I've always done badly for maths almostly entirely because of careless mistakes. Think addition/subtraction/multiplication/division errors, wrong signs, wrong numbers, pressing the wrong keys on the graphic calculator, copying the question wrongly, etc etc.
I'm am absolutely sure that my math is OK. Everytime I get a question wrong and I redo it, I can get the right answer. My methods to solving questions are correct, it just happens that the numbers are wrong due to little mistakes, which I think is due to my laziness when I was in secondary school. Foundation's weak, maybe?
It is bloody frustrating. I've done every single JC's math prelim papers for 2010 and almost 2011, and these mistakes never go away. I need advice on what to do so as to not throw away a good grade due to sotong mistakes. Fire away.
Thanks in advance.
check
check
check
check
Since your workings are correct, always take your answers and work backwards
I tend to be quite careless too. Like mistyping an extra digit or omitting certain calculator values by pressing the keys too quickly..
What i have been doing to prevent such silly mistakes from occuring would be to look at my calculator screen and check the input values for just a second more to double confirm that they are correct (only takes a second more.. which can be potentially valuable and time saving .. if you are prone to such mistakes)
This ensures that if i do get a wrong answer, it is not a calculation mistake but a fundermentals mistake.. which i would then go back to the paper and check my formulas, correct it ..
Also when you have doubts. Immediately look back to quash your fears. Else half way through you might panic and then give up on a question that you normally could solve
Hi donkhead333,
It is good that you already make a note of the specific errors you tend to make. Just remind yourself consciously when you are doing the questions that you should look out for them.
If you are already applying correct methods to solve problems, you are not weak, foundationally speaking. Stop thinking about your lack of competency because that will affect your ability to improve and excel further due to the conditioning of the mind.
Jiayou!
Cheers,
Wen Shih
Do your work systematically.
Write down the formula first before actually using the formula. That way you rely less on mental work and will have a lower tendency to make mistakes. For example, don't just write
F = 2 * 5 = 10 ms-2
Instead, write
F = ma = 2*5 = 10 ms-2
I also always tell my students to write down a statement beforehand to show what they are doing. For example:
2+ 2 = 5
This will net you zero marks because no one knows what you're doing. On the other hand,
Length of section AB = 2 + 2 = 5 m
This will still get you partial marks (even though the arithmetic is wrong) because the examiner knows what you're trying to drive at.
Hi,
you will also need to have quick check methods to ensure you are correct.
Some personal tips to share that I share with all my students.
1) WRITE CLEARLY. There are times where because of untidy handwriting, the student misinterprets his/her workings. Do not get into this category.
2) Cross product, i.e. a x b = c. Carelessness can be avoided if you simply take a.c and b.c and ensure both are zero.
3) Definite Integral. Check using GC!!! When questions ask for exact values or "without using a graphic calculator", it does not mean you cannot use GC to verify! All the more it hints you to use the GC to verify your answer!
These are some that comes to my head at the moment... Will update when more comes in.
Practice.
Practice.
Practice.
Don't lose concentration.
Focus
Focus
Focus.
Check
Recheck
Check
See the clock
Check timing, don't waste time, allocate sufficiently
After done all questions - do a post mortem - see where you went wrong. Use logic to improve what was done
Originally posted by donkhead333:I've always done badly for maths almostly entirely because of careless mistakes. Think addition/subtraction/multiplication/division errors, wrong signs, wrong numbers, pressing the wrong keys on the graphic calculator, copying the question wrongly, etc etc.
I'm am absolutely sure that my math is OK. Everytime I get a question wrong and I redo it, I can get the right answer. My methods to solving questions are correct, it just happens that the numbers are wrong due to little mistakes, which I think is due to my laziness when I was in secondary school. Foundation's weak, maybe?
It is bloody frustrating. I've done every single JC's math prelim papers for 2010 and almost 2011, and these mistakes never go away. I need advice on what to do so as to not throw away a good grade due to sotong mistakes. Fire away.
Thanks in advance.
In addition to checking, you could also try practising more of similar papers over and over again.
