How to stop making stupid mistakes in maths
Hi, I am desperate for an A* IN REGULAR maths (I take FM too!), but every paper I do, I don't lose marks from not knowing content, I lose it from silly, stupid, dumb mistakes. Truthfully, I really love maths, but my exams are in 8 months and I feel like I am losing the will to continue because I genuinely love the subject but keep making so easily avoidable mistakes that might cost the ENTIRE question
Examples from today alone:
- In integration, I will forget to divide by the inside function in reverse chain rule (e.g (2x + 1)^-1 would be (1/2)ln|2x+1| but i would write just ln|2x+1|)
- Incorrect expansion leading to sign errors.
- When I was doing a binomial approximation, I interepreted 1/ sqrt(2x+1) as (2x+1)^0.5 and not to the power of -0.5
I have tried slowing down, writing everything out, I have noted down every single mistake I have ever done, but it's going nowhere. I feel hopeless.
Please help
Examples from today alone:
- In integration, I will forget to divide by the inside function in reverse chain rule (e.g (2x + 1)^-1 would be (1/2)ln|2x+1| but i would write just ln|2x+1|)
- Incorrect expansion leading to sign errors.
- When I was doing a binomial approximation, I interepreted 1/ sqrt(2x+1) as (2x+1)^0.5 and not to the power of -0.5
I have tried slowing down, writing everything out, I have noted down every single mistake I have ever done, but it's going nowhere. I feel hopeless.
Please help
Original post by willwillwill1
Hi, I am desperate for an A* IN REGULAR maths (I take FM too!), but every paper I do, I don't lose marks from not knowing content, I lose it from silly, stupid, dumb mistakes. Truthfully, I really love maths, but my exams are in 8 months and I feel like I am losing the will to continue because I genuinely love the subject but keep making so easily avoidable mistakes that might cost the ENTIRE question
Examples from today alone:
- In integration, I will forget to divide by the inside function in reverse chain rule (e.g (2x + 1)^-1 would be (1/2)ln|2x+1| but i would write just ln|2x+1|)
- Incorrect expansion leading to sign errors.
- When I was doing a binomial approximation, I interepreted 1/ sqrt(2x+1) as (2x+1)^0.5 and not to the power of -0.5
I have tried slowing down, writing everything out, I have noted down every single mistake I have ever done, but it's going nowhere. I feel hopeless.
Please help
Examples from today alone:
- In integration, I will forget to divide by the inside function in reverse chain rule (e.g (2x + 1)^-1 would be (1/2)ln|2x+1| but i would write just ln|2x+1|)
- Incorrect expansion leading to sign errors.
- When I was doing a binomial approximation, I interepreted 1/ sqrt(2x+1) as (2x+1)^0.5 and not to the power of -0.5
I have tried slowing down, writing everything out, I have noted down every single mistake I have ever done, but it's going nowhere. I feel hopeless.
Please help
A few things
•
The more papers/questions you do, the fewer mistakes youll end up making as you do tend to remember them and usually dont make them too much again.
•
Do create a list of important mistakes and review it. For each of them, think of a way to avoid it (not just by saying learn it better, which would be a cop out).
•
For the log one, you could work back from your answer and differentiate log(2x+1) to get 2/(2x+1). Using substitution is slightly longer but arguably a bit safer than reverse chain. So get in the habit of working back if its easy and if theres a safe method use it / check your answer with it.
•
Guestimate/approximate an answer. Does it make sense, so would an integral have approximately the right value if you simplified it. Would an algebraic expression make sense if a variable was zero. Or ... For the binomial, if x=0.105 then 1/sqrt(2x+1)=1/1.1=0.90909. Does your appoxiation match that?
•
Personally, Id not say that slowing down or simply reading through your work really works that well. You really need to work out that youve made a mistake first, then work out how to find it.
•
Sometimes doing harder questions (so at least the usual exam questions) helps as you make more mistakes/better understanding so the train hard, fight easy.
