- A two-digit number is 4 times the sum of its digits. When 27 is added to the number, its two digits swap places. What is the number?
- A Southland farmer has 60 metres of fencing to make a rectangular pen against a long straight shed wall. The wall forms one side, so only three sides need fencing. What is the largest area the pen can have?
- The numbers a and b satisfy 2ᵃ = 5 and 5ᵇ = 8. What is the value of ab?
- A group of teachers and students goes on a camp at Tongariro. The mean age of the whole group is 18. The teachers have a mean age of 42 and the students a mean age of 14. What fraction of the group are teachers?
- A drinking glass is a cone with its point at the bottom. It is full of feijoa juice to a depth of 12 cm. Ana drinks until the juice is 6 cm deep. What fraction of the juice did she drink?
- The lines y = 2x + 1 and y = 7 − x and the x-axis enclose a triangle. What is its area?
- Without a calculator, find √(20 × 21 × 22 × 23 + 1).
- A rectangular garden in Nelson has a perimeter of 34 m and a diagonal of 13 m. What is its area?
- A cylindrical tank with internal diameter 16 cm holds some water. A solid ball of diameter 12 cm is dropped in and sinks so it is completely under the water. By how much does the water level rise?
- At a Wellington school, 60% of students walk to school. Of the walkers, 25% were late at least once this term. Of the other students, 40% were late at least once. A student who was late at least once is picked at random. What is the probability that they walk?
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