Free Maths Olympiad Practice Tests: 17 Full Papers
Seventeen complete AMC and UKMT papers with no payment and no card, plus how to get real value from each one.
Almost every site offering free maths olympiad practice tests wants something first: an email, a trial signup, a card on file that quietly renews. We took a different view. Seventeen complete papers on this site are open to anyone, with no payment, no trial and no card - and this page tells you exactly which ones and how to use them.
They are not samples or teasers. Each is a full paper with the real timing, the real marking scheme including any negative marking, instant scoring and a worked solution on every question.
What is actually free
Seventeen papers across six competitions, each sat online with a timer:
| Competition | Free papers | What each one is |
|---|---|---|
| AMC 8 | 2 | One topic-wise, one full mock |
| AMC 10 | 3 | Number theory, algebra, and a full mock |
| AMC 12 | 3 | Three complete mocks |
| UKMT Junior Challenge | 3 | Three complete papers |
| UKMT Intermediate Challenge | 3 | Three complete papers |
| UKMT Senior Challenge | 3 | Three complete papers |
Behind them sit 120 papers and 3,450 questions in total, every one written to its competition's published specification. The free seventeen are genuinely representative of the rest, not a thinner version of it.
Start with a cold paper, before you revise anything
The most useful hour in anyone's preparation is the first full paper, sat before any revision at all. It is uncomfortable and it is worth more than a week of reading, because it tells you the one thing no syllabus can: where you actually are.
Students resist this because a low score feels like a bad start. It is the opposite. A baseline you did not prepare for is the only score you can honestly measure improvement against, and it costs you one sitting.
If you sit only one free paper, make it a full mock rather than a topic paper, and sit it cold.
- AMC 8 Full Mock - Paper 1
- AMC 10 Full Mock - Paper 1
- AMC 12 Mock Paper 1
- UKMT Junior Challenge - Paper 1
- UKMT Intermediate Challenge - Paper 1
- UKMT Senior Challenge - Paper 1
The marking is the part most practice sites get wrong
Every one of these competitions marks differently, and the differences change what you should do in the hall. Our papers apply each scheme exactly, so your practice score means what it says.
| Competition | Marking | What it means for you |
|---|---|---|
| AMC 8 | +1 correct, nothing for wrong or blank | Answer every question. A blank is never right. |
| AMC 10 / 12 | +6 correct, 0 wrong, +1.5 blank | A blind guess averages 1.2 - less than the blank. Guess only after eliminating two options. |
| UKMT Junior | 5 or 6 marks, no penalty | Answer everything. |
| UKMT Intermediate | Banded: -1 on Q16-20, -2 on Q21-25 | A blind guess on the last five is worth -0.4. |
| UKMT Senior | +4 correct, -1 wrong, every question | A blind guess is worth exactly zero. |
Read that table twice. The correct exam behaviour on the AMC 8 - answer everything - is actively wrong on the AMC 10 and on the UKMT Senior Challenge. Students who carry one habit across competitions lose marks they never see.
How to get value from a free paper
A paper you sit casually teaches you almost nothing. Four habits make the difference, and none of them cost anything.
Time it honestly. One sitting, no phone, no checking a solution halfway through. If you stop the clock you have measured your mathematics but not your exam.
Mark your confidence as you go. Put a dot beside anything you were unsure of. When you mark the paper, a dotted question you got right is a warning rather than a win - you will not be lucky twice.
Redo every miss untimed before reading the solution. If it comes out in four quiet minutes, the problem was pace, and pace is fixed by different work than knowledge is. If it does not, the worked solution is now worth reading properly.
Log the cause, not the topic. "Geometry" tells you nothing. "Misread which angle was asked for" tells you what to change. Most students find three or four causes repeat across every paper they sit.
Where the free papers end and the series begins
Seventeen papers is enough to establish a baseline, learn the marking, and build the review habit. It is not enough to prepare fully, because once you have sat a paper you can never sit it cold again.
The full series carry 120 papers between them - 3,450 questions, all with worked solutions - and are priced per series rather than per paper: AMC 8 and UKMT Junior at Rs 799, AMC 10 and UKMT Senior at Rs 899, AMC 12 and UKMT Intermediate at Rs 1,199.
That said: work the free ones first. If the habits in this article do not change your score, more papers will not either, and we would rather tell you that than sell you something.
When papers stop being the answer
Papers diagnose. They do not teach. If your error log keeps returning the same cause after three papers - you cannot set up a counting problem, or you never see the auxiliary line - repetition is practising the gap rather than closing it.
That is the point at which a teacher earns their fee. Our courses run live small-group and one-to-one sessions built around what a student's own error log exposes. Until then, the free papers and an honest log will take you further than most paid material.
The short version
Seventeen full papers, no payment and no card, across the AMC and the three UKMT challenges. Sit one cold before you revise. Learn your competition's marking, because the right strategy on one is the wrong strategy on another. Log causes rather than topics. Then decide whether you need more papers or a teacher - the free set is enough to tell you which.
Sources
Questions people ask
Are these practice tests really free?
Yes. Seventeen full papers require no payment, no card and no trial signup. They are complete papers rather than samples: real timing, the competition’s real marking scheme, instant scoring and a worked solution on every question. The paid series exist because there are 120 papers in total and each can only be sat cold once.
Which free paper should I start with?
A full mock rather than a topic paper, sat cold before any revision. AMC 8 Full Mock Paper 1, AMC 10 Full Mock Paper 1, AMC 12 Mock Paper 1, or Paper 1 of whichever UKMT challenge matches your year group. The score will be lower than you expect, and that is exactly what makes it useful.
Do the free papers use real negative marking?
Yes, where the competition uses it. The UKMT Senior Challenge deducts a mark for every wrong answer; the Intermediate Challenge deducts 1 on questions 16-20 and 2 on questions 21-25; the AMC 10 and 12 award 1.5 for a blank. Our marking applies each scheme exactly, so a practice score reflects what the same performance would earn on the day.
How many practice papers does a student actually need?
Six to eight full timed papers across a preparation, plus topic papers while a topic is still being built. Beyond that the limiting factor is review, not volume: one paper properly reviewed - every miss redone untimed, every cause logged - is worth more than three papers that were only marked.
Are these the official past papers?
No. They are original papers written to each competition’s published specification, matching the format, marking and difficulty curve. Official past papers from the MAA and the UKMT are free and worth using too, but the supply is finite - this series adds papers you have never seen.
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