•
Try doing some work in "exam settings", so get used to the environment and try and ensure it doesnt affect you / make more mistakes.
(edited 4 weeks ago)
Original post by mqb2766
A few things
Theres no silver bullet but doing something like the above should help and maths is a subject where its easy to make the odd silly mistake.
•
The more papers/questions you do, the fewer mistakes youll end up making as you do tend to remember them and usually dont make them too much again.
•
Do create a list of important mistakes and review it. For each of them, think of a way to avoid it (not just by saying learn it better, which would be a cop out).
•
For the log one, you could work back from your answer and differentiate log(2x+1) to get 2/(2x+1). Using substitution is slightly longer but arguably a bit safer than reverse chain. So get in the habit of working back if its easy and if theres a safe method use it / check your answer with it.
•
Guestimate/approximate an answer. Does it make sense, so would an integral have approximately the right value if you simplified it. Would an algebraic expression make sense if a variable was zero. Or ... For the binomial, if x=4, then 1/sqrt(2x+1) = 1/3. Does your appoxiation match that?
•
Personally, Id not say that slowing down or simply reading through your work really works that well. You really need to work out that youve made a mistake first, then work out how to find it.
•
Sometimes doing harder questions (so at least the usual exam questions) helps as you make more mistakes/better understanding so the train hard, fight easy.
•
Try doing some work in "exam settings", so get used to the environment and try and ensure it doesnt affect you / make more mistakes.
In the last 3 months I have done by mean average ~2 hours per day, yet I see no improvement. I'm just getting wrroied. I do hard questions too, but still. I guess I'll keep going, but maybe do 3-4 a day until the exams.
Original post by willwillwill1
In the last 3 months I have done by mean average ~2 hours per day, yet I see no improvement. I'm just getting wrroied. I do hard questions too, but still. I guess I'll keep going, but maybe do 3-4 a day until the exams.
Its hard to say what will work for a particular person, but the above should help and in particular try to efficiently verify an answer - so work backwards or sub simple values into an answer and see if it makes sense.
For the binomial one, you could also note your "x" term was positive whereas the correct one would be negative as the 1/sqrt(1+2x) is < 1 when x>0 but sqrt(1+2x) is > 1. Its partially about thinking why an answer makes sense, rather than just "Ive got an answer, it must be right". The old saying in computing is "if youve not tested it, it doesnt work".
Youre still covering the syllabus, so its not surprising that you make mistakes on new stuff as thats natural. Maybe every so often do a mix of questions from past papers for the topics youve done (if you do edexcel, then maybe aqa or vice versa, so you leave the proper papers for revision closer to the exam) and see if you notice an improvement on the topics youve covered?
(edited 4 weeks ago)
Original post by mqb2766
Its hard to say what will work for a particular person, but the above should help and in particular try to efficiently verify an answer - so work backwards or sub simple values into an answer and see if it makes sense.
For the binomial one, you could also note your "x" term was positive whereas the correct one would be negative as the 1/sqrt(1+2x) is < 1 when x>0 but sqrt(1+2x) is > 1. Its partially about thinking why an answer makes sense, rather than just "Ive got an answer, it must be right". The old saying in computing is "if youve not tested it, it doesnt work".
Youre still covering the syllabus, so its not surprising that you make mistakes on new stuff as thats natural. Maybe every so often do a mix of questions from past papers for the topics youve done (if you do edexcel, then maybe aqa or vice versa, so you leave the proper papers for revision closer to the exam) and see if you notice an improvement on the topics youve covered?
For the binomial one, you could also note your "x" term was positive whereas the correct one would be negative as the 1/sqrt(1+2x) is < 1 when x>0 but sqrt(1+2x) is > 1. Its partially about thinking why an answer makes sense, rather than just "Ive got an answer, it must be right". The old saying in computing is "if youve not tested it, it doesnt work".
