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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 19 points

1.A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?[3]
- A(1, 3)
- B(1, 7)
- C(5, 3)
- D(7, 7)
- E(7, 3)
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.An isosceles triangle has an angle of 100 degrees. How big is each of the other two angles?[4]
- A20
- B40
- C45
- D80
- E100
4.A solid is built from unit cubes. The two pictures show it from above and from the front. What is the smallest number of cubes it could be made of?[4]
Text description of the figure
Two views side by side. The view from above is a solid 2 by 2 square of four cells. The view from the front is a solid 2 by 2 square, so the solid is two columns wide and reaches two cubes high.
- A4
- B5
- C6
- D7
- E8
5.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

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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.E — (7, 3)KA-0145Grid coordinates and lattice reasoning
- AI moved left instead of right, subtracting the 4 rather than adding it.
- BI moved left and up, reversing both directions.
- CI swapped the two coordinates round before moving.
- DI moved up instead of down, adding the 2 rather than subtracting it.
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.B — 40KA-0080Properties of triangles and quadrilaterals
- AI subtracted 100 from 180 and then divided by four instead of by two.
- CI assumed the two equal angles are always 45 degrees.
- DI gave what is left after taking 100 from 180 without splitting it between the two angles.
- EI made the 100 one of the equal pair, which would already exceed 180 degrees on its own.
4.C — 6KA-0081Views of a solid: top, front, side
- AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
- BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
- DI added an extra cube that neither view requires.
- EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.
5.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.

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