Tap a speaker to listen. Then try saying it yourself! Tap it again to stop.
Loading…
Worksheet generator
Pick what you want, print the page. The answer key comes with it, on its own sheet, and it tells you the mistake behind every wrong choice — not just which letter is right.
This exact URL always produces this exact sheet — bookmark it and the answer key will still match next term. Print with your browser; the controls and the site navigation are left off the page.
1.Four road signs are shown. Exactly one of them has two lines of symmetry. Which one is it?[3]
Text description of the figure
Four outlined shapes side by side, labelled A to D: a plain rectangle, an isosceles triangle, a five-pointed star, and an arrow pointing right.
Athe rectangle
Bthe isosceles triangle
Cthe star
Dthe arrow
Enone of them
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 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
5.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
6.How many lines of symmetry does a regular hexagon have?[4]
A2
B3
C4
D6
E12
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.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
9.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
10.On a die, opposite faces add to 7. A die rests on a table with 3 on top. What do the four side faces add up to?[5]
A10
B12
C14
D17
E18
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.A — the rectangleKA-0004Line and rotational symmetry
BI found the vertical fold that works and assumed a second one must work as well without testing it.
CI saw that the star looks very symmetric and picked it without counting how many lines of symmetry it actually has.
DI counted the horizontal fold and then counted the vertical one too, even though the two halves do not match.
EI only tested vertical folds on every shape and concluded that no shape had two lines.
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.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.
5.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.
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 — 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 — 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.
9.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.
10.C — 14KA-0139Dice and cube face relationships
AI subtracted only the top face from 21, forgetting the hidden bottom face as well.
BI guessed four middling numbers and added them without using the total of all six faces.
DI subtracted only the bottom face of 4 from the total of 21.
EI added the four largest numbers on the die rather than the four that are actually at the sides.