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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 20 points

1.On a standard die opposite faces add to 7. Two dice are stacked. The touching faces show 3 on the upper die and 5 on the lower. What number is on the bottom face?[4]
- A1
- B2
- C3
- D4
- E5
2.A flag shape is rotated a quarter turn clockwise about its bottom-left corner. Which of the descriptions matches the result?[4]
Text description of the figure
A flag shape drawn as an upright pole with a small triangle attached to the top right of the pole, standing on a marked corner point at the bottom of the pole.
- Athe pole points right and the triangle is below it
- Bthe pole points right and the triangle is above it
- Cthe pole points left and the triangle is above it
- Dthe pole points down and the triangle is to the left
- Ethe pole points up and the triangle is on the left
3.A photograph is enlarged so that each side becomes 3 times as long. How many times bigger is its area?[4]
- A3 times
- B6 times
- C9 times
- D12 times
- E27 times
4.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
- A30
- B60
- C90
- D120
- E240
5.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

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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.B — 2KA-0016Dice and cube face relationships
- AI used the upper die's touching face instead of the lower one, so I worked from 3 rather than 5.
- CI gave the number on a touching face itself rather than the number opposite it.
- DI subtracted 3 from 7 because I confused which die was sitting on which.
- EI gave the lower die's upward face, which is the number I was told, not the hidden one underneath.
2.A — the pole points right and the triangle is below itKA-0039Reflections, rotations, translations
- BI turned the pole the right way but kept the triangle on the side it started on.
- CI turned the shape anticlockwise instead of clockwise.
- DI turned the shape half a turn instead of a quarter turn.
- EI reflected the shape in a vertical line instead of rotating it.
3.C — 9 timesKA-0042Scaling and similar figures
- AI applied the length scale factor straight to the area.
- BI doubled the scale factor because area involves two dimensions, instead of squaring it.
- DI multiplied the scale factor by four, as though area scaled with the number of sides.
- EI cubed the scale factor, which is the rule for volume rather than area.
4.D — 120KA-0148Clock geometry: hands, angles, times
- AI gave the angle for a single hour mark rather than the four marks between the hands.
- BI counted two hour marks instead of four.
- CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
- EI measured the angle the long way round the clock face instead of the smaller one.
5.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.

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