Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 How many squares does a cube net have?
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6.
2 A 3 by 3 by 3 cube is painted and split up. Write how many small cubes have 3 painted faces and how many have none.
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8 corners and 1 centre.
3 An equilateral triangle has rotational symmetry of order 3. How many degrees is one step?
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120°.
Level 2 · Core
4 Which of these five-square arrangements can be completed into a cube net by adding one square?
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Only P has a band of four with one cap, so only it can be completed: P only.
5 A row of 7 tiles must be symmetrical about its middle tile. Write the position that partners position 2, and the number of tiles still needed if positions 1 to 4 are already filled.
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Position 2 partners 6, and 3 tiles are still needed.
6 A square is turned three steps of its rotational symmetry. How many degrees is that?
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270°.
Level 3 · Challenge
7 A solid 4 by 4 by 4 cube is painted all over and split into small cubes.1 8 small cubes have three painted faces.
2 24 small cubes have exactly two painted faces.
3 12 small cubes have exactly two painted faces.
Which statements are correct?
2 24 small cubes have exactly two painted faces.
3 12 small cubes have exactly two painted faces.
Which statements are correct?
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The 8 corners always have three faces (1 ✓). Each of the 12 edges now has 2 middle cubes, so 12 × 2 = 24 have exactly two (2 ✓, 3 ✗). 1 and 2.
8 Write the largest two-digit number with a horizontal line of symmetry, and the order of rotational symmetry of a regular hexagon.
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88 and order 6.
9 A regular hexagon is turned two steps of its rotational symmetry. How many degrees is that?
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2 × 60 = 120°.