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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 21 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 square of side 6 cm is cut along a midline into two identical rectangles. What is the perimeter of one of them?[4]
- A12
- B15
- C18
- D24
- E36
3.How many lines of symmetry does a regular hexagon have?[4]
- A2
- B3
- C4
- D6
- E12
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 circle of radius 5 is drawn inside a square of side 10, touching all four sides. What fraction of the square is outside the circle, to the nearest tenth?[5]
Text description of the figure
A square with a circle drawn inside it, the circle touching the midpoint of each of the four sides. The region inside the square but outside the circle is shaded.
- A0.1
- B0.2
- C0.3
- D0.5
- E0.8

Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 3 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.

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.C — 18KA-0084Area by dissection and rearrangement
- AI added the two different side lengths without doubling for the opposite pair.
- BI halved the square's perimeter of 24 and adjusted by three, treating the cut as if it removed length.
- DI gave the perimeter of the whole square instead of one of the pieces.
- EI gave the area of the square rather than the perimeter of a piece.
3.D — 6KA-0085Line and rotational symmetry
- AI checked only the vertical and horizontal folds and stopped there.
- BI counted the lines through opposite corners and forgot the ones through opposite edges.
- CI assumed a hexagon behaves like a rectangle with a couple of extra folds.
- EI counted each line twice, once from each end.
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 — 0.2KA-0052Area by subtraction (shaded regions)
- AI estimated by eye from the four corner pieces without comparing them to the whole square.
- CI used a diameter of 5 instead of a radius of 5 when working out the circle's area.
- DI assumed the circle covers half the square because it touches all four sides.
- EI found the fraction covered by the circle and gave that instead of the fraction outside it.

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