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Math 8

Math 8 · Worksheets

Mixed review · Measurement, geometry and data

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

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Mixed review · Measurement, geometry and data

Math 8 · maddyhelps.com

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

  1. What is the surface area of a cube with edges of 4 cm?

    1. a) 16 cm²
    2. b) 48 cm²
    3. c) 64 cm²
    4. d) 96 cm²

  2. An object's top view is 2 rows of 3 squares. Its front view is 3 squares in a row, with 1 more square on top of the left-hand one. What is the least number of cubes the object can have?

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

  3. Three cubes sit in a row on a table, and a fourth cube sits on top of the left-hand one. What does the top view show?

    1. a) 4 squares in a row
    2. b) 3 squares in a row
    3. c) 2 squares in a column
    4. d) 4 squares in an L shape

  4. A top view shows how many cubes are in each stack. The back row reads 3, 2 and the front row reads 1, 1, from left to right. What does the front view show?

    1. a) a column of 4 squares on the left and 3 on the right
    2. b) a column of 3 squares on the left and 2 on the right
    3. c) a column of 1 square on the left and 1 on the right
    4. d) 4 squares in a 2 by 2 block

  5. What faces does the net of a triangular prism have?

    1. a) 1 triangle and 3 rectangles
    2. b) 3 triangles and 2 rectangles
    3. c) 2 triangles and 3 rectangles
    4. d) 2 triangles and 2 rectangles

  6. Triangle A has sides of 5 cm, 7 cm and 9 cm. Which triangle must be congruent to it?

    1. a) a triangle with sides of 9 cm, 5 cm and 7 cm
    2. b) any triangle with a perimeter of 21 cm
    3. c) a triangle with sides of 10 cm, 14 cm and 18 cm
    4. d) any triangle with two sides of 5 cm and 7 cm

  7. Three cubes sit in a row on a table, and a fourth cube sits on top of the left-hand one. What does the view from the right side show?

    1. a) 4 squares in an L shape
    2. b) 3 squares in a row
    3. c) 1 square
    4. d) 2 squares in a column

  8. A company's sales fell for two years, then rose for the last three months. Its ad shows a line graph of only those three months. What makes the graph misleading?

    1. a) It hides the longer trend by choosing a short time range.
    2. b) Its numbers must be wrong, since sales went up.
    3. c) Its horizontal axis has uneven intervals between months.
    4. d) The line graph should have been a circle graph.

  9. A triangular prism is 10 cm long. Its ends are right triangles with sides of 3 cm, 4 cm and 5 cm. What is its surface area?

    1. a) 60 cm²
    2. b) 126 cm²
    3. c) 132 cm²
    4. d) 144 cm²

  10. Triangle JKL is congruent to triangle MNO, with the vertices matching in that order. Angle J = 50° and angle K = 70°. What is angle O?

    1. a) 120°
    2. b) 70°
    3. c) 50°
    4. d) 60°

Answer key · Mixed review · Measurement, geometry and data

Math 8 · maddyhelps.com

  1. d) 96 cm² — A cube has 6 square faces, each 4 × 4 = 16 cm², so its surface area is 6 × 16 = 96 cm². 64 is 4 × 4 × 4, the volume in cm³ — a different measurement — and 48 cm² counts only the three faces you can see at once.
  2. b) 7 — The top view shows 6 stacks, so there are at least 6 cubes, and the front view shows that one of the two left-hand stacks is 2 cubes tall while every other stack is 1. So the least is 6 + 1 = 7. 4 counts only the squares in the front view, and 8 makes both left-hand stacks 2 tall — that fits the views too, but it is not the least.
  3. b) 3 squares in a row — From above, the cube on top hides the cube under it, so you see one square for each spot on the table: 3 in a row. The L shape of 4 squares is the front view — the top view cannot show which stacks are taller.
  4. b) a column of 3 squares on the left and 2 on the right — From the front, each column shows its tallest stack, and taller stacks at the back rise above the short ones in front. The left column has stacks of 3 and 1, so it shows 3 squares; the right has 2 and 1, so it shows 2. Showing only the front row forgets the stacks behind it, and 4 and 3 add the stacks, counting cubes that are hidden.
  5. c) 2 triangles and 3 rectangles — A triangular prism has a triangle at each end, and each of the triangle's 3 sides is joined to the other end by a rectangle: 5 faces in all. A triangle has 3 sides, so it needs 3 rectangles, not 2, and a prism always has two matching ends.
  6. a) a triangle with sides of 9 cm, 5 cm and 7 cm — Three side lengths fix a triangle's size and shape, and the order they are listed in does not matter — 9, 5 and 7 are the same three sides. 10, 14 and 18 is the same shape twice as big, which is similar, not congruent, and a matching perimeter or two matching sides still leaves room for a different triangle.
  7. d) 2 squares in a column — From the right, the three cubes on the table line up one behind another, so they look like a single square, and the extra cube, on top of the one furthest away, shows above it: 2 squares in a column. 1 square forgets that a side view shows the tallest stack in each line, even at the back, and the L shape is the front view.
  8. a) It hides the longer trend by choosing a short time range. — Every number on the graph can be correct and it still misleads: showing only the three months of growth hides two years of falling sales, so the story looks like the opposite of what happened. Nothing in the description suggests uneven intervals, and a circle graph cannot show change over time at all.
  9. c) 132 cm² — Each triangular end is ½ × 3 × 4 = 6 cm² — the two shorter sides are the base and the height, because they meet at the right angle. The three rectangles are 3 × 10, 4 × 10 and 5 × 10, which add to 120 cm², so the total is 6 + 6 + 120 = 132 cm². 144 cm² forgets to halve for the triangles, and 126 cm² counts only one end.
  10. d) 60° — Angle O matches angle L, and the angles of triangle JKL add to 180°: L = 180° − 50° − 70° = 60°, so angle O = 60°. 70° is angle N, which matches K, and 120° adds the two given angles instead of taking them away from 180°.