Is Memorising Squares and Cubes Beyond 30 Worth It?

QUANT

Somewhere in most preparation plans there is a line item about memorising tables: squares to 30, cubes to 20, and then a question about whether to push further. It feels like a solved, checkable task in a section full of unsolved ones, which is exactly why it attracts more attention than it deserves.

The honest answer is that there is a point where memorisation stops paying, it arrives earlier than most lists suggest, and the reason is not about effort. It is about how often the fact appears against what else that study time could buy. This piece works through where the line sits, what belongs on the list instead, and why the appeal of this task is itself worth examining.

How a Memorised Fact Actually Pays

Work out the mechanism and the answer falls out, because this is an arithmetic question rather than a matter of opinion.

A memorised fact saves you the few seconds it would have taken to compute. That saving is real and small. Its value across a preparation is the saving multiplied by how often the fact appears, and appearance frequency is what collapses as you go further up the tables.

Squares of small numbers appear constantly, inside other calculations as much as on their own. Squares in the twenties appear regularly. Squares in the forties appear occasionally, and when they do, computing one takes a few seconds anyway. The saving stays roughly constant while the frequency falls, which is what makes the return curve bend so sharply.

Where the Line Reasonably Sits

Notice that the last two items are not tables at all. They are techniques, and they cover an unbounded range rather than a fixed list, which is why they return more than extending any table would.

The List Almost Nobody Prioritises

If you take one recommendation, take this one, because it returns more than every square above 30 combined.

Knowing the percentage equivalents of common fractions, and reading in either direction, converts a large amount of arithmetic into recognition. Percentage change questions, profit and loss work, ratio problems and data interpretation all lean on it constantly, and it appears far more often than any large square does.

Arithmetic has historically been the largest contributor to QA, so a fact that speeds up arithmetic broadly is worth more than one that speeds up a narrow computation occasionally. That is the whole case, and it is why this list beats extending the squares.

Techniques Cover Unbounded Ranges

A technique for squaring numbers near a round base handles every number in that range, not the ones you happened to memorise. That is a structurally better purchase.

The same applies to squares ending in five, to multiplying numbers close to each other, and to using differences of squares to turn an awkward product into an easy one. Each takes an hour to learn properly and then covers an open-ended set of cases.

Against that, memorising ten more squares covers exactly ten more cases and only if those cases turn up. The comparison is not close, and it holds no matter how good your memory is.

What you could learn	Coverage	Frequency of use
Squares to 30	30 specific facts	High
Squares 31 to 50	20 more facts	Low, and computable in seconds
Squaring technique near a base	An open range	Moderate, and it generalises
Fraction to percentage equivalents	A short list	Very high across arithmetic
Cubes beyond about 15	Few facts	Low

Recognition Matters More Than Recall

There is a subtler point here that changes what the list is for.

The valuable skill is usually not producing a square on demand. It is noticing that a number in front of you is a perfect square, or a multiple of one, or close to one. That is recognition, and it is what turns a messy-looking expression into something that simplifies.

Recognition builds from exposure rather than from drilling a list. A candidate who has worked through a lot of number system and algebra questions starts seeing these structures without having set out to memorise them, and that seeing is what actually saves time inside a question.

What the Evening Could Have Bought

Every hour spent extending tables is an hour not spent on something else, and that comparison is the real argument.

The alternatives are unglamorous and they move scores. A conditioned mock taken in one sitting with sectional limits enforced. Review that runs longer than the mock and sorts attempts by time taken as well as outcome. Concentrated work on the two or three question types your review keeps flagging. Rehearsing selection rules until they run without a decision.

None of those has a completion point, which is exactly why they lose to a memorisation list on any given evening. Recognising that pull is most of the defence against it.

How to Learn the List That Does Pay

Since the recommendation is to swap one list for another, it is worth saying how to actually install the fraction and percentage equivalents, because drilling them as a table is the slow way.

Learn them inside questions rather than in isolation. When a percentage appears in a problem, deliberately convert it to a fraction before computing, even when you would not normally bother. The conversion is doing real work in that question, so the association forms in the context where you will need to retrieve it, which is what makes recall automatic rather than effortful.

Build in both directions from the start. Candidates typically learn to go from fraction to percentage and never practise the reverse, then meet a percentage in a question and compute rather than recognise. Both directions appear and the reverse one appears more often in the arithmetic where this pays.

Expect it to take a couple of weeks of ordinary practice rather than an evening of drilling. That is slower than memorising a table and it produces the thing you actually wanted, which is recognition under time pressure rather than recall when prompted.

When Extending It Is Reasonable

There is a case for going further and it is narrow, so it is worth being specific rather than dismissive.

If your review shows you losing time specifically to arithmetic on large numbers, and the same few values keep appearing, then adding those values is a targeted fix responding to evidence. That is different from working through a list because the list exists.

The test is whether you can name the questions that would have been faster. If you can, extend the list to cover them. If you cannot, you are buying a feeling of preparedness rather than a saving.

One Thing Worth Confirming

Candidates sometimes ask whether any of this matters given what is available in the exam interface, and it is worth settling rather than assuming.

Confirm what the interface provides for your cycle from the official source rather than from a forum, since that is the kind of detail worth checking directly and it is published. Whatever the answer, the argument above does not change much, because the saving from a memorised fact is a few seconds either way and the case rests on frequency rather than on whether computation is possible.

The Wider Pattern This Belongs To

This question is one instance of something that shapes a lot of preparation decisions badly, and naming the pattern is more useful than settling this one case.

Tasks with clear boundaries attract disproportionate time. Memorising a table, finishing a chapter, completing a book, watching a video series: each has a defined end, produces a sense of completion, and can be reported as done. Tasks without boundaries do not compete well against them on any particular evening, even when they are worth several times as much.

The unbounded tasks are the ones that move scores. Getting better at selecting which questions to attempt has no completion point. Neither does improving how fast you recognise a question type, or how reliably you hold a reading budget, or how honestly you review. You cannot finish any of them, so they never produce the small satisfaction that a finished list does.

The practical defence is to schedule the unbounded work first and let the bounded tasks fill whatever is left, rather than the other way round. Candidates who do it in the natural order find the bounded tasks expand to fill the available evenings, and the work that would have moved the score keeps getting postponed to a week that never arrives.

The Summary

Memorised facts pay by frequency of appearance, and frequency falls off sharply while the per-use saving stays roughly constant. That is why the return curve bends early rather than continuing.

Squares to about 30, cubes to about 15 and powers of 2 to about 12 cover most of what recurs. Beyond that, techniques beat tables because they cover open-ended ranges rather than specific facts, and the genuinely high-value list is fraction to percentage equivalents, which speeds up arithmetic broadly and gets skipped in favour of larger squares.

Recognition matters more than recall, and it builds from exposure rather than drilling. Extend a list only when your review names the questions it would have helped. And be honest about why memorisation attracts time: it is the only part of this preparation with a visible end, which is not the same as being the part that pays.

If memorisation is where your evenings go, that is worth checking against what your mock review actually flags. A CAT preparation strategy review will show where your time is genuinely being lost, and a personalised CAT preparation plan puts the hours there instead.