TARA Problem Solving: the 3 question types & maths skills you actually need

Every Problem Solving question hands you a small, self-contained scenario — a handful of numbers, a short description of a situation, sometimes a simple table — and asks you to work out something specific from it.

There's no formula to revise in advance and no subject content to learn: the arithmetic involved rarely goes beyond what's covered by the middle of secondary school, and often sits well below it.

What's actually being measured is whether you can take a problem you've never seen before, work out which numbers in front of you actually matter, choose the right operations, and carry them through accurately under time pressure.

That's a deliberately different thing from a maths exam. A maths exam usually rewards knowing a method in advance and applying it correctly.

Problem Solving gives you no advance warning of the method at all — each question is built to feel unfamiliar, so the only way through is to reason out, from scratch, what the problem is actually asking and how the numbers you've been given connect to it.

The maths itself, in isolation, is basic. The reasoning about which basic maths to use, and in what order, is the actual skill on the table.

That distinction matters for how you prepare. Drilling harder maths content won't move your score much, because the module was never testing harder content to begin with.

What helps is practicing the specific reasoning patterns TARA uses — which is exactly what the 3 named question types further down this page are. You can start working through the practice bank free before you decide whether to go further.

Courses like Economics and Management, Mechanical Engineering, or Management Science attract applicants with strong grades across the board — that's the entry price, not the differentiator.

What predicted grades struggle to show is something more specific: can this candidate look at an unfamiliar set of numbers or data and work out what's relevant, choose a sensible method, and reach a correct answer without being talked through it first.

That's closer to what a first-year problem set, a lab report, or a live case study actually demands than any single A-level paper is designed to test.

Because Problem Solving doesn't test subject content, it can't be crammed the way A-level material can, and a strong performance doesn't automatically track with strong maths grades either — which is exactly why it's used as an additional, separate signal rather than a substitute for the rest of an application.

Which courses require it, and how heavily each department weighs it, varies by university and can shift between admissions cycles, so it's worth checking your specific course's page directly rather than assuming — Oxford confirms its own course list on its official admissions tests page, and UCL does the same on its tests, tasks and interviews page.

The reason universities bother testing this at all is that the skill doesn't stop being useful once you have an offer.

A first-year engineering problem set, an economics dataset, a lab report with a results table, or a business case study all hand you more information than you actually need, and expect you to work out which parts matter before you can even start calculating.

Filtering signal from noise in a pile of numbers is a skill in its own right, not a side effect of already being good at maths.

It shows up constantly outside a degree too — reading a phone contract, comparing two job offers built on different pay structures, working out whether "buy five, get one free" actually beats a straight percentage discount.

None of that requires maths beyond what Problem Solving already tests. It requires noticing which numbers you've actually been given answer the question in front of you, and which ones are just there.

Problem Solving is 22 multiple-choice questions in 40 minutes — the same format as Critical Thinking, five options each with one correct answer, and no penalty for a wrong guess, as set out on UAT-UK's own TARA page.

That works out to the same average of just under one minute fifty seconds per question.

A question with one short calculation and no distracting extra data can take a fraction of that once you've had some practice; a Finding Procedures question with several steps and a table to read can easily take two or three times as long.

Budget flexibly across the module rather than pacing every question identically, and if time is running out, guess rather than leave a question blank — there's nothing to lose.

For how this timing fits alongside Critical Thinking and the Writing Task, see the full format and timing breakdown in our complete guide.

One rule catches people out more than any other: calculators and dictionaries are banned throughout the entire test, not just in the Writing Task. Every calculation in Problem Solving has to be done by hand, in your head or on paper.

That's precisely why the maths skills covered below stay deliberately basic — the module is built to be solvable with mental arithmetic and simple written working.

Practicing with a calculator to hand teaches you nothing about doing the same calculation without one on the day, so if you've been reaching for one while revising, that's worth changing before test day rather than after it.

Like Critical Thinking, Problem Solving isn't a new invention.

Oxford and UCL's previous test, the Thinking Skills Assessment (TSA), used the same three question type names — Relevant Selection, Finding Procedures, Identifying Similarity — and a near-identical maths appendix, taught through much the same style of worked example.

When TSA was discontinued and UAT-UK introduced TARA for 2026/27 entry, this part of the test carried across largely intact — a transition confirmed by Cambridge Assessment's own closure notice for its admissions testing service, which set the move to UAT-UK in motion.

What did change is the administration format. Standard TSA put all 50 questions — 25 Problem Solving and 25 Critical Thinking — into a single 90-minute sitting, interleaved together and presented roughly in order of difficulty.

TARA separates the two completely:

Problem Solving is its own standalone, 22-question, 40-minute module, sat on its own rather than mixed in with Critical Thinking questions.

So if you're working from older TSA Problem Solving material, the question types and the maths behind them are still directly useful — just don't practice switching between the two skills mid-timer, because that's not how TARA is actually run.

See our full TSA vs TARA guide for the rest of the detail.

TARA scores Problem Solving on its own scale from 1.0 to 9.0, reported separately from Critical Thinking.

UAT-UK has stated on its own TARA page that the scale is designed so a typical candidate scores around 4.5, and that roughly the top 10% of candidates score above 7.0 — the same two figures that apply to Critical Thinking, since both modules share the same scoring design.

Scores are capped at 1.0 on the low end and 9.0 on the high end.

Published score histograms suggest Problem Solving results tend to sit a little higher than Critical Thinking's, clustering somewhere around 4.5 to 5.5 rather than lower down the scale — but that's a visual read of a published chart rather than an exact figure UAT-UK has stated in text, so treat it as a rough shape rather than a number to plan around.

The two solid figures worth remembering are the ones above: a typical score around 4.5, and the top 10% of candidates sitting above 7.0.

Because the two modules are scored and reported separately, it's entirely normal to do noticeably better on one than the other, and universities that use TARA can see both individually rather than a single blended figure.

For the full breakdown of both modules across the October 2025 and January 2026 sittings, see our TARA scoring guide.

Here's where the key numbers sit:

TARA's own Content Specification includes an appendix listing exactly which maths skills Problem Solving draws on, and it's a shorter, more basic list than most candidates expect walking in. Work through it honestly before test day.

If a line makes you pause, that's worth ten minutes of mental arithmetic practice now, done without a calculator, rather than finding out under a 40-minute clock.

Here's the full list:

If you worked through that list without needing to double back, the maths itself isn't your limiting factor — put your practice time into the reasoning patterns covered in the 3 question types below instead.

If a couple of lines did catch you out, five or ten minutes of deliberate practice on just those operations, done without a calculator, is a better use of prep time than working through full past papers you can't yet do by hand.

There's no official past-paper archive to draw on yet either — see our honest note on what Problem Solving practice material actually exists before test day.

If you'd rather see the reasoning in action than read about it, you can register free and try a real question yourself right now.

Before you dive into the worked examples, it helps to see how Problem Solving sits alongside Critical Thinking and the Writing Task — see the module-by-module breakdown in our complete guide, or jump straight in below.

Each question below is a real question from our practice bank, worked through step by step so you can see the reasoning in full rather than just read a description of it. Have a go before you reveal the answer.