- Solve log₂ x + log₄ x + log₁₆ x = 7.
- Find the exact value of √(7 + 4√3) − √(7 − 4√3).
- A is (1, 2) and B is (7, 10). Point P lies on the x-axis and is the same distance from A as from B. Find P.
- A teacher changes every test mark by doubling it and then adding 5. The new marks have a mean of 65 and a standard deviation of 12. What were the mean and standard deviation of the original marks?
- For which values of k does the line y = kx − 1 touch the parabola y = x² + 3 at exactly one point?
- A triangular garden bed in Hamilton has sides 5 m, 7 m and 8 m. Find its exact area.
- The tangent to y = x³ at the point (1, 1) meets the curve again at another point. Find that point.
- A particle starts at the origin with velocity v = 3t² − 12t + 9 m/s, for t in seconds. How far does it travel in total in the first 4 seconds?
- 1% of people at a clinic have a condition. A test is positive for 90% of people who have it and for 5% of people who do not. A person tests positive. What is the probability they have the condition?
- A sector of a circle has a perimeter (two radii plus the arc) of 20 cm. What is the largest area it can have?
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