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1.The L-shaped figure is made of unit squares. What is its perimeter?[3]
Text description of the figure
An L-shaped figure made of unit squares: a vertical column 3 squares tall and 1 square wide, with 2 extra squares attached along the bottom to the right, so the shape covers 5 unit squares in total.
A5
B10
C12
D14
E16
2.Which of these arrangements of six squares cannot be folded into a closed cube?[3]
Text description of the figure
Four arrangements of six squares labelled A to D. A is a T shape, B is a straight line of six squares, C is a staircase of pairs, and D is a cross with a column of four and one square on each side.
Athe T shape
Bthe straight line of six
Cthe staircase
Dthe cross
Ethey all fold
3.Which of these is true of every rectangle?[3]
Aall four sides are the same length
Bthe diagonals cross at right angles
Cit has four lines of symmetry
Dthe angles add to 180 degrees
Ethe two diagonals are the same length
4.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
5.A floor measuring 6 by 4 units is covered exactly with tiles measuring 2 by 1, with no gaps and no overlaps. How many tiles are needed?[3]
A8
B10
C12
D24
E48
6.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
7.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
8.How many lines of symmetry does a regular hexagon have?[4]
A2
B3
C4
D6
E12
9.A square sheet is folded in half top to bottom, then in half left to right. One hole is punched through all the layers. How many holes are in the unfolded sheet?[5]
Text description of the figure
Three steps in a row: a square sheet, the same sheet folded in half top to bottom into a wide rectangle, and that rectangle folded in half left to right into a small square with a single punched hole near its centre.
A1
B2
C4
D6
E8
10.A square sheet is folded in half, then in half again. Two holes are punched through all the layers. How many holes are there when it is unfolded?[5]
A2
B4
C6
D8
E16
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 7 · 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.C — 12KA-0013Perimeter and area of rectilinear shapes
AI counted the unit squares that make up the shape, which is the area rather than the perimeter.
BI walked around the outline but skipped the two short steps at the inner corner.
DI added the perimeters of the two rectangles the shape is made of, counting the shared edge twice.
EI counted the edges of all five unit squares, which counts every internal edge as well.
2.B — the straight line of sixKA-0048Nets and folding, 2D to 3D
AI assumed any arrangement that is not a simple line must fail to fold.
CI thought a staircase would overlap when folded, without tracking a single face through the fold.
DI picked the cross because it looks unusual, even though it is the most familiar cube net there is.
EI checked that each arrangement had six squares and assumed six squares is enough.
3.E — the two diagonals are the same lengthKA-0079Properties of triangles and quadrilaterals
AI confused a rectangle with a square, which is only one special kind of rectangle.
BI remembered a fact about squares and rhombuses and applied it to every rectangle.
CI counted the two diagonals as lines of symmetry, which only works for a square.
DI used the angle sum of a triangle on a four-sided shape.
4.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.
5.C — 12KA-0086Tiling and tessellation
AI divided the floor area by 3 instead of by the tile area of 2.
BI laid tiles along the edges only and never filled the middle.
DI gave the area of the floor rather than the number of tiles that cover it.
EI multiplied the floor area by the tile area instead of dividing.
6.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.
7.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.
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.C — 4KA-0020Paper folding and hole punching
AI forgot that the punch goes through every layer at once, not just the top one.
BI undid only one of the two folds before counting the holes.
DI doubled for the first fold and then added two more rather than doubling a second time.
EI counted a fold that was never made, doubling three times instead of twice.
10.D — 8KA-0134Paper folding and hole punching
AI forgot that the punch goes through every layer, not just the top one.
BI undid only one of the two folds before counting.
CI doubled twice for the folds but added the second hole instead of doubling for it too.
EI counted three folds instead of two, doubling one time too many.