For some people, once they get use to writing the same equations and going through the similar procedures again and again, they will be able to detect/feel something is wrong whenever they did something incorrectly, even if they are going at optimal speed.
1. Checking NEVER MEANS to read through your solution, your tutor/teacher should give your some instruction on how to check answers for each type of question.
Taking maclaurin series expansion as an example, after you arrive at the final answer, i.e writing y in terms of powers series up to x cube perhaps, you should do some checking similar to the following: Substitute x=0.1 into the original y and your power series up to x cube, if your answer is correct, the difference should only occur from the 4th d.p. or at most from the 3rd d.p. If the two values are 2.49049 and 2.4895 resepctively, most likely you have made a careless mistake at the sign of the x cube. All checking strategies should be speedy and efficient.
Originally posted by frekiwang:1. Checking NEVER MEANS to read through your solution, your tutor/teacher should give your some instruction on how to check answers for each type of question.
Taking maclaurin series expansion as an example, after you arrive at the final answer, i.e writing y in terms of powers series up to x cube perhaps, you should do some checking similar to the following: Substitute x=0.1 into the original y and your power series up to x cube, if your answer is correct, the difference should only occur from the 4th d.p. or at most from the 3rd d.p. If the two values are 2.49049 and 2.4895 resepctively, most likely you have made a careless mistake at the sign of the x cube. All checking strategies should be speedy and efficient.
These methods are good and I use them frequently. The most frustrating part is when I know my answer is wrong, but can't find the mistake after numerous rounds of checking.
But I can spot the mistake in >2seconds after getting back the paper....
Hi donkhead333,
When you get the paper back, you are seeing the questions with fresh eyes, so it is easier to locate the places where you went wrong.
Thanks.
Cheers,
Wen Shih
No, you do not get the my point.
You should never read your solution for checking.
Example, after substituting a value, you realise there should be a mistake somewhere in your working. DO NOT GO BACK AND READ YOUR SOLUTION, most of the times it is just a waste of time as very few ppl are capable of locating the mistake in a few minutes. The best way, is to IGNORE/COVER the flawed working and re-do it on the next page, most likely your 2nd round answer will be different and correct (if you make the same mistake again, the mistake is no longer a 'careless' mistake, it has something to do with your foundation)
Hi,
Here are some specific instances of mistakes I have seen.
Example 1:
y^2 = x^2 - a^2
=> y = x - a [incorrect simplification].
Example 2:
Sketch the solution curve for x > 0.
The student then draws the curve for all values of x [incorrect domain].
Example 3:
Given X ~ N(a, b), Y ~ N(c, d),
the student then computes Var(X_1 + X_2 + X_3 - 2Y) as
3b - 4d or 3b + 2d [incorrect application of the variance result].
Example 4:
To find P(X > a), the student uses continuity correction and writes it as
P(X > a - 0.5) [incorrect continuity correction value].
Example 5:
To find the integral of (cos x)^3 with respect to x, the student writes
(1/4) (cos x)^4
or
(cos x)^4 / (-4 sin x) [incorrect application of the integration result].
Thanks.
Cheers,
Wen Shih
Hi,
More examples for students' reference :)
Example 6:
Find the set of values of x for which a certain inequality is to be solved.
The student writes the answer as x > a [not meeting the question's requirement].
Example 7:
Suppose the result to be shown by induction is
sum {r = 1 to n} (r + 1) / (2^r) = 3 - (n + 3)(1/2)^n
and the student is attempting to prove that a proposition is true for n = k + 1.
He writes
sum {r = 1 to k + 1} (r + 1)/(2^r)
= 3 - (k + 3)(1/2)^k + (k + 2) / (2^(k + 1))
= 3 - (1/2)^k [ (k + 3) + (k + 2)/2 ],
thereby making the negative sign error.
Example 8:
The function f is defined by f : x -> ..., x < a.
The student is asked to find the inverse of f in a similar form and writes his answer as
f(x) = ... [not meeting the question's requirement].
Example 9:
A question about vectors asks the student to find the coordinates of the point F which is the foot of a perpendicular of a point to the plane. He writes the answer in column vector form [not meeting the question's requirement].
