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 Which rule fits this table?
Show worked solution
2 × 10 = 4 × 5 = 5 × 4 = 10 × 2 = 20, so y = \(\dfrac{20}{x}\). y = 12 − x fits the first and last columns but gives 8 at x = 4; y = 5x and y = 14 − 2x fit only x = 2.
2 A trip takes 6 hours at 80 km/h. Find the length of the trip, and the time it would take at 96 km/h.
Show worked solution
Distance = 80 × 6 = 480 km. Time = 480 ÷ 96 = 5 h.
3 The graph shows a cycle ride. What was the speed, in km/h, during the fastest section?
Show worked solution
The steepest section is from 3 h to 4 h: 10 − 4 = 6 km in 1 h, so 6 km/h. The others are 4 ÷ 2 = 2 km/h, stopped, and 2 ÷ 2 = 1 km/h.
Level 2 · Core
4 The graph shows a walker’s distance from home. Which description fits?
Show worked solution
Out: 8 km in 2 h = 4 km/h. Flat from 2 h to 3 h: stopped for 1 h. Back: 8 km in 7 − 3 = 4 h = 2 km/h. So Away at 4 km/h, stops for 1 h, returns at 2 km/h. 8 km/h reads the distance as the speed; returning at 4 km/h assumes the same speed both ways; uphill and downhill reads the graph as a picture of the path.
5 15 workers take 8 days to finish a job. Find the total work in worker-days, and how many workers are needed to finish it in 6 days.
Show worked solution
Total work = 15 × 8 = 120 worker-days. Workers = 120 ÷ 6 = 20.
6 A car travels 150 km at 75 km/h, then another 150 km at 50 km/h. What is its average speed, in km/h, for the whole trip?
Show worked solution
Times: 150 ÷ 75 = 2 h and 150 ÷ 50 = 3 h. Total: 300 km in 5 h, so the average speed is 60 km/h. (75 + 50) ÷ 2 = 62.5 is wrong, because more time is spent at 50 km/h.
Level 3 · Challenge
7 Three statements:
1 If y = k/x and y = 6 when x = 4, then y = 3 when x = 8.
2 If 5 pumps empty a tank in 12 hours, then 3 pumps take 7.2 hours.
3 A walker who covers 9 km in 2 hours 15 minutes has an average speed of 4 km/h.
Which statements are correct?
1 If y = k/x and y = 6 when x = 4, then y = 3 when x = 8.
2 If 5 pumps empty a tank in 12 hours, then 3 pumps take 7.2 hours.
3 A walker who covers 9 km in 2 hours 15 minutes has an average speed of 4 km/h.
Which statements are correct?
Show worked solution
k = 4 × 6 = 24 and 24 ÷ 8 = 3 (1 ✓). 5 × 12 = 60 pump-hours, so 3 pumps take 60 ÷ 3 = 20 hours; 7.2 is the direct-variation slip 12 × 3 ÷ 5 (2 ✗). 2 h 15 min = 2.25 h and 9 ÷ 2.25 = 4 (3 ✓). 1 and 3.
8 A walks from home along a track; B walks along the same track towards home, starting 12 km away, at the same moment. When and where do they meet?
Show worked solution
A: 12 km in 4 h = 3 km/h, so A is 3t km from home. B: 12 km in 6 h = 2 km/h towards home, so B is 12 − 2t km from home. 3t = 12 − 2t gives 5t = 12, t = 2.4 h, and 3 × 2.4 = 7.2 km from home. Check: 12 − 2 × 2.4 = 7.2 ✓.
9 12 workers can finish a job in 10 days. After 4 days, 3 of the workers leave and the rest carry on at the same rate. How many days does the whole job take, from start to finish?
Show worked solution
Total = 12 × 10 = 120 worker-days. In 4 days: 12 × 4 = 48 done, 72 left. 9 workers take 72 ÷ 9 = 8 more days. Whole job: 4 + 8 = 12 days.