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 A job needs at least 4 metres of cable. Rolls come in 3 m, 5 m, 8 m and 12 m. What is the shortest roll that will do?
Show worked solution
Only 3 m is too short. Of the three that are long enough, the shortest is 5 m.
2 There are 45 books and a shelf holds 7. Write how many shelves can be completely filled, and how many shelves are needed to hold every book.
Show worked solution
6 shelves are full (6), and the 3 left over still need one more, so 7 shelves are needed.
3 A car holds 4 children. How many cars are needed for 35 children?
Show worked solution
35 ÷ 4 = 8 remainder 3, and the 3 still need a car, so 9.
Level 2 · Core
4 A lift can carry at most 450 kg. Which of these loads is the heaviest it is allowed to carry?
Show worked solution
495 kg is over the limit. "At most 450" includes 450 itself, so the heaviest allowed is 450 kg.
5 A tank needs at least 2.5 litres. Bottles hold 0.4 litres. Write the result of 2.5 ÷ 0.4, and the number of whole bottles needed.
Show worked solution
2.5 ÷ 0.4 = 6.25. Six bottles give only 2.4 L, so 7 are needed.
6 How many complete sets of 6 can be made from 40 items?
Show worked solution
40 ÷ 6 = 6 remainder 4, and 4 items do not make a set, so 6.
Level 3 · Challenge
7 A coach holds 48 passengers and 250 people need to travel.1 5 coaches carry 240 people.
2 5 coaches are enough.
3 6 coaches are needed.
Which statements are correct?
2 5 coaches are enough.
3 6 coaches are needed.
Which statements are correct?
Show worked solution
5 × 48 = 240 (1 ✓), which is 10 short of 250, so 5 is not enough (2 ✗) and 6 coaches are needed (3 ✓). 1 and 3.
8 A lift takes at most 450 kg. Six people weigh 95, 90, 85, 80, 75 and 70 kg. Write the total weight of all six, and the largest number of them who can ride together.
Show worked solution
All six weigh 495 kg, over the limit. Leaving out the heaviest gives 90 + 85 + 80 + 75 + 70 = 400 kg, so 5 can ride.
9 Tickets cost $7 each and someone has $50. How many tickets can they buy?
Show worked solution
50 ÷ 7 = 7 remainder 1, and $1 does not buy a ticket, so 7.