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. What is the area of a triangle with vertices at (0, 0), (4, 0), and (0, 3)?

    Answer: 6

    The triangle has base 4 and height 3 along the coordinate axes, so its area is (1/2)(4)(3) = 6.

  2. A chord is 4 units from the center of a circle with radius 5. What is the length of the chord?

    Answer: 6

    The perpendicular bisects the chord; half-chord = √(5² − 4²) = √9 = 3, so the chord length is 6.

  3. Two angles of a triangle measure 45° and 75°. What is the measure of the third angle?

    Answer: 60°

    The interior angles of a triangle sum to 180°, so the third angle is 180° − 45° − 75° = 60°.

  4. In a right triangle, one leg is 7 and the hypotenuse is 25. What is the length of the other leg?

    Answer: 24

    By the Pythagorean theorem, the other leg is √(25² − 7²) = √(625 − 49) = √576 = 24.

  5. Two similar triangles have corresponding sides in the ratio 3:5. What is the ratio of their areas?

    Answer: 9:25

    Areas of similar figures scale as the square of the linear ratio: (3/5)² = 9/25.

  6. What is the area of a regular hexagon with side length 2?

    Answer: 6√3

    A regular hexagon with side s has area (3√3/2)s²; with s = 2 the area is (3√3/2)(4) = 6√3.