Index Numbers, Practice Questions

The six questions below rise in difficulty across the whole chapter, from a single price index to a composite index built from several weighted items and a multi-year chain. Give yourself roughly four to seven minutes per question and work on paper first, writing every line the way you would in the real exam, quote the formula, substitute the numbers, then state the answer as a bare index or a price in ringgit.

Resist the urge to peek.

Only once you have committed to a full answer should you open the solution and mark yourself line by line. When your working differs from ours, stop at the exact line where the two part company; that single step is almost always where the mark was lost.

Because Add Math is marked analytically, quoting the correct formula and substituting correctly still earns method marks even when the final arithmetic slips, so always write the formula before you compute.

Before you begin, hold on to what an index number means: the base year is set to $100$, so an index above $100$ shows a rise and one below $100$ shows a fall. An index of $125$ is a $25\%$ increase and $90$ is a $10\%$ drop.

A composite index behaves the same way for a whole basket of items. Keeping this in mind lets you sense-check almost every answer: if you know the price went up, an index below $100$ is a signal that something has gone wrong.

Add Math is marked analytically, which means marks are attached to steps, not only to the final number. When you check your own script, award yourself credit the way a marker would: look for the correct formula written down before any numbers, a substitution with each value in the right place, and a final figure that means what the question asked for.

Work through the checklist below on every question, and be honest about the exact line where a mark was earned or lost.

• Formula mark: did you write $I=\frac{P_{1}}{P_{0}}\times100$ or $\bar{I}=\frac{\sum I_{i}w_{i}}{\sum w_{i}}$ before substituting?
• Substitution mark: are the base price and current price in the right positions, base year on the bottom, current year on top?
• Working mark: for a composite index, did you multiply each index by its weight, add, then divide by the total weight and not by the number of items?
• Answer mark: is the final index left as a bare number, and any price stated in ringgit with a sensible size?
• If your final number is wrong but the formula and substitution are right, give yourself the method marks, that is exactly what a real marker does.

Marking yourself is powerful, but it is hard to see your own blind spots. In a one-to-one lesson our teacher watches the exact line where a mark slips away, dividing by the number of items instead of the total weight, putting the current price on the bottom, or forgetting to divide by $100$ when chaining indices across years, and corrects the habit on the spot.

Because our teachers are experienced, you work with someone who explains the why behind each step. Lessons are taught in English, while SPM papers are set in both Malay and English, so we make sure the notation reads the same to you either way.