Common Mistakes in Singapore GCE O Levels Secondary Maths: Prime Numbers, Real Numbers, Integers ,Rational, and Irrational Numbers

The GCE O Levels Maths syllabus in Singapore covers a wide range of topics, including Prime Numbers, Real Numbers, and the classification of Rational and Irrational Numbers. While these concepts are fundamental, students often make common mistakes that can affect their performance in the exams. Let’s dive into some of these errors and how to avoid them.

Here is the Number System.

**Classification of Numbers**

In secondary math, understanding the different types of numbers is key.

**Confusing Prime Numbers**

A common error is mistaking all odd numbers for prime numbers. While many primes are odd, not all odd numbers are prime. Remember, a prime number has exactly two distinct factors: 1 and itself. For instance, 9 is odd but not prime because it’s divisible by 3.

**Misclassifying Decimals**

Students often incorrectly assume that all decimals are rational because they think all decimals either terminate or repeat. However, numbers like *π* or √2 are irrational since their decimal expansions are non-terminating and non-repeating.

**Errors in Number Classification**

Another mistake is misidentifying numbers in equations. For example, students might classify a fraction like 3/4 as irrational. Remember, rational numbers can always be expressed as a fraction with integer values in the numerator and denominator.

**Overgeneralizing Number Properties**

Students sometimes assume that the sum or product of two irrational numbers is always irrational. This isn’t always true. For example, √2 x √2 = 2 is rational, while *π* + √2 remains irrational.

**Integers**

Integers are whole numbers, including positive numbers, negative numbers, and zero. They don’t include fractions or decimals.

**Conclusion**

Understanding these concepts and avoiding these common mistakes can significantly boost your performance in the GCE O Levels Maths exam. Regular practice and careful analysis are key to mastering these fundamental topics.

**Tips**

Qns 1: Do you know what is a rational number?

Ans: Rational numbers are numbers that we can put in fractions. i.e 2/5, 7/11

Exam Tip:

- All integers are rational. i.e 3 can be expressed as 3/1.
- 22/7 is rational but (put pie symbol) is not! 22/7 is only a good estimation of pie!

Qns 2: Do you know what is a prime number?

Ans: Numbers that can only be divided by 1 and itself.

Exam Tip: 0 and 1 are neither prime or composite numbers!

Qns 3: Do you know all non-terminating repeating decimal numbers can be put into a fraction and hence they are rational numbers?

Ans: For instance: 0.22222222… = 2/9

Qns: Is zero an integer?

Ans: Yes!!

Exam Tip: 0 is neither positive or negative but it is an integer!

That’s all!

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