AMC 10 Geometry — Paper 1
AMC 10 geometry practice paper: 30 problems on triangles, circles, coordinate geometry, solids and similarity, each with a full worked solution.
About this test
AMC 10 Geometry — Paper 1 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
- Right triangles — 1 question
- Circles and squares — 1 question
- Similarity — 1 question
- Polygon angles — 1 question
- Coordinate distance — 1 question
- Trapezoids — 1 question
- Space diagonals — 1 question
- Inscribed angles — 1 question
- Equilateral triangles — 1 question
- Shoelace formula — 1 question
- Power of a point — 1 question
- Inradius — 1 question
- Arc length — 1 question
- Rectangles — 1 question
- Cylinders — 1 question
- Angle bisectors — 1 question
- Reflections — 1 question
- Annulus — 1 question
- Heron's formula — 1 question
- Tangent lengths — 1 question
- Special right triangles — 1 question
- Midpoint triangles — 1 question
- Lines and circles — 1 question
- Cones — 1 question
- Parallelograms — 1 question
- Spheres — 1 question
- Exterior angles — 1 question
- Distance to a line — 1 question
- Cyclic quadrilaterals — 1 question
- Geometric mean relations — 1 question
Difficulty spread
- 4 easy questions
- 14 medium questions
- 3 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
Are there diagrams?
No, and that is deliberate. Every configuration is described completely in words, naming the vertices and the order of the points, so you practise building the picture yourself. That is a real AMC skill, because the contest diagram is often missing or misleading.
Which topics does this paper cover?
Right triangles, similarity, polygon angles, circles and inscribed angles, power of a point, tangent lengths, Heron, the inradius, coordinate geometry with the shoelace formula, and the volumes of cylinders, cones and spheres.
How is it scored?
Real AMC 10 rules: 6 points for a correct answer, 1.5 for a blank and 0 for a wrong one. Leaving a question you truly cannot start is worth more than a guess.
How long should it take?
75 minutes, the real AMC 10 length. If you finish early, spend the remaining time re-deriving the questions you were unsure of rather than submitting.