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Additional Mathematics chapter guide

Index numbers in SPM Additional Mathematics

You can write the index formula, but wordy multi-item questions make you lose track.

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An index number compares a value now with the value in a base year, with the base year set to 100. This page shows the four skills in the chapter and the order to learn them.

The chapter belongs to SPM Additional Mathematics and sits in the Form 4 topics. The ideas are short, but the wording of a question can hide what is being asked.

What are the skills in this chapter?

Each lesson builds on the one before it.

  1. Calculating a price index from two values: the one-item formula and its rearrangements.
  2. Combining weighted indices: why a composite index is a weighted average, not a plain one.
  3. Finding missing weights or component indices: setting up an equation for the unknown.
  4. Interpreting a composite index without confusing base years: reading what a number means between two later years.

Test the whole chapter with the index numbers practice set.

Why is an index between two years not a subtraction?

Here is an example. A price index for school lunches, with 2020 as the base year, was 120 in 2022 and 150 in 2024.

A student subtracts and says the price rose by 30% between 2022 and 2024. That is not right, because both numbers are measured against 2020, not against each other.

The correct comparison divides: 150 ÷ 120 = 1.25, so the price rose by 25% between 2022 and 2024. The 30 points are points against the base year. They are not a percentage of the 2022 price.

That one mistake loses marks in this chapter, so read the base year before any calculation.

Who should start where?

A student new to the chapter starts with the price index lesson, even if the formula feels familiar. The rearrangements, such as finding the old price from the index, are where marks go.

A student comfortable with one item can move to weighted indices. A student who already handles weighted indices can go straight to missing values. If fractions and percentages themselves are shaky, try the percentage, base and index explorer first.

When does one-to-one help?

The lessons explain the formula, but they cannot watch you work. A teacher can see which line you skip when you set up a wordy multi-item question, which is what online one-to-one Additional Mathematics tuition is for.

Common questions

What does an index number actually measure?

It compares a value now with a value in a base year, scaled so the base year equals 100. An index of 130 means the value is 30% higher than in the base year. It is a comparison, not an amount.

Do I need to memorise several formulas?

There are two to hold on to: the index for one item, and the weighted average for a composite index. Every other question type is one of those two formulas rearranged for a missing value.

Where do students lose marks in this chapter?

Two slips cost the most: averaging the indices without the weights, and confusing which year is the base. Writing the base year and the weights beside each item before calculating removes both problems.

Which lesson should I start with?

Start with the price index from two values. The other lessons use it as a building block, and a short check on your own answers tells you whether you are ready for the weighted questions.

Keep going

If you know the formula but get lost in the wording of a multi-item question, a one-to-one Add Maths teacher can watch you set it up and show where the reading goes wrong. Tell us the form and which index question stalls you.

  • Online one-to-one lessons for your child with an experienced teacher.
  • Your first class is a one-hour trial, from RM50. The fee is agreed before you book.
  • Happy with the teacher? Continue with lessons of about 1.5 hours. If not, ask for another teacher.
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