Practice Test GeeksCOMC - Canadian Open Mathematics Challenge Practice Test
← All COMC Flashcard Decks

COMC Geometry and Combinatorics Flashcards

6 cards from real COMC practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 COMC Geometry and Combinatorics flashcards as text

  1. How many diagonals does a regular octagon have?

    Answer: 20

    An n-gon has n(n−3)/2 diagonals; for an octagon: 8(8−3)/2 = 8×5/2 = 20.

  2. What is the total surface area of a cube with edge length 3?

    Answer: 54

    A cube has 6 square faces each of area 3² = 9, so total surface area = 6 × 9 = 54.

  3. What is the area of a rhombus whose diagonals have lengths 8 and 10?

    Answer: 40

    The area of a rhombus is half the product of its diagonals: (1/2)(8)(10) = 40.

  4. How many triangles can be formed by connecting vertices of a regular hexagon?

    Answer: 20

    Any 3 of the 6 vertices form a unique triangle: C(6,3) = 6!/(3!×3!) = 20.

  5. A circle is inscribed in a square with side length 4. What is the area of the circle?

    Answer: 4π

    The inscribed circle's diameter equals the side of the square, so r = 2 and area = π(2²) = 4π.

  6. How many paths are there from one corner to the opposite corner of a 3×3 grid, moving only right or up?

    Answer: 20

    Each path uses exactly 3 right and 3 up steps; the number of orderings is C(6,3) = 20.