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1.A net of six squares folds into a cube. One square is shaded. Which square ends up opposite the shaded one?[4]
Text description of the figure
A net of six squares in a cross shape: a vertical column of four squares labelled 1, 2, 3, 4 from the top, with square 5 attached to the left of square 2 and square 6 attached to the right of square 2. Square 1 is shaded.
Asquare 2
Bsquare 3
Csquare 4
Dsquare 5
Esquare 6
2.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
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.An isosceles triangle has an angle of 100 degrees. How big is each of the other two angles?[4]
A20
B40
C45
D80
E100
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.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
7.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
8.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
9.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
A30
B60
C90
D120
E240
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 8 · 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 — square 3KA-0005Nets and folding, 2D to 3D
AI picked the square directly next to the shaded one in the net, but neighbours in the net share an edge on the cube.
CI counted to the far end of the column, assuming the square furthest away in the net is the one opposite.
DI picked one of the side flaps because it is not touching the shaded square in the drawing.
EI picked the other side flap for the same reason, without tracking what happens as the net folds.
2.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.
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.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.
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.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.
7.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.
8.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.
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 — 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.