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1.A solid block is built from unit cubes and measures 4 by 3 by 2. How many unit cubes does it contain?[3]
Text description of the figure
A rectangular block built from unit cubes, 4 cubes long, 3 cubes deep and 2 cubes tall, drawn so that both layers are visible.
A9
B12
C18
D20
E24
2.A rectangle has a perimeter of 20 cm. One of its sides is 6 cm. What is its area in square centimetres?[3]
A14
B24
C40
D60
E96
3.In a triangle, one angle measures 30 degrees. Of the other two angles, one is exactly twice the other. What is the largest angle in the triangle?[3]
A50 degrees
B75 degrees
C100 degrees
D150 degrees
E90 degrees
4.What is the size of one interior angle of a regular twelve-sided polygon?[3]
A150 degrees
B30 degrees
C165 degrees
D1800 degrees
E144 degrees
5.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
6.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
7.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
8.How many lines of symmetry does a regular hexagon have?[4]
A2
B3
C4
D6
E12
9.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
A30
B60
C90
D120
E240
10.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
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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 — 24KA-0038Building and counting with unit cubes
AI added the three measurements together instead of multiplying them.
BI counted one layer of 4 by 3 and forgot that the block is two layers tall.
CI read the block as 3 by 3 by 2 because the drawing hid the far column.
DI counted only the cubes whose faces I could actually see in the picture.
2.B — 24KA-0083Perimeter and area of rectilinear shapes
AI subtracted 6 from 20 and gave that, which is neither a side nor an area.
CI took the other side to be 20 minus 6 divided by 2, forgetting there are two sides of each length.
DI multiplied the perimeter by half the known side instead of finding the missing side first.
EI used 16 as the other side, taking 20 minus 6 plus 2 rather than working from the perimeter properly.
3.C — 100 degreesKA-0152Angles on lines, in triangles, in polygons
AI found the smaller of the two unknown angles and stopped before doubling it.
BI split the remaining 150 degrees into two equal halves instead of a one-to-two split.
DI split the remainder evenly into 75 and 75, then doubled one of them.
EI assumed that the largest angle in a triangle like this must be a right angle.
4.A — 150 degreesKA-0170Angles on lines, in triangles, in polygons
BI found the exterior angle and answered with that instead of the interior one.
CI used 360 divided by 12 subtracted from 195, or otherwise slipped a step in the arithmetic.
DI gave the total of all twelve interior angles rather than one of them.
EI used a ten-sided polygon by mistake.
5.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.
6.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.
7.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.
8.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.
9.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.
10.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.