- Tama and Ana share a jar of marbles in the ratio 3 : 5. Ana then gives Tama 10 of her marbles, and now they have the same number. How many marbles are there altogether?
- At the Ōtautahi Saturday market, Mere spends half of her money plus $2 more at the first stall. At the second stall she spends half of what is left plus $2 more. She now has $5. How much money did she start with?
- In a regular polygon, each interior angle is 4 times as big as each exterior angle. How many sides does the polygon have?
- Without a calculator, work out 2026² − 2025².
- Hemi thinks of a number. He multiplies it by 3, subtracts 7, then halves the result. His answer is 4 more than the number he started with. What was his number?
- What is the last digit of 7²⁰²⁶ (7 multiplied by itself 2026 times)?
- A spinner has three sectors: red with an angle of 90°, blue with 150° and green with 120°. Rāwiri spins it twice and records whether both spins land on the same colour. He does this 720 times. About how many times should he expect the same colour twice?
- An analogue clock with a 12-hour face gains 3 minutes every hour. It is set to the correct time at 9:00 am on Monday. How long until it next shows the correct time?
- What is the smallest positive whole number n that makes 360 × n a perfect cube?
- Tama scored 90 in a class test. When his score is taken out, the mean score of the class drops from 72 to 70. How many students are in the class, including Tama?
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