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Math 7

Math 7 · Worksheets

Mixed review · Circles, geometry and data

Ten questions of mixed difficulty, covering Circles and area, Data and probability, Geometry. Print it, or work through it on screen — the answer key starts on its own page.

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Mixed review · Circles, geometry and data

Math 7 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A triangle has a base of 10 cm and a height of 6 cm. What is its area?

    1. a) 16 cm²
    2. b) 8 cm²
    3. c) 60 cm²
    4. d) 30 cm²

  2. Point P is on the perpendicular bisector of segment AB, and PA = 7 cm. What must be true?

    1. a) PB = 3.5 cm
    2. b) PB = 7 cm
    3. c) PB can be any length
    4. d) PB = 14 cm

  3. An angle of 130° is cut by its angle bisector. What is the size of each of the two new angles?

    1. a) 50°
    2. b) 65°
    3. c) 25°
    4. d) 260°

  4. A rectangle has corners at (−3, 2), (4, 2), (4, −1) and (−3, −1). What is its perimeter?

    1. a) 16 units
    2. b) 20 units
    3. c) 8 units
    4. d) 21 units

  5. A circle has a radius of 6 cm. What is its diameter?

    1. a) 18.84 cm
    2. b) 3 cm
    3. c) 12 cm
    4. d) 36 cm

  6. The point (3, −2) is rotated 180° about the origin. What is its image?

    1. a) (−3, 2)
    2. b) (−3, −2)
    3. c) (3, 2)
    4. d) (2, 3)

  7. You fold a sheet of paper so that point A lands exactly on point B, then unfold it. What is the fold line?

    1. a) a line parallel to segment AB
    2. b) a line through A, perpendicular to segment AB
    3. c) the straight line that joins point A to point B
    4. d) the perpendicular bisector of segment AB

  8. What is the mean of 3, 5, 6, 10 and 11?

    1. a) 7
    2. b) 35
    3. c) 6
    4. d) 8

  9. A parallelogram has a base of 9 cm, slanted sides of 5 cm and a height of 4 cm. What is its area?

    1. a) 28 cm²
    2. b) 18 cm²
    3. c) 36 cm²
    4. d) 45 cm²

  10. Point P is in quadrant III. It is 3 units from the x-axis and 5 units from the y-axis. What are its coordinates?

    1. a) (−5, 3)
    2. b) (−3, −5)
    3. c) (5, 3)
    4. d) (−5, −3)

Answer key · Mixed review · Circles, geometry and data

Math 7 · maddyhelps.com

  1. d) 30 cm² — A triangle is half of a parallelogram with the same base and height, so its area is b × h ÷ 2 = 10 × 6 ÷ 2 = 30 cm². 60 cm² forgets to halve, and 16 adds the base and height instead of multiplying them.
  2. b) PB = 7 cm — Every point on a perpendicular bisector is the same distance from both ends of the segment — that is what the construction guarantees — so PB = PA = 7 cm. Thinking only the midpoint is equally far from A and B misses the rest of the line.
  3. b) 65° — Bisecting means cutting into two equal parts, so each new angle is 130° ÷ 2 = 65°. 260° doubles instead of halving, and 50° is what is left of a straight angle, 180° − 130°, which is a different angle.
  4. b) 20 units — From x = −3 to x = 4 is 7 units (3 to reach the y-axis and 4 more), and from y = −1 to y = 2 is 3 units, so the perimeter is 7 + 3 + 7 + 3 = 20 units. Taking 3 from 4 gives a width of 1 and a perimeter of 8 — count across the axis, not the gap between the digits. 21 is the area.
  5. c) 12 cm — The diameter goes all the way across through the centre, so it is two radii long: 2 × 6 = 12 cm. 3 cm halves the radius instead of doubling it, and 18.84 cm multiplies by π, which gives half the circumference.
  6. a) (−3, 2) — A half turn about the origin carries a point to the opposite side of the origin, so both coordinates change sign: (−3, 2). (3, 2) and (−3, −2) change only one sign — those are reflections in an axis — and (2, 3) is only a quarter turn.
  7. d) the perpendicular bisector of segment AB — The fold sends A onto B, so every point on the crease is the same distance from A as from B, and the crease crosses AB at its midpoint at a right angle — exactly a perpendicular bisector. It cannot pass through A, because A lands on B, not on itself.
  8. a) 7 — Add the numbers and share the total equally: 3 + 5 + 6 + 10 + 11 = 35, and 35 ÷ 5 = 7. 35 stops before dividing, 6 is the median and 8 is the range.
  9. c) 36 cm² — The area of a parallelogram is base × height, and the height is measured straight up from the base, at a right angle: 9 × 4 = 36 cm². 45 cm² uses the slanted side, which is longer than the height, and 18 cm² halves as if it were a triangle.
  10. d) (−5, −3) — How far a point is from the x-axis is how far up or down it is, which is its y-coordinate; how far it is from the y-axis is its x-coordinate. In quadrant III both are negative, so P is (−5, −3). (−3, −5) matches each distance to the axis it names, which puts the numbers the wrong way round.