not only in year 11 content but also year 10. the fundamentals are super important, such as for chemistry: what is an atom, molecule, chemical, isotope, etc. its really easy to just gloss over these simple defintions and terms but they will ultimately screw you over later, as everything else naturally builds on top of this. for example my first chem test was on all the decays of nuclei. i recall there was one question asking for one isotope that was used in medical industries, and in my response i referred to the isotope as an atom or element or something, causing me to lose a lot of marks on a 7 marker. these terminologies are super important not only for your responses, but also your understanding, because they are so fundamental to the subject.

now i am not an expert at chemistry at all but id say that there is probably some basic notion of reactivity that was taught very early on in the syllabus. it is quite easy to be ignorant of these small details, but definetly make sure you understand why reactivity differs, what factors are at play, etc and make sure to connect everything back to the fundamentals of chemistry, such as electrons in valence shell blah blah blah. if you understand how everything connects back to the basic "axioms" of the subject, then the content will much more naturally make sense and you can better answer any question they give you. eg in physics, always keeping the super fundamental ideas of newtons laws of motion, conservation of energy and momentum, vector and scalar quantity in the back of your mind effectively answers 90% of mod 5 questions, and reduces the amount of mistakes you will make.

I agree that understanding fundamentals is of great value, and looking into the "why"s. @liamkk112, your understanding of physics can explain the propane v. cyclopropane without knowing the chemistry. Many chemical reactions occur for the same reason that a ball at the top of a hill will roll down if bumped - it is moving to a lower energy state. The bonds around an atom tend to point in directions to maximise the distances between them. Why? Because the bonds in these cases are covalent and so consist of pairs of electrons and so each repels the other (Coulomb's Law). For an atom with four bonds, the energy minimum / most stable configuration is for them to point to the corners of a tetrahedron, with an angular separation of about 109.5 degrees. This is exactly what is found in propane.

Cyclopropane, on the other hand, has its three carbon atoms bound into a triangular ring. Thus, its C-C-C bond angles are 60 degrees, which puts considerable strain on the bonds, weakening them - they are much easier to break and the dominant mode of reaction is addition, forming a propane chain by breaking open the ring. Propane's dominant reaction is substitution as this maintains the unstrained tetrahedral geometry.

The question asked, showing the two molecules, is testing not only whether the student knows what geometry is ideal, but also why deviation from it has consequences. The reactivity of many compounds either reflects geometric properties, or can be deduced by considering how / why a drive towards an alternative configuration is desirable.

 

[Luukas.2]

3. get out of your comfort zone

a common mistake i always made in year 11 is that i would be quite demotivated to spend time on the questions that i was not entirely comfortable with answering. however, this is probably the most important thing that many people neglect. while yes, it is a good idea to keep spamming out questions in the topics you're comfortable with, definetly spend a lot of time on fixing up the patches in your knowledge, even if its frustrating. for example in ext 1 i would always neglect combinatorics as i would always think that there was a new method to solve every question lol, super annoying. but then approaching the trials i spent all of the class time we had given for revision on combinatorics, just going through the textbook derivations of everything, all of the questions i could find etc and ultimately forcing myself to not just do integration questions or whatever actually made me a lot more confident in the topic, and then in the trials i didnt get any combinatorics questions wrong at all (damn q10 in hsc though).

On this point, I would encourage not only working on topics that you find challenging, but also seeking out questions that cross multiple topics. These can often involve different approaches and new ways of looking at questions. They also help you to develop insight into the links between topics. Multiple topics in a question is a very effective way to make questions harder. It also makes recognising which algoirithmic approaches might apply less obvious, which hampers students relying on algorithmic as opposed to conceptual understanding.

 

[eternallyboreduser]

How can we improve this? I find that in some exams (e.g. my chem module 1 exam for tutoring. there was a q which gave us the diagram of cyclopropane and propane and asked why cyclopropane was more reactive under the same conditions. I know the answer now and it makes sense but during the exam I had no clue what it was) there are qs that I havent ever seen and i just have no clue how ti approach them.

