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.
35 questions · official format, shuffled order
1 The sum of the first five odd numbers is
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1 + 3 + 5 + 7 + 9 = 25 — the sum of the first n odd numbers is always n × n.
2 A jug holds 1.5 litres. How many 250 mL glasses can be filled from three full jugs?
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1 500 ÷ 250 = 6 glasses a jug, so 3 × 6 = 18.
3 A number rounded to the nearest 10 is 70, and rounded to the nearest 5 is 65. What is the largest the number could be?
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It must lie in both ranges, 65 to 67. The largest is 67.
4 A large cube is built from 64 small cubes. How many of the small cubes can be seen from the outside?
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64 − 8 = 56.
5 Which of these has the greatest value?
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three quarters of a half = 3/8 = 0.375, which beats 1/4, 1/5 and 1/6.
6 Each term in this sequence is double the one before. Which term is the first to be greater than 1 000?
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3, 6, 12, 24, 48, 96, 192, 384, 768, 1 536 — the 10th term is the first over 1 000.
7 A bag holds 4 red, 5 blue and 6 green marbles. Without looking, what is the fewest marbles you must take out to be certain of having two of the same colour?
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Three marbles could be red, blue and green. The 4th must match one of them.
8 A square has a perimeter of 48 cm. It is cut into four equal strips. What is the perimeter of one strip?
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2 × (12 + 3) = 30 cm.
9 What is the sum of all the two-digit numbers that read the same backwards as forwards?
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11 × (1 + 2 + … + 9) = 11 × 45 = 495.
10 A rectangular garden 15 m by 8 m is fenced with a post every metre around the edge, including one at each corner. How many posts are needed?
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The perimeter is 2 × (15 + 8) = 46 m, so 46 posts.
11 You have a 3-litre jug and a 5-litre jug, both empty, and a tap. Each fill, empty or pour counts as one step. What is the fewest steps needed to have exactly 4 litres in the 5-litre jug?
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Those 6 steps leave 4 litres in the 5-litre jug.
12 25% of 40% of 300 is
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40% of 300 = 120, and 25% of 120 = 30.
13 A rectangle is three times as long as it is wide, and its perimeter is 64 cm. How wide is it?
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64 ÷ 8 = 8 cm.
14 Which of these is closest to two thirds?
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0.666… − 0.66 is about 0.007, the smallest gap: 0.66.
15 How many minutes are there from 10:48 am to 1:15 pm?
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120 + 27 = 147 minutes.
16 A ladder has 20 rungs, equally spaced 25 cm apart. The bottom rung is 25 cm above the ground. How high is the top rung?
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20 × 25 = 500 cm = 5 m.
17 Three workers, all working at the same rate, take 8 days to build a wall. How many days would six workers take?
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The job is 3 × 8 = 24 worker-days; 24 ÷ 6 = 4 days.
18 Which solid has 8 vertices and 6 faces?
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A rectangular prism (a box) has 8 corners and 6 faces. A triangular prism has 6 and 5; a square pyramid 5 and 5; a hexagonal pyramid 7 and 7.
19 I think of a number, add 5, multiply by 3 and subtract 9. The answer is 30. What was my number?
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30 + 9 = 39; 39 ÷ 3 = 13; 13 − 5 = 8.
20 Which of these numbers has exactly three factors?
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25 has factors 1, 5 and 25 only. 12 has six, 15 has four, 21 has four.
21 A solid cube with 2 cm edges weighs 64 g. A cube of the same material with 1 cm edges weighs
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64 ÷ 8 = 8 g.
22 A 5 km race has a marker every 400 m from the start, and one more at the finish line. Not counting the start, how many markers are there?
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12 markers at 400 m, 800 m … 4 800 m, plus one at 5 000 m: 13.
23 In a code, A = 1, B = 2, C = 3 and so on up to Z = 26. The word CAB is worth 3 + 1 + 2 = 6. Which of these words is worth exactly 20?
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DIG = 4 + 9 + 7 = 20. BED = 11, FACE = 15, HIDE = 26.
24 Square tiles 20 cm by 20 cm are laid to cover a floor 3 m by 2.4 m exactly. How many tiles are needed?
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15 × 12 = 180 tiles.
25 The angles inside a quadrilateral add to 360°. The angles inside a triangle add to 180°. A pentagon can be cut into three triangles from one corner, so its angles add to
Show worked solution
3 × 180 = 540°.
26 A train leaves at 9:40 am and travels 180 km at a steady 90 km/h. When does it arrive?
Show worked solution
180 ÷ 90 = 2 hours. 9:40 + 2 h = 11:40 am.
27 Which set of three lengths could be the sides of a triangle?
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4 + 5 = 9 > 8, so 4 cm, 5 cm, 8 cm works. 1 + 2 = 3, 2 + 3 < 6 and 3 + 4 < 9 all fail.
28 A shop reduces all its prices by 20%. A week later it raises the reduced prices by 20%. Compared with the original, the final price is
Show worked solution
$100 → $80 → $96, which is 4% less. The 20% up is taken of the smaller amount.
29 What is the 100th odd number?
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The nth odd number is 2n − 1, so the 100th is 199.
30 A rectangle has an area of 48 cm² and whole-number sides. How many different rectangles are possible?
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1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8: 5 rectangles.
31 In a group of 24 children, two thirds are girls. Three quarters of the girls have brown hair. How many girls do not have brown hair?
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⅔ of 24 = 16 girls; ¼ of 16 = 4.
32 Using each of these four cards once, what is the largest even four-digit number that can be made?
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9 642 — the 2 goes last so the 9, 6 and 4 can lead.
33 Half of the students in a class are boys. A third of the boys wear glasses, and 4 boys wear glasses. How many students are in the class?
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12 boys, so 24 students.
34 This spinner has 8 equal sections, 3 of them red. If it is spun 400 times, about how many times would you expect red?
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400 ÷ 8 = 50, and 3 × 50 = 150.
35 The numbers 1 to 9 are placed in a 3 by 3 grid so that every row, every column and both diagonals add to 15. What number must go in the centre?
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Four lines total 60, and the nine numbers total 45, so the centre counted three extra times adds 15: the centre is 5.