AMC 10 Geometry — Paper 2
Premium AMC 10 geometry paper: 30 hard problems on Ptolemy, Brahmagupta, power of a point, medians, circumradius and surface paths, with worked solutions.
About this test
AMC 10 Geometry — Paper 2 is a full 30-question paper you attempt online in 75 minutes. It follows the American Mathematics Competition 10 pattern, so the timing, the question style and the marking match the real exam. There is no negative marking, so it is worth attempting every question. Leaving a question blank still earns 1.5 marks.
You get your score the moment you submit, question by question, with a step-by-step solution to every problem. 25 questions in 75 minutes. A high score qualifies for the AIME.
What it covers
Sections
- Medians — 1 question
- Tangent circles — 1 question
- Area ratios — 1 question
- Circumradius — 1 question
- Perpendicular bisectors — 1 question
- Inscribed squares — 1 question
- Surface paths — 1 question
- Regular hexagons — 1 question
- Rotations — 1 question
- Sectors — 1 question
- Ptolemy's theorem — 1 question
- Centroids — 1 question
- Similar solids — 1 question
- Angle chasing — 1 question
- Thales — 1 question
- Overlapping regions — 1 question
- Parallel lines — 1 question
- Isosceles trapezoids — 1 question
- Circumcircles — 1 question
- Surface area — 1 question
- Law of cosines — 1 question
- Pick's theorem — 1 question
- Lateral surface — 1 question
- Reflection principle — 1 question
- Rhombuses — 1 question
- Clock angles — 1 question
- Triangle inequality — 1 question
- Inscribed spheres — 1 question
- Medians and area — 1 question
- Brahmagupta's formula — 1 question
Difficulty spread
- 9 medium questions
- 2 hard questions
Before you start
15 questions · 45 minutes.
- Each correct answer scores 6 points.
- Each unanswered question scores 1.5 points.
- A wrong answer scores 0 — a blank is worth more than a guess unless you can eliminate at least three options.
- No calculators. Rough work on paper.
This paper covers Geometry only, so a weak score points at one topic rather than leaving you guessing.
A look at the questions
Questions people ask
How does this compare with Geometry Paper 1?
It is the premium tier. Paper 1 tests whether you know each formula; this one expects you to already know them and asks you to combine two or three, which is where AMC 10 questions 20 to 25 sit.
Which theorems does it use?
Ptolemy, Brahmagupta, Pick, the median-length formula, the circumradius relation R = abc/4K, power of a point, the reflection principle for shortest paths, and unfolding for paths across a solid surface.
Are there diagrams?
No. Every configuration is described completely in words, naming the vertices and the order of the points. Building the picture yourself is a real contest skill, since the given diagram is often absent or drawn misleadingly.
How is it scored?
Real AMC 10 rules: 6 points for a correct answer, 1.5 for a blank, 0 for a wrong one. On a paper this hard, leaving a question you cannot start genuinely beats guessing.