From my years of teaching, I have found 5 Common Mistakes that students always make for their Math Exam. Math does not just include solving problem sums, it requires the student to be able to analyse the information being presented as well. The mistakes I have included in this post is a result of the student’s carelessness or inability to understand the slight difference in words used for the questions.
1. ….. of the remainder
This is perhaps one of the most common mistakes that students make. When we say “20% of the remainder”, we need to times 20 % to the remainder /(leftover). Sometimes, students fail to understand this and multiply 20% by the whole amount.
For example, John spend 1/5 of his money on food and 20% of the remainder on clothes. What fraction of his money did he spent on clothes?
Firstly, 1 – 1/5 = 4/5.
The remainder is 4/5.
Then, we convert 20% to 1/5.
Finally, 1/5 * 4/5 = 4/25
2. Increase to… / Increase by…
Students usually fail to understand the difference between “increase to” and “increase by”. “Increase to…” means we are given the final value after adding in the increased amount. “Increase by…”means we are given the change in value.
Example: The number of students increased to 100 means the final number is 100. The number of students increase by 100 means you have to add 100 to the initial number to get the final number.
Similarly, the number of students increased to 200% of the original number, means the final number is 2 times of the original number. The number of students increased by 200% means the final number is 3 times of the original number.
3. A is 20% of B / A is 20% more than B
When we say A is 20% of B, it means A is 1/5 of B. In other words, A has 1 unit while B has 5 units.
When we say A has 20% more than B, it means A has 1/5 more than B. So B has 5 units, while A has 6 units.
4. Workings are written wrongly
Below are some examples of wrong workings that will cause your marks to be deducted even though your answers are correct.
1/2 = 12 apples (Wrong)
1 unit = 12 apples (Correct)
1/2 * 100 = 50% (Wrong)
1/2 * 100% = 50% (Correct)
9.30 a.m + 2.5 = 12pm (Wrong)
The correct way to show the working above is to draw a time line.
5. Place vs Value
Students often are confused between Place and Value.
For example, in the number 120, the digit 2 is the TENS place while the digit 2 has value of 20.
Similarly, in the number 0.12, the digit 2 is in the HUNDREDTHS place while the digit 2 has value of 0.02.
Do avoid these common mistakes in your exams and you can save a lot of marks. There may be more mistakes than these. If you have more to add, feel free to comment below.
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