Find the amount for one unit first, then compare like with like.
Practice test 1 is free. No card needed.
Rates and speed questions are solved by finding the amount for one unit, such as the cost of a kilogram. Children in Year 7 now sit the exam in Year 8 , expected in June 2027.
Checked by the SelectiveReady team on 12 October 2026 · Updated 27 October 2026 · How we check facts
Independent. Not affiliated with the Victorian Department of Education or ACER.
A rates and speed question compares amounts per unit: which bag of rice is cheapest per kilogram, how fast a ride was, or what speed a trip home needs. It sits in the Mathematics part, which shares a 60-minute sitting with Quantitative Reasoning.
ACER says the Maths part tests year-level maths knowledge and reasoning, and using maths in real-world contexts. Shopping and travel are two everyday settings for that.
These three are our own questions, from easier to harder. Each one shows the answer and the working, so read them with your child.
As you read, check the units in the working first. A time written as a decimal of an hour, or a price compared per bag instead of per kilogram, is the slip behind the wrong options.
A shop sells rice in four bag sizes. Which bag is the best buy, meaning the lowest cost per kilogram?
Answer: C
Answer: C
Work out the cost of 1 kg for each bag: $2.90, $5.40 ÷ 2 = $2.70, $12.50 ÷ 5 = $2.50 and $26.00 ÷ 10 = $2.60. The 5 kg bag is cheapest per kilogram. The tempting 10 kg bag assumes the biggest bag is always the best value, but here it costs 10 cents more per kilogram.
Ruby cycles 24 km along a rail trail in 1 hour 20 minutes. What is her average speed?
Answer: A
Answer: A
Turn the time into minutes: 1 hour 20 minutes is 80 minutes. She rides 24 ÷ 80 = 0.3 km each minute, so in 60 minutes she rides 0.3 × 60 = 18 km. Her speed is 18 km/h. The tempting 20 km/h treats 1 hour 20 minutes as 1.2 hours, but 20 minutes is one third of an hour, not 0.2.
Hamish drives 120 km to the beach at an average speed of 60 km/h, then drives home by the same road. He wants his average speed for the whole trip there and back to be 48 km/h. What must his average speed be on the way home?
Answer: B
Answer: B
Average speed is total distance ÷ total time. 240 km at 48 km/h takes 240 ÷ 48 = 5 hours. The trip there took 120 ÷ 60 = 2 hours, leaving 3 hours for 120 km home: 40 km/h. The tempting 36 km/h assumes 48 is halfway between the two speeds, but he spends longer at the slower speed, so that does not work.
Bring everything down to one unit before comparing, because a rate is an amount for each one of something. These steps are ours, drawn from the working in the answers above.
Divide to get the price of 1 kg, or the distance in 1 hour. Then compare like with like.
1 hour 20 minutes is 80 minutes, not 1.2 hours. Work in minutes, then scale up to 60.
Distance is speed times time. Rearrange it to find whichever one is missing.
Average speed is total distance divided by total time. Never just average the two speeds.
Make sure the answer is in the units the question asks for, such as km/h or dollars per kilogram.
Each wrong option below takes a shortcut that sounds sensible. For each one, ask your child which shortcut it takes, then redo that step with the units written in.
Use supermarket shelf labels as a ready-made lesson. Cover the unit price, pick two sizes of the same item, and ask your child which is cheaper per 100 g or per kilogram. Then check against the label.
On a car trip, note the distance and the time taken, and work out the average speed together. Ask what speed you would need to arrive ten minutes sooner.
Three questions show the method; a timed sitting shows whether your child still converts the units when the clock is running. Practice test 1 in our selective entry practice tests is free and follows the real exam's parts and times.
For more worked items, see our maths sample questions. For the whole part, see VIC selective entry mathematics.
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.