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Ontario MPT overview

Ontario MPT: Spatial sense: geometry and measurement

Angles and polygons, the Pythagorean relationship, transformations, area, surface area and volume, metric unit conversions and circles.

  • 16 questions
  • Topic drill
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Spatial sense: geometry and measurement · Question 1Score 0/0

A rectangular prism is 5 cm by 4 cm by 3 cm. What is its volume?

Study reference: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 4 Spatial Sense strand — Grades 3–8 strand E, Grade 9 strand E

All 16 questions in this test

Every question and its answer choices. The correct answers and explanations appear when you take the test above.

  1. A rectangular prism is 5 cm by 4 cm by 3 cm. What is its volume?

    1. 60 cm³
    2. 94 cm³
    3. 47 cm³
    4. 12 cm³

  2. Two angles are supplementary. One measures 128°. What is the other?

    1. 232°
    2. 128°
    3. 52°
    4. 62°

  3. Point (−1, 4) is translated 5 units right and 3 units down. Where is its image?

    1. (4, 1)
    2. (4, 7)
    3. (2, 9)
    4. (−6, 7)

  4. Find the area of a trapezoid with parallel sides 8 cm and 14 cm and a height of 5 cm.

    1. 560 cm²
    2. 110 cm²
    3. 27 cm²
    4. 55 cm²

  5. Which quadrilateral always has four equal sides but not necessarily four right angles?

    1. Rhombus
    2. Rectangle
    3. Trapezoid
    4. Kite

  6. A 6 cm by 4 cm photo is enlarged so that its 6 cm side becomes 15 cm. How long is the enlarged 4 cm side?

    1. 10 cm
    2. 22.5 cm
    3. 13 cm
    4. 9 cm

  7. Two angles of a triangle measure 48° and 67°. What is the third angle?

    1. 115°
    2. 245°
    3. 25°
    4. 65°

  8. Point (3, −2) is reflected in the x-axis. What are the coordinates of its image?

    1. (3, 2)
    2. (−3, 2)
    3. (−3, −2)
    4. (2, 3)

  9. Using the π key, what is the volume of a cylinder with a 4 cm radius and 10 cm height, to the nearest cm³?

    1. 503 cm³
    2. 1 005 cm³
    3. 251 cm³
    4. 126 cm³

  10. How many faces, edges and vertices does a triangular prism have?

    1. 4 faces, 6 edges, 4 vertices
    2. 5 faces, 8 edges, 5 vertices
    3. 6 faces, 12 edges, 8 vertices
    4. 5 faces, 9 edges, 6 vertices

  11. What is the area of a parallelogram with a base of 11 cm and a height of 6 cm?

    1. 33 cm²
    2. 66 cm²
    3. 34 cm²
    4. 17 cm²

  12. What is the sum of the interior angles of a hexagon?

    1. 540°
    2. 360°
    3. 1 080°
    4. 720°

  13. A 2.4 m board is cut into pieces 30 cm long. How many pieces are there?

    1. 0.08
    2. 12
    3. 8
    4. 80

  14. How many square centimetres are in 1 square metre?

    1. 100
    2. 10 000
    3. 1 000 000
    4. 1 000

  15. A right triangle has legs of 9 m and 12 m. How long is the hypotenuse?

    1. 21 m
    2. 108 m
    3. 15 m
    4. 10.5 m

  16. To the nearest tenth, what is the area of a circle with a radius of 6 cm? (Use the π key.)

    1. 18.8 cm²
    2. 452.4 cm²
    3. 37.7 cm²
    4. 113.1 cm²

Spatial sense: geometry and measurement: key rules to remember

Our summary of what the official handbook says on this topic, in our own words. Read it before or after the practice questions above, then check the original chapter. Read the official chapter ↗

Ontario Curriculum, Spatial Sense strand (Grades 3–8 E; Grade 9 E)

  • Triangle angles sum to 180°; polygon interior sum (n − 2) × 180°; supplementary = 180°.
  • Quadrilateral properties (rhombus: four equal sides).
  • Pythagorean relationship a² + b² = c².
  • Area: parallelogram bh; trapezoid (a + b)h ÷ 2; circle πr²; 1 m² = 10 000 cm².
  • Volume: prism lwh; cylinder πr²h; surface area of a prism.
  • Transformations on a grid: reflection in x-axis (x, −y); translations.
  • Similar figures: scale factor.
  • Triangular prism: 5 faces, 9 edges, 6 vertices (Euler: F − E + V = 2).

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