Example 10:
Refer to Q8 in 2010 H2 Maths exam paper 2. The student goes on to find the number of ways, rather than giving the answer as a probability.
Thanks.
Cheers,
Wen Shih
Hi,
3rd part posting about common mistakes.
Example 11:
The student is asked to sketch the curve y = (x + 4) / (x(x + 3)).
Referring to the GC and sketching the graph, he misses out the minimum turning point on the negative x-axis, because it is not obvious from the calculator.
Example 12:
Refer to Q11 in 2010 H2 Maths exam paper 1. The student sketches the curve with GC using the parametric equations and misses out one branch of the curve as well as the oblique asymptotes.
Example 13:
Find the probability that their average mass will lie within 60 kg from 100 kg.
The student proceeds to find
P(60 <= X-bar <= 100),
as a result of wrongly interpreting the information.
Example 14:
The mean daily sales over a period of 12 days is found to be 129.5 with variance 172, the student is asked to carry out a hypothesis test.
He then mistakes 172 to be the population variance or s^2 when it is referring to a sample variance.
Thanks.
Cheers,
Wen Shih
"Everyone makes mistakes. That's why there is an eraser on every pencil."
Wow, thanks for the advice!
Just wondering - what's wrong with example 13?
Within 60 from 100 means
between 40 and 160
It's English ;)
Hi donkhead333,
"from 100" - We take 100 as the reference value.
"within 60" - Add 60 to the reference value gives us the upper limit 160. Take away 60 from the reference value gives us the lower limit 40.
Thus we obtain a range of values between 40 and 160.
In N08/P2/Q1(iv), we encounter a similar type of phrasing:
...for which the value of g(x) is within +/-0.5 of the value of f(x).
It is thus important to know how to interpret this information correctly :)
Thanks.
Cheers,
Wen Shih
finish paper in 2 hrs, use 1hr check :S :S :S ...if u can...
Hi,
Here is a list of common mistakes to avoid, nicely organised in a single document for all students to reflect upon on their last-lap towards the exam next week:
http://wenshih.files.wordpress.com/2010/02/common-mistakes-to-avoid.pdf
It is also beneficial for students to look back at past problems they have solved and ensure that familiarity with a variety of problem-solving approaches have been firmly established. Past problems from these sources will be most relevant:
1. JC 1 MYE 2010,
2. JC 1 Promo 2010,
3. JC 2 MYE 2011,
4. JC 2 Prelim 2011,
5. Nov 2010 H2 Maths Exam,
6. Nov 2009 H2 Maths Exam,
7. Nov 2008 H2 Maths Exam,
8. Two other schools' prelim 2011 papers you have done.
Jiayou!
Cheers,
Wen Shih
Originally posted by wee_ws:Hi,
Here is a list of common mistakes to avoid, nicely organised in a single document for all students to reflect upon on their last-lap towards the exam next week:
http://wenshih.files.wordpress.com/2010/02/common-mistakes-to-avoid.pdf
It is also beneficial for students to look back at past problems they have solved and ensure that familiarity with a variety of problem-solving approaches have been firmly established. Past problems from these sources will be most relevant:
1. JC 1 MYE 2010,
2. JC 1 Promo 2010,
3. JC 2 MYE 2011,
4. JC 2 Prelim 2011,
5. Nov 2010 H2 Maths Exam,
6. Nov 2009 H2 Maths Exam,
7. Nov 2008 H2 Maths Exam,
8. Two other schools' prelim 2011 papers you have done.
Jiayou!
Cheers,
Wen Shih
Thanks for sharing
http://wenshih.files.wordpress.com/2010/02/common-mistakes-to-avoid.pdf
This is extremely useful stuff.
Hi,
Thanks eagle for your encouragement :)
I made this mistake in this question about transformation on one occasion. Given the graph of y = f(2x), one is asked to sketch the graph of y = f(2x - 4). I simply took it as a translation of 4 units to the right when it should have been a translation of 2 units to the right.
Thus one should ask what substitution should x be made to decide on the correction transformation. In the example, x is substituted with x - 2 to obtain f(2x - 4) from f(2x).
Thanks.
Cheers,
Wen Shih