Recommended ESAT Prep Resources: Books, Practice Papers, and Online Tools

Think of preparing for something like the ESAT as training for an epic quest, not just a single boss fight.

02:49 03 May 2025

Think of preparing for something like the ESAT as training for an epic quest, not just a single boss fight. If you only use one map (say, just past papers), you get really good at navigating that path—but what if the terrain shifts a little? Suddenly, you’re in the weeds.

Why Mixing Up Resources Is Brilliant

• Different angles, deeper roots—Each book, video, or app has its own way of explaining things. Sometimes a new voice or a weird analogy is all it takes for a tricky concept to click.

• More connections—The brain loves patterns and links. When you see the same idea pop up in ten different places, you start to spot the common threads. That’s real understanding—not just memorizing, but synthesizing.

• Keeps things fresh—Let’s be real: variety prevents burnout. One day it’s Feynman, the next it’s a Brilliant.org puzzle, then a meme about Schrödinger’s cat. Learning feels more like play, less like a grind.

Using ESAT Past Papers as Your Foundation

That’s a very solid move. The ESAT past papers are like treasure maps—they show you not only what kind of gold is out there, but also help you practice spotting the traps and tricky wording that can trip people up. You’ll get familiar with the question style, the pacing, and the pattern of topics, which is half the battle for most standardized tests.

But… (there’s always a but, right?) Past papers are fantastic for pattern recognition, but they do have their limits. Sometimes, test writers like to toss in a curveball or repackage old problems in new, sneaky ways. If you only stick to past papers, you might miss out on some deeper understanding or new directions the test could take.

Master Past Papers—But Don’t Stop There

• Do them timed and untimed. Timed gets you ready for the real thing, untimed lets you deeply reflect and learn.

• After finishing, review every mistake. It helps very much. Even the ones you think were “silly.” Often, they highlight weak spots in your knowledge or test strategy.

• Try to categorize the questions by topic or skill. You’ll see what comes up most and where you need extra reps.

Deepen Your Conceptual Understanding

• Once you spot a topic you struggle with (say, combinatorics, or kinematics, or tricky graphs), hit the textbooks or trusted resources for that area.

• Don’t just aim to solve the problems—aim to understand the methods behind them. That’s what lets you handle unexpected twists.

Go Beyond the Usual—Impressive, Challenging Resources

Here’s where you can get a little wild and impressively nerdy (in the best way):

• The Feynman Lectures on Physics (for the physical sciences): They’re famous for a reason. Beautifully written, deep, and sometimes challenging. Even just dipping in can give you a new perspective.

• Art of Problem Solving (AoPS): Their books and online resources for math olympiad training go deeper than most school curricula and really build mathematical thinking.

• Brilliant.org: Interactive and fun, especially for topics like maths, logic, and physics. Great for filling in gaps and stretching your mind.

• Cambridge STEP papers: If you want to train your brain for higher-level problem-solving, try some questions from the STEP (Sixth Term Examination Paper). They’re harder than ESAT, but wrestling with them will make the real test feel lighter.

• Isaac Physics: Created by Cambridge, it’s full of physics and maths problem sets tailored for UK uni applicants. Absolutely worth your time.

Go Book-Hunting

1. “How to Solve It” by George Pólya

If you haven’t met this classic yet, you’re in for a treat. Pólya gives you a whole toolkit for problem-solving—math or otherwise. Short chapters, practical wisdom, zero fluff. It’s the kind of book that makes you want to grab a pencil and tackle the next challenge with a grin.

1. “Thinking Physics” by Lewis Carroll Epstein

This one’s pure fun and full of “wait, really?” moments. Each page is a quirky physics puzzle with answers that make you rethink what you thought you knew. No heavy math, just clear-headed common sense and a lot of a-ha! moments.

1. “Calculus Made Easy” by Silvanus P. Thompson

First published in 1910 and still a delight. Thompson writes like your witty, slightly eccentric uncle who just really wants you to see how cool calculus is. It’s refreshingly readable—even, dare I say, charming.

1. “The Art of Mathematics: Coffee Time in Memphis” by Béla Bollobás

Imagine sitting down with a master mathematician over coffee, swapping brain teasers and clever proofs. That’s this book. Not all problems are easy, but they’re all intriguing, and the atmosphere is relaxed, not intimidating.

1. “Mathematics and Plausible Reasoning” by George Pólya 

This one’s a bit deeper—a two-volume journey into how mathematicians actually think when they’re exploring, guessing, and making sense of the unknown. Perfect for stretching your intuition beyond rote formulas.

1. “The Pleasures of Counting” by T.W. Körner

A Cambridge legend, Körner’s writing is witty, honest, and deeply curious. This book wanders through math’s real-world power, from codebreaking to chaos theory. You’ll finish chapters feeling like you’ve just had a good chat with an old friend who happens to be a mathematical wizard.

1. “QED: The Strange Theory of Light and Matter” by Richard Feynman

Maybe you have a lot of Feynman, but if you don’t have this one—grab it. It’s Feynman at his most lucid and playful, explaining quantum electrodynamics without frying your brain.

1. “What Is Mathematics?” by Richard Courant and Herbert Robbins

A classic from the 1940s, still fresh and relevant, this book takes you on a grand tour of mathematical ideas—logic, number theory, geometry, calculus. It’s not flashy, but it’s solid gold for building intuition.

1. “The Princeton Companion to Mathematics” (ed. Timothy Gowers)

This one’s a beast—like a giant encyclopedia of all things math. You don’t read it cover to cover, you wander through it. Dip in anywhere, and you’ll find a new curiosity. Perfect for those long, rainy afternoons with a mug of tea.

About Coffee Breaks & Wandering Minds

Now, the idea of using your breaks for more “study-lite” activities, like apps or quick quizzes, can work sometimes. But here’s the secret sauce a lot of people miss: Your brain needs time to wander.

 

• Incubation is real

Some of your best insights come when you’re not actively thinking about a problem. Ever had a eureka moment in the shower or while out for a walk? That’s your subconscious at work!

 

• Curiosity craves novelty

Following “absolutely strange things”—art, music, daydreaming, a walk outside, even people-watching at a café—feeds your creative side. That, in turn, can help with problem-solving in the most unexpected ways.

 

• Balance is power

Give your brain the gift of unstructured time. It’s not laziness—it’s vital maintenance. Sometimes, chasing the white rabbit is exactly what you need to come back sharper.

You’re setting yourself up not just to ace a test, but to actually love the process—and that’s where the magic happens.

Next time you reach for your phone mid-break, try this instead: 

• Stare out the window.
• Doodle aimlessly.
• Listen to a song you’ve never heard before.
• Read a poem.
• Or just let your mind drift and see where it goes.

You might be surprised at the ideas that bubble up. Science is everywhere, and sometimes it sneaks in through the back door when you’re not looking.

Mix It Up

Don’t just study—explore! Let your curiosity lead you down those dusty stacks and into the wild corners of knowledge.

Occasionally, challenge yourself with resources just outside your comfort zone. If you’re great at algebra but not so much at mechanics, lean into that weakness. Stop avoiding it, that’s exactly where your treasure is buried. Discuss tricky problems with friends, tutors, or even forums online. Explaining your reasoning is a superpower for learning.

Sometimes the best breakthroughs come when you’re just playing with ideas, not grinding. Try some recreational maths problems, or physics brainteasers, or even relevant YouTube channels (like 3Blue1Brown, Numberphile, or Veritasium).

The best discoveries are often the ones you never set out to find. And if you stumble on a book that lights a fire in you, or even just makes you smile at a clever proof, consider it a win. That’s the true scholar’s joy.