Where can I find qs like these? Most qs on selective school papers r relatively easy and dont test anything out of the ordinary for mod1

 

[eternallyboreduser]

1. reading/exploring widely

this is, in my opinion, probably the most underrated technique. the hsc syllabus often seems quite limiting in its scope, and to be honest it is, but looking at other sources can be super helpful. even just watching videos on other countries' high school syllabus can help a lot, as they often provide alternative perspectives that allow you to approach questions in many different ways. for example in physics, hsc teaches all of the concepts without calculus, but understanding how many formulas came to be by using calculus definetly helped me to understand what they actually meant. first year university content can also be quite useful too, such as for combinatorics in extension 1, since these ideas are universal and its not like the hsc is the only one to be teaching these topics (would recommend this video if you're struggling with combinatorics:

). having an additional layer of understanding is also great to provide some higher level information, just make sure its not too overkill, but again first year uni content is typically quite safe.

2. fundamentals first, then all else and always link back

unfortunately in year 11 i decided to pick 3 sciences, though i eventually decided to drop to only take physics. chem was literally the worst class ever for me, and in hindsight its because i really neglected to fully absorb the fundamentals, not only in year 11 content but also year 10. the fundamentals are super important, such as for chemistry: what is an atom, molecule, chemical, isotope, etc. its really easy to just gloss over these simple defintions and terms but they will ultimately screw you over later, as everything else naturally builds on top of this. for example my first chem test was on all the decays of nuclei. i recall there was one question asking for one isotope that was used in medical industries, and in my response i referred to the isotope as an atom or element or something, causing me to lose a lot of marks on a 7 marker. these terminologies are super important not only for your responses, but also your understanding, because they are so fundamental to the subject.

now i am not an expert at chemistry at all but id say that there is probably some basic notion of reactivity that was taught very early on in the syllabus. it is quite easy to be ignorant of these small details, but definetly make sure you understand why reactivity differs, what factors are at play, etc and make sure to connect everything back to the fundamentals of chemistry, such as electrons in valence shell blah blah blah. if you understand how everything connects back to the basic "axioms" of the subject, then the content will much more naturally make sense and you can better answer any question they give you. eg in physics, always keeping the super fundamental ideas of newtons laws of motion, conservation of energy and momentum, vector and scalar quantity in the back of your mind effectively answers 90% of mod 5 questions, and reduces the amount of mistakes you will make.

3. get out of your comfort zone

a common mistake i always made in year 11 is that i would be quite demotivated to spend time on the questions that i was not entirely comfortable with answering. however, this is probably the most important thing that many people neglect. while yes, it is a good idea to keep spamming out questions in the topics you're comfortable with, definetly spend a lot of time on fixing up the patches in your knowledge, even if its frustrating. for example in ext 1 i would always neglect combinatorics as i would always think that there was a new method to solve every question lol, super annoying. but then approaching the trials i spent all of the class time we had given for revision on combinatorics, just going through the textbook derivations of everything, all of the questions i could find etc and ultimately forcing myself to not just do integration questions or whatever actually made me a lot more confident in the topic, and then in the trials i didnt get any combinatorics questions wrong at all (damn q10 in hsc though).


overall id say that i was also quite similar to you in year 11, especially in the sciences i found it so frustrating that every question seemed to require a completly different approach that seems to appear out of nowhere, as if they are just wanting to you to "use a trick" that doesn't properly test your knowledge. i would say the best thing to do is just to practice as much as you can, expose yourself to as many questions as possible, but before you do that really make sure all of your baseline knowledge is there first, draw mind maps, flowcharts, whatever lets you connect up all of the information in the subject in an intuitive manner and lets you understand how different concepts intertwine and come to be. do not just ignorantly spam out questions, at least in the beginning write down everything you think that could be relevant to a question, what techniques do you think that you could use, also possibly if theres two different methods to answer the question to double check the answer, take your time and make sure you can analyse the question as deeply as possible. also know that memorisation of some things is important, especially in chem, but never ever EVER make the mistake of just looking at a question and going "oh, that looks like a question ive seen before" because that is a big trap that you think will save you time but might end up with you losing all your marks. so always try to look at every question as if you've never seen it before, consider everything before jumping in and answering the question, this way your response will be more calculated.

uhh sorry for the end bit its a bit unclear but hopefully the numbered parts are clear : ) good luck

I'll give this a try, thanks for the detailed response