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.
15 questions · official format, shuffled order
1 Which of these shapes has exactly one pair of parallel sides?
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A trapezium has exactly one pair of parallel sides. The other four all have two pairs.
2 A row of 11 tiles must be symmetrical about its middle tile. What is the fewest tiles that still need colouring?
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Pairs 5–7 already match. Tiles 8, 9, 10 and 11 must copy 4, 3, 2 and 1: 4 tiles.
3 A regular pentagon is turned about its centre through two steps of its rotational symmetry. How many degrees has it turned?
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One step is 72°. Two steps: 2 × 72 = 144°.
4 Digits are written in this plain seven-segment style. Which two-digit number is the largest that reads the same when turned upside down?
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96 turned upside down is 96 again (the 9 becomes a 6 at the back, the 6 becomes a 9 at the front). 69 and 88 also work but are smaller; 98 becomes 86 and 99 becomes 66; 100 has three digits.
5 A triangle has sides 7 cm, 7 cm and 10 cm.
1 It is isosceles.
2 It has exactly one line of symmetry.
3 Its largest angle is opposite the 10 cm side.
Which statements are correct?
1 It is isosceles.
2 It has exactly one line of symmetry.
3 Its largest angle is opposite the 10 cm side.
Which statements are correct?
Show worked solution
Two equal sides: isosceles (1 ✓). One line of symmetry through the apex (2 ✓). The largest angle faces the longest side, 10 cm (3 ✓). 1, 2 and 3.
6 On a scale drawing, 1 grid square stands for 2.5 m. A pool is drawn 6 squares long and 4 squares wide. What is the real perimeter of the pool?
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15 m by 10 m. Perimeter 2 × (15 + 10) = 50 m.
7 Which of these shapes tessellates on its own — covers a flat surface with no gaps and no overlaps?
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Three regular hexagons meet at a point: 3 × 120° = 360°. Pentagons (108°), octagons (135°) and heptagons leave gaps, and circles cannot touch along edges.
8 The shaded cells are reflected in the dashed line. Columns are lettered P to U and rows are numbered. Into which cell does the shaded cell R4 land?
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R4 is one column left of the line, so its image is one column right of it, in the same row: S4.
9 Which quadrilateral has four equal sides but does not have to have four right angles?
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A rhombus has four equal sides; its angles come in two equal pairs that need not be 90°. A square is the special rhombus whose angles are all right angles.
10 A shape has rotational symmetry of order 6 and no line of symmetry. Through how many degrees must it turn before it first looks the same?
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360 ÷ 6 = 60°. The lack of line symmetry does not change this.
11 How many lines of symmetry does a regular octagon have, and what is its order of rotational symmetry?
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Four lines through opposite corners and four through opposite sides: 8 lines, order 8.
12 Which of these capital letters has both a line of symmetry and rotational symmetry of order 2?
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H has two mirror lines and looks the same turned 180°. A and T have only a mirror line; N has only the half-turn; L has neither.
13 A map is drawn to a scale where 1 cm stands for 4 km. A park on the map is a rectangle 3.5 cm by 2 cm. What is the real area of the park?
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14 km by 8 km. 14 × 8 = 112 km². (Scaling the map area of 7 cm² by 4 gives 28, which is wrong: both sides scale.)
14 An isosceles triangle has one angle of 40°. Which of these could be its other two angles?
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If 40° is the apex, the base angles are (180 − 40) ÷ 2 = 70° and 70°. If 40° is a base angle, the others are 40° and 100°, which is not offered. (40° and 110° adds to 190°.)
15 A tile pattern uses squares and equilateral triangles meeting at each point.
1 Two squares and three triangles can meet at a point with no gap.
2 Three squares and one triangle can meet at a point with no gap.
3 Four squares meet at a point with no gap.
Which statements are correct?
1 Two squares and three triangles can meet at a point with no gap.
2 Three squares and one triangle can meet at a point with no gap.
3 Four squares meet at a point with no gap.
Which statements are correct?
Show worked solution
2 × 90 + 3 × 60 = 360 (1 ✓). 3 × 90 + 60 = 330, leaving a gap (2 ✗). 4 × 90 = 360 (3 ✓). 1 and 3.