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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.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 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
6.How many lines of symmetry does a regular hexagon have?[4]
A2
B3
C4
D6
E12
7.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
8.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
9.Two circles touch on the outside. One has a radius of 3 cm and the other a radius of 5 cm. How many centimetres apart are their centres?[4]
A2
B4
C8
D15
E16
10.Two triangles are similar. The sides of the smaller are 3/5 as long as the matching sides of the larger. The smaller triangle has area 18 square cm. What is the area of the larger triangle?[4]
A30 sq cm
B50 sq cm
C45 sq cm
D10.8 sq cm
E90 sq cm
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 4 · 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.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.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.
6.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.
7.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.
8.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.
9.C — 8KA-0147Circles: radius, diameter, and touching circles
AI subtracted the radii, which is the answer when one circle sits inside the other.
BI averaged the two radii instead of adding them.
DI multiplied the radii together rather than adding them.
EI added the two diameters instead of the two radii.
10.B — 50 sq cmKA-0164Scaling and similar figures
AI scaled the area by 5/3, using the side ratio directly instead of its square.
CI multiplied the area by 2.5, halfway between the side ratio and its square.
DI scaled by 3/5 instead of 5/3, making the larger triangle smaller.
EI multiplied by 5 and ignored the 3 in the ratio entirely.