Youre still covering the syllabus, so its not surprising that you make mistakes on new stuff as thats natural. Maybe every so often do a mix of questions from past papers for the topics youve done (if you do edexcel, then maybe aqa or vice versa, so you leave the proper papers for revision closer to the exam) and see if you notice an improvement on the topics youve covered?
Thanks. Although we already finished the syllabus. Which is worrying. I'll probably swot it out for the next 7 months, and see where I get to.
Original post by willwillwill1
Thanks. Although we already finished the syllabus. Which is worrying. I'll probably swot it out for the next 7 months, and see where I get to.
You must have covered it last year and doing FM this year? Others may chip with some tips, but just getting some regular practice in (so maybe work though other exam board papers first) and get in the habit of trying to verify solutions (efficiently) and understanding expressions, etc. The boundaries were on the high side this year, but youve got a reasonable amount of time to practice and whatever you do should apply to the FM stuff as well.
Post the odd mistake here if you want another person to look at it.
Original post by willwillwill1
Hi, I am desperate for an A* IN REGULAR maths (I take FM too!), but every paper I do, I don't lose marks from not knowing content, I lose it from silly, stupid, dumb mistakes. Truthfully, I really love maths, but my exams are in 8 months and I feel like I am losing the will to continue because I genuinely love the subject but keep making so easily avoidable mistakes that might cost the ENTIRE question
Examples from today alone:
- In integration, I will forget to divide by the inside function in reverse chain rule (e.g (2x + 1)^-1 would be (1/2)ln|2x+1| but i would write just ln|2x+1|)
- Incorrect expansion leading to sign errors.
- When I was doing a binomial approximation, I interepreted 1/ sqrt(2x+1) as (2x+1)^0.5 and not to the power of -0.5
I have tried slowing down, writing everything out, I have noted down every single mistake I have ever done, but it's going nowhere. I feel hopeless.
Please help
Examples from today alone:
- In integration, I will forget to divide by the inside function in reverse chain rule (e.g (2x + 1)^-1 would be (1/2)ln|2x+1| but i would write just ln|2x+1|)
- Incorrect expansion leading to sign errors.
- When I was doing a binomial approximation, I interepreted 1/ sqrt(2x+1) as (2x+1)^0.5 and not to the power of -0.5
I have tried slowing down, writing everything out, I have noted down every single mistake I have ever done, but it's going nowhere. I feel hopeless.
Please help
I used to do the same but I forced myself to detail EVERYTHING. It's annoying at first and you'll probably lose time but it's a lot easier to pick up on those kind of mistakes when they stick out.
(edited 4 weeks ago)
Original post by Priyapsa
I used to do the same but I forced myself to detail EVERYTHING. It's annoying at first and you'll probably lose time but it's a lot easier to pick up on those kind of mistakes when they stick out.
I get extra time so perhaps this is something I will force myself to get more into the rythm of. I just did one more past paper before bed and got 73/80 (I didn't do the last 20 marks, but I am sure I could honestly do them). I lost marks on so much easily avoidable stuff, such as incorrectly manipulating integrands (like taking out a multiple, and forgetting to apply it to a second term), getting my SOH CAH TOA the wrong way round, and misreading the question when it says to use the diagram to aid me - i was entirely correct in my reasoning, but just didn't use the diagram.
I feel very nervous.
Original post by willwillwill1
I get extra time so perhaps this is something I will force myself to get more into the rythm of. I just did one more past paper before bed and got 73/80 (I didn't do the last 20 marks, but I am sure I could honestly do them). I lost marks on so much easily avoidable stuff, such as incorrectly manipulating integrands (like taking out a multiple, and forgetting to apply it to a second term), getting my SOH CAH TOA the wrong way round, and misreading the question when it says to use the diagram to aid me - i was entirely correct in my reasoning, but just didn't use the diagram.
I feel very nervous.
I feel very nervous.
wbf, thats hardly a bad mark and you will improve with a bit of regular practice. Youre probably being a bit hard on yourself.
What as the trig problem?
