Problem-Solving-Worksheet-Maths

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Problem Solving Worksheet: Never 
Make the Same Mistake Again 
Worksheet by iCanStudy Student Louis Huynh, contribution by Derrick Mah 
Important note 
Be as specific as you can be. The more specific you are, the better you can fix your issues 
and NEVER. MAKE. THE SAME. MISTAKE. 
Why is this important? 
We have the notion that doing questions over and over again will make us better and 
improve our grade. While true in a sense, the students who ace their math exams can solve 
problems within the time limit and 100% accuracy. Not only this, but some top students 
seemingly spend significantly less time focusing on maths and more on other subjects such 
as chemistry, biology, digital solutions, history etc. 
So, what’s the trick? What’s the life hack? Just be born smart? No. The answer is simple. 
They have a deep understanding of the topic and do not need to spend time doing 100 
variations of a question asking for the same thing. Instead, they just need to do 5. 
Having a deep understanding of a topic is a whole different ballpark but if you want to see 
tangible results and save more time, then here is a basic guideline in never making the same 
mistake. 
After a while, you find that you start automatically asking these questions when you get a 
question wrong. At that point, you can refrain from having to use this worksheet. 
 
 
What was the 
question? 
Format: Topic title, question 
type (SF, CF, CU) 
What kind of mistake did 
you make? 
Even if you got an answer correct, 
was it the best possible method to 
achieve that answer? If not, then 
consider it to be a mistake. 
Why did you make this mistake? 
Was it due to misunderstanding the 
question? A lack of working? Or was it due 
to a gap in your fundamental understanding 
of the topic? 
How will you ensure that you will never make this 
mistake again? 
Will you relearn the topic? Will you add more to your working out? 
 
 
 
 
 
 
 
Example 1: Unit 3 Exam 
revision Question set 4, 
question 4, CF 
To find the maximum rate of 
change, I calculated the x-
intercept of the derivative. 
I mistook finding the maximum rate of 
change with stationary point. 
Firstly, I need to understand that “maximum rate” implies 
calculating the derivative, which is the rate of change at any 
given point on a curve. To find the maximum rate, I have to 
calculate the maximum turning point of the derivative 
function because that is the highest rate. The x-intercept of 
a derivative graph means that the rate of change is 0. 
Alternatively, I could find the derivative of the derivative and 
its x-intercept for the same value. 
Example 2: Sometimes, 
you can come up with 
your own questions 
I used the circumference of a 
circle instead of the area of a 
circle to find the shaded area 
I was thinking about the previous 
question, which asked for 
circumference. I wasn’t in the correct 
mindset due to misinterpreting the 
word “shaded area”. This was due to a 
lack of logic regarding what the 
question was asking me for. 
Next time I will write out the whole formula from the 
formula booklet and double-check whether the formula I 
wrote out helps me answer the question. I can also visually 
shade the area that I want (i.e. whole circle - sector) 
Example 3: 
You will find that you get 
used to this column 
more quickly than 
others. 
 
I incorrectly identified the 
interior angle of the bearing as 
30 degrees instead of 50 
degrees. The question said the 
true bearing was 050, but I 
measured the 50 degrees from 
the 90-degree line instead of 
true north. 
I had poor logic in understanding how 
bearings work, as I didn’t measure 
from true north. I also didn’t try and get 
the interior angle in various ways. 
Next time double-check the value of the interior angle by 
first drawing the true bearing and then finding the 
complimentary angle from that.