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5 on the sheet, 84 match these filtersReshuffle Start overseed 9

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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 23 points

1.One pipe fills a pool in 12 hours and another fills it in 4 hours. With both running, how many hours does the pool take to fill?[4]
- A3
- B4
- C6
- D8
- E16
2.A rectangle measures 30 cm by 0.4 m. What is its area in square centimetres?[4]
- A0.12
- B12
- C120
- D1200
- E12000
3.Seven cups all stand upside down. In one move you must turn over exactly two cups. Can all seven ever stand the right way up?[5]
- AYes, in 4 moves
- BYes, in 7 moves
- CYes, but it takes many moves
- DIt depends which two cups you pick
- ENo, it is impossible
4.On the street grid shown you may only walk right or down. One junction is closed. How many routes go from the top-left corner to the bottom-right corner?[5]
Text description of the figure
A grid of streets with junctions arranged 4 across and 4 down. The junction one step right and one step down from the top-left corner is marked closed with a cross.
- A8
- B10
- C12
- D18
- E20
5.A room is 8 m long, 4 m wide and 2 m high. An ant walks across the floor and the walls from one bottom corner to the far top corner. What is the shortest distance in metres?[5]
Text description of the figure
The floor of a room, 8 metres by 4 metres, drawn flat, with one 8-metre-by-2-metre wall unfolded upwards from its far edge. A straight line joins the ant's starting corner on the floor to the opposite corner on the unfolded wall.
- A9.2
- B10
- C11
- D12
- E14

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Answer key — Math Kangaroo practice

Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.

1.A — 3KA-0116Combined work rates
- BI gave the faster pipe's time on its own, forgetting the slower one helps as well.
- CI halved the slower pipe's time rather than adding the two rates.
- DI averaged the two times, which would only be right if the pipes took turns.
- EI added the two times, which makes two pipes slower than one - an impossible answer.
2.D — 1200KA-0128Check units and re-read before bubbling
- AI worked entirely in metres and gave the answer in square metres.
- BI multiplied 30 by 0.4 without converting the metres to centimetres at all.
- CI converted 0.4 m to 4 cm rather than 40 cm.
- EI converted 0.4 m to 400 cm, moving the decimal point one place too far.
3.E — No, it is impossibleKA-0028Parity arguments
- AI found a sequence that turned over most of the cups and assumed the last one could be fixed somehow.
- BI matched the number of moves to the number of cups without checking whether the target is reachable at all.
- CI assumed that with enough moves any arrangement can be reached.
- DI thought the choice of which cups to flip could change whether the target is reachable.
4.A — 8KA-0031Counting paths on a grid
- BI assumed closing one junction removes about half the routes and halved the total of 20.
- CI counted the routes that pass through the closed junction and gave that instead of the ones that avoid it.
- DI subtracted only the 2 routes that reach the closed junction, not all the routes that continue through it.
- EI counted every route on the open grid and forgot to remove the ones through the closed junction.
5.B — 10KA-0082Shortest paths on and around shapes
- AI measured the straight line through the middle of the room, but the ant has to stay on the surfaces.
- CI unfolded the room but folded out the short wall rather than the one that makes the shortest route.
- DI chose an unfolding that gives a longer straight line and did not compare it with the others.
- EI walked along the edges of the room, 8 then 4 then 2, instead of cutting straight across the surfaces.

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