Original post by mqb2766
wbf, thats hardly a bad mark and you will improve with a bit of regular practice. Youre probably being a bit hard on yourself.
What as the trig problem?
What as the trig problem?
I just fear I'll have a bad day and that'll be 20% or 30% of my mark as opposed to 9.75%. I basically did tan-1 ( adjactent / opposite) as opposed to opposite/adjacent, any ways to avoid trig-related errors like that?
Apart from the above, take a break. Pace yourself.
As much as I love maths, I stop once I feel fatigued. (Well, if you feel fatigued for days, then there might be a problem, but I'll let you figure it out by then)
As much as I love maths, I stop once I feel fatigued. (Well, if you feel fatigued for days, then there might be a problem, but I'll let you figure it out by then)
(edited 4 weeks ago)
Original post by willwillwill1
I just fear I'll have a bad day and that'll be 20% or 30% of my mark as opposed to 9.75%. I basically did tan-1 ( adjactent / opposite) as opposed to opposite/adjacent, any ways to avoid trig-related errors like that?
Bad days can occur but if youre doing regular practice for 6 months and do it under "exam conditions" when necessary, its honestly not that likely. Even if you have 1 bad paper, the other two probably wont be. Dont be too hard on yourself
For tan, it represents the gradient (of the hypotenuse) so it must be opp/adj if you draw the right triangle. So its zero (tan and gradient) when the angle is zero as the hypotenuse is horizontal and it gradually gets larger as the opp is extended upwards. Thinking of the right triangle and circle interpretation can help if/when you get stuck and Ill dig a link out tomorrow.
(edited 4 weeks ago)
Original post by mqb2766
Bad days can occur but if youre doing regular practice for 6 months and do it under "exam conditions" when necessary, its honestly not that likely. Even if you have 1 bad paper, the other two probably wont be. Dont be too hard on yourself
For tan, it represents the gradient (of the hypotenuse) so it must be opp/adj if you draw the right triangle. So its zero (tan and gradient) when the angle is zero as the hypotenuse is horizontal and it gradually gets larger as the opp is extended upwards. Thinking of the right triangle and circle interpretation can help if/when you get stuck and Ill dig a link out tomorrow.
For tan, it represents the gradient (of the hypotenuse) so it must be opp/adj if you draw the right triangle. So its zero (tan and gradient) when the angle is zero as the hypotenuse is horizontal and it gradually gets larger as the opp is extended upwards. Thinking of the right triangle and circle interpretation can help if/when you get stuck and Ill dig a link out tomorrow.
nah ik how to intepret it, i drew it out and such, it's just i accidentally put them in the calc the wrong way
Original post by willwillwill1
nah ik how to intepret it, i drew it out and such, it's just i accidentally put them in the calc the wrong way
Id probably need to see the question and maybe what you did, but usually guestimating it is a quick way to check, so the usual tan is 1 when the angle is 45 or pi/4, so if you put them in your calc the wrong way round, youd get > 1 when you know its < 1, or the flip.
(edited 4 weeks ago)
Original post by willwillwill1
nah ik how to intepret it, i drew it out and such, it's just i accidentally put them in the calc the wrong way
Commenting not just on this but the whole thread:
You're completed the syllabus and getting 90+% in practice papers. You're going to be fine. I understand the worry about "a bad paper", but there are 3 papers, the chances of them all being bad are miniscule. (Plus, if you're still working on maths, I'd be very surprised if that 90+% doesn't creep up to at least 95+% by the time of the exams).
That said, I'd say a general theme in the mistakes you've described is not having a general "feel" for how the answer should behave. (i.e. 1/sqrt(2x+1) is going to be smaller than 1, whether tan(x) is small, near 1 or near infnity depending on the value of x). It's worth improving this skill, because it's generally useful, particularly if you want to study maths post A-level. These days I find I largely decide whether I should use sin/cos/tan/cot etc. based on "what should the answer look like when the angle is very small/very large?".
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