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 lengths is the longest?
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2.05 km, 205 000 cm and 2 050 000 mm are all 2 050 m. 2 500 m is longer.
2 What is the perimeter of this L-shape, in centimetres? Two sides are not labelled.
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The missing sides are 4 and 5. 5 + 2 + 4 + 5 + 9 + 7 = 32 cm — the same as the 9 by 7 rectangle around it.
3 A 12 by 9 rectangle has a 4 by 3 rectangular hole cut out of it. What is the area of the shaded part, in square units?
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12 × 9 = 108, and the hole is 4 × 3 = 12. 108 − 12 = 96.
4 Rectangle P is 16 cm by 4 cm. Square Q has the same area as P. What is the perimeter of Q?
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16 × 4 = 64, and 8 × 8 = 64, so Q has side 8 cm and perimeter 4 × 8 = 32 cm.
5 What is the area of this right-angled triangle, in square centimetres?
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The rectangle would be 14 × 9 = 126, and the triangle is half: 63 cm².
6 A rectangle has a perimeter of 70 cm. Its length is 2.5 times its width. What is its width?
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Length + width = 35 cm, and that is 2.5w + w = 3.5w. So w = 35 ÷ 3.5 = 10 cm (and the length is 25 cm).
7 Three squares with sides 7, 5 and 3 units share a corner. The outer ring and the inner square are shaded.1 The outer ring has an area of 24 square units.
2 The unshaded ring has an area of 15 square units.
3 The shaded area is 33 square units altogether.
Which statements are correct?
2 The unshaded ring has an area of 15 square units.
3 The shaded area is 33 square units altogether.
Which statements are correct?
Show worked solution
49 − 25 = 24 (1 ✓). 25 − 9 = 16, not 15 (2 ✗). Shaded: 24 + 9 = 33 (3 ✓). 1 and 3.
8 What is the area of this parallelogram, in square centimetres?
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12 × 7 = 84 cm². Using the slanted 9 cm gives 108, which is wrong: the height is measured straight up.
9 On a map, 1 cm stands for 2.5 km. Two towns are 6.4 cm apart on the map. How far apart are they really, in metres?
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6.4 × 2.5 = 16 km, which is 16 000 m.
10 Two identical rectangles, 11 cm by 4 cm, are joined along a long side. What is the perimeter of the new shape?
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2 × (11 + 8) = 38 cm. Doubling one rectangle's perimeter (60) counts the shared 11 cm edge twice.
11 A rectangular rug is 1.5 m long and 40 cm wide. What is its area in square centimetres?
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1.5 m = 150 cm. 150 × 40 = 6 000 cm².
12 A rectangle has whole-number sides. Its area is 96 cm² and its perimeter is 40 cm. What are its length and width?
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Length + width must be 40 ÷ 2 = 20. Only 12 and 8 add to 20 (and 12 × 8 = 96 ✓).
13 This staircase shape is drawn on a 1 cm grid. What is its perimeter?
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The steps add up to 6 across and 6 down, so the perimeter equals that of the 6 by 6 square: 24 cm.
14 A piece of wire is bent into a rectangle 14 cm by 6 cm. The same wire is then straightened and bent into a square. What is the area of the square?
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Wire: 2 × (14 + 6) = 40 cm. Square side: 40 ÷ 4 = 10 cm. Area: 10 × 10 = 100 cm².
15 A fun run is 3.2 km long.
1 That is 3 200 m.
2 Four laps of a 750 m track would be longer than the run.
3 3.2 km is 320 000 cm.
Which statements are correct?
1 That is 3 200 m.
2 Four laps of a 750 m track would be longer than the run.
3 3.2 km is 320 000 cm.
Which statements are correct?
Show worked solution
3.2 × 1 000 = 3 200 m (1 ✓). 4 × 750 = 3 000 m, which is shorter (2 ✗). 3 200 m × 100 = 320 000 cm (3 ✓). 1 and 3.