5 common mistakes made by IGCSE Math students
By Owen Cheong
(Math, Physics, Chemistry tutor at The Edge Learning Center)
IGCSE Math examination is coming soon! I guess many candidates are planning to do lots of past papers before the exam. However, it is also very important for you to avoid careless mistakes when doing papers. Here are the 5 common mistakes made by students based on my experience and the examiners’ report. It might be helpful for you to read this article before you start doing a paper.
One of the most common algebra mistakes is to conclude that (a+b)² is equal to a²+b². Unfortunately, it is not that straightforward. It is important to remind yourself that both (a+b)² and (a-b)² require to do FOIL. Another way is to remember these 3 identities for your exam:
(a+b)² = a² + 2ab + b²
(a-b)² = a² – 2ab + b²
(a+b)(a-b) = a² – b²
Calculating the mean of grouped data
When given a grouped data, students are frequently asked to calculate the mean of that data set. Here is an example:
The table below gives some information about the incomes, HK$I, of 100 people in Hong Kong.
Some students make mistakes by using lower bound or upper bound to calculate the mean. In order to calculate the mean of a grouped data, the first step is to determine the midpoint of each class:
Then, multiply these midpoints by the frequency of the corresponding classes. This result divided by the total frequencies will be the value of the mean.
Estimating interquartile range from a cumulative frequency curve
Some students misuse the critical values for lower quartile and upper quartile to calculate the interquartile range when given the cumulative frequency curve. For example, here shows a cumulative frequency diagram about the scores of 500 people in a Math quiz.
Here is the working from a student:
Unfortunately, the student forgot to drop the critical values to the x-axis. Here is the correct way to show your working:
Therefore, the interquartile range should equal to 40 – 24 = 16
Working out the upper bound or lower bound of a value
You need to be extremely careful when you are asked to find an upper bound or lower bound of a value given a formula. Here is an example:
a = 13.5,correct to 1 decimal place
b = 8.7,correct to 1 decimal place
Work out the lower bound for the value of a – b
At first glance, we should work out lower bound for a and b separately:
Then, many students would think that the lower bound for a – b is equal to 13.45 – 8.65 = 4.8, which is not a correct answer.
Another common approach is to first calculate a – b, which is equal to 4.8, and then take the lower bound of this value, which is 4.75. Again this is not the correct approach.
In order to tackle this type of problem, we should first list out the upper bound AND lower bound of each variable at the same time:
Then, we should analyze which combination makes the final value becomes maximum or minimum. In this example, we need to find the lower bound of a – b, so in order to minimize a – b, we should minimize a and maximize b. In other words, we should take the lower bound of a and upper bound of b. Therefore, the lower bound of a – b is equal to 13.45 – 8.75 = 4.7
Solving linear inequality
When we perform addition, subtraction, multiplication and division with an inequality, we can say that they are nearly identical to perform all these operations to an equation. HOWEVER, THERE IS ONE IMPORTANT EXCEPTION: Whenever you multiply or divide by a negative number in an inequality, you must flip the inequality sign!
In order to test your understanding of the exception rule, let’s do a proofreading exercise:
The working for the original equation is correctly illustrated in the first column. Can you spot the first mistake that has been made on the second and third column?
In the second column, the first mistake appears in step 2 (3rd line) since if we subtract by 3 on both sides, the inequality sign should keep the same. Remember that the exception rule only applies to multiplication and division.
In the third column, the first mistake appears in step 1 (2nd line) since if we multiply by -6 on both sides, the inequality sign must be flipped.
Here is the correct way to solve this inequality:
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