If you are looking to take Mathematics in JC beyond H2 Maths, you may be considering whether to take H3 Maths or Further Maths during your A-Levels.

*Since both of them are ‘harder’ than H2 Maths, how are they different, and which should you choose?*

Here’s what’s you need to know:

Contents

## Syllabus

Here are the different topics that you will be taught in either subject:

H3 Maths | Further Maths |
---|---|

Functions | Algebra and Calculus |

Sequences and Series | Discrete Mathematics, Matrices and Numerical Methods |

Inequalities | Probability and Statistics |

Numbers | – |

Counting | – |

*The first 2 chapters of H3 maths (functions, sequences and series) are an extension of what you will learn in H2 Maths.*

In H3 Maths, you will learn to prove properties and results, as well as solve non-routine problems.

**There is a great emphasis on proofs**, and you’ll be taught some proving techniques, including:

- Proof by contradiction
- Proof of existence
- Proof by construction

*As such, it will be good to master these different proving techniques if you intend to do well in H3 Math.*

Meanwhile, for Further Maths, **you will be learning topics from these 2 main sections**:

- Pure Mathematics
- Probability and Statistics

Some of these may be additional knowledge that expands on what you’ve learnt in H2 Maths.

**There is quite a heavy emphasis on Probability and Statistics too**, where you will learn topics including:

- Discrete random variables
- Continuous random variables
- Hypothesis testing and Confidence intervals
- Non-parametric tests

*You may want to note that Probability and Statistics are not taught in H3 Maths.*

### How hard are both of these subjects?

**Further Maths may test quite a bit on interpreting mathematical solutions**. As a result, some of your questions may become essay-based, which is slightly different from a conventional Maths exam.

*However, you would still be able to practice the concepts beforehand with past year questions. If you have enough practice, you may be able to be better prepared for the questions.*

For H3 Maths, you will be solving questions that may be quite ‘weird’, where there may be some that you have not seen before!

**It will be harder to practice for H3 Maths questions** as they are much more abstract.

## Grading

For H3 Maths, **you will receive one out of these 4 grades**:

- Fail
- Pass
- Merit
- Distinction

Meanwhile, Further Maths is an H2 subject, similar to H2 Maths.

As such, the score that you receive (**A to U**) will be counted into your overall Rank Points.

*This is something you may want to consider, as H3 Maths may be an add-on to make your A-Level certificate ‘look nicer’.*

## Assessment

**Here are the different types of assessments** you’ll be tested on for both subjects:

H3 Maths | Further Maths |
---|---|

Paper 1 (3h) 8-10 questions | Paper 1 (3h) 10-12 questions on Pure Mathematics |

– | Paper 2 (3h) 5-6 questions on Pure Mathematics (50%) + 5-6 questions on Probability and Statistics (50%) |

**The Further Maths paper is slightly more rigorous** in the sense that you will be taking two 3-hour papers. Furthermore, around 25% of the marks will be on Probability and Statistics.

Meanwhile, **H3 Maths only has one 3-hour paper** that has 8-10 questions.

*This will usually be at the end of the A-Level calendar, after the exams for most H2 subjects have been completed.*

## Number of years

H3 subjects are usually offered only after the end of JC1, **when you have shown an aptitude for the H2 subjects that you have taken**.

*This is mainly because H3 subjects are much tougher as it goes deeper into the subject compared to H2 subjects.*

Due to the requirement for H3 subjects, you will take H3 Math only for one year, while **you will take 2 years to study for Further Maths**.

## JCs that offer the subjects

While all JCs will offer H3 Maths, **3 JCs and Millennia Institute (MI) do not offer Further Maths**.

*You can find out the differences between Millennia Institute and a JC in this guide here.*

If you want to take Further Maths as one of your H2 subjects, here are some things you may want to consider:

- You may need to go for a selection test
- Most JCs require you to take both H2 Maths and Further Maths together

Since you are taking 2 Maths subjects, **you will only be able to take one Science subject (usually Physics)** as you’ll need another contrasting subject.

As such, this may **limit your choices** if you are looking to take a double science subject combination.

*You may also want to note that you are unable to take triple science in JC!*

## Eligibility

**If you wish to take Further Maths in JC1**, your O-Level scores for both A Maths and E Maths would have to be rather high. Furthermore, some JCs would require you to sit for a selection test to determine if you are suitable to take Further Maths.

H3 subjects usually require you to score well during your promotional exams for that particular topic, and you may need to do well in your other subjects too.

*This is because your school wants to make sure that you’ll be able to cope with the rigour of taking an H3 subject on top of your 4 core subjects.*

## Timetable

**Further Maths will usually have a smaller cohort compared to other subjects**, but your timetable should still be within the normal school timings.

Meanwhile, H3 Maths may have an even smaller cohort compared to Further Maths, and **you may be taught this subject outside of the normal school curriculum**.

*You may have to stay back on some school days to attend your tutorials, so it’s something you may want to take note of, especially if you are participating in a CCA.*

## Verdict

Here is a **summary of the comparison between these 2 subjects**:

H3 Maths | Further Maths | |
---|---|---|

Syllabus | Pure Mathematics | Pure Mathematics + Probability and Statistics |

Types of questions | Can be rather abstract | It may be possible to practice techniques for questions |

Grading | Distinction, Merit, Pass, Fail | Counts towards Rank Points (A-U) |

Paper 1 | 3h 8-10 questions | 3h 10-12 questions on Pure Mathematics |

Paper 2 | NA | 3h 5-6 questions on Pure Mathematics (50%) + 5-6 questions on Probability and Statistics (50%) |

Number of years | 1 (after JC1) | 2 (at start of JC1) |

JCs that offer subject | All | 4 JCs do not offer it |

Eligibility | Do well in Maths promotional exam and other subjects | Do well for O-Level A and E Maths May need to sit for selection test |

Timetable | May be outside normal school timings | Should be within normal school timings |

## Conclusion

Both H3 Maths and Further Maths will allow you to **go in-depth into mathematical concepts** that are beyond the scope of H2 Maths.

*While both of them have their own difficulties, it may be possible that H3 is tougher as you are tested on more abstract concepts!*

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