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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 20 points

1.Which of these numbers can be divided exactly by both 4 and 9?[4]
- A96
- B117
- C132
- D144
- E153
2.Two similar triangles have areas of 9 and 25 square units. A side of the smaller one is 6 units. How long is the matching side of the larger one?[4]
- A8
- B10
- C12
- D15
- E18
3.A cube 3 units on each side is built from unit cubes and painted all over the outside. How many of the small cubes have no paint on them at all?[4]
- A0
- B1
- C6
- D8
- E27
4.A photograph measures 8 cm by 12 cm. It is enlarged so that the shorter side becomes 20 cm, and the shape is not distorted. How long is the longer side of the enlargement?[4]
- A24 cm
- B30 cm
- C32 cm
- D4.8 cm
- E18 cm
5.A club has 8 members. In how many ways can a group of 3 be chosen to attend a conference, if the three places are all the same?[4]
- A56
- B336
- C24
- D112
- E28

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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.D — 144KA-0063Divisibility rules: 2, 3, 4, 5, 9, 10
- AI checked that it divides by 4 and stopped without testing the 9.
- BI checked the digit sum for 9 and stopped without testing the 4.
- CI saw an even number with a digit sum of 6 and treated 6 as good enough for 9.
- EI tested 9 with the digit sum and assumed any odd multiple of 9 also divides by 4.
2.B — 10KA-0087Scaling and similar figures
- AI added the difference between the areas' square roots to the side rather than multiplying by their ratio.
- CI doubled the side because the larger area is roughly double the smaller.
- DI used the ratio of the areas as if it were the ratio of the lengths, then adjusted.
- EI multiplied the side by the ratio of the areas divided by three, mixing up which ratio applies to lengths.
3.B — 1KA-0089Building and counting with unit cubes
- AI assumed every small cube touches the outside somewhere.
- CI counted the cubes at the centre of each face, which are painted on one side.
- DI counted the corner cubes, which are the most painted rather than the least.
- EI gave the total number of small cubes instead of the unpainted ones.
4.B — 30 cmKA-0155Scaling and similar figures
- AI kept the difference of 4 cm between the two sides instead of keeping their ratio.
- CI added 20 to 12 rather than scaling 12.
- DI used the scale factor upside down and multiplied 12 by 8/20 instead of 20/8.
- EI multiplied 12 by 1.5, the ratio between the original sides, instead of by the enlargement factor.
5.A — 56KA-0163Selections of a few objects
- BI counted ordered selections, so I counted the same three people once for every order they could stand in.
- CI multiplied the 8 members by the 3 places, which counts something quite different from a selection.
- DI divided the 336 ordered selections by 3 instead of by 3 factorial.
- EI chose 2 people rather than 3.

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