Year 9 extension

1. Hemi writes 4⁵ + 4⁵ + 4⁵ + 4⁵ on the whiteboard and says it equals 2ⁿ. What is n?
2. A Wellington surf shop raises the price of a wetsuit by 20%. A month later it takes 20% off the new price, and the wetsuit now costs $192. What was the original price?
3. Aroha and Tama share some money in the ratio 3 : 5. Aroha then gives Tama $12, and the ratio becomes 1 : 3. How much money is there altogether?
4. How many integers n satisfy −7 < 3 − 2n ≤ 9?
5. Mere cycles from her house up to a lookout in the Waitākere Ranges at 12 km/h, then comes straight back down the same road at 24 km/h. What is her average speed for the whole trip?
6. Squares are drawn outward on all three sides of a right-angled triangle. The three squares have a total area of 200 cm². How long is the longest side of the triangle?
7. A straight line passes through (1, 7) and (4, 1). At what point does it cross the line y = x?
8. A square is drawn inside a circle of radius 5 cm so that all four corners of the square touch the circle. What is the area inside the circle but outside the square?
9. Kahu rolls two fair six-sided dice and adds the numbers. What is the probability that the total is a prime number?
10. Eight students at a Tauranga school record how many books they read in the holidays. The five-number summary is: minimum 4, lower quartile 6, median 9, upper quartile 13, maximum 20 (quartiles found as the medians of the lower and upper halves). What is the mean number of books?