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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.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
3.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
4.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
5.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
6.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
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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.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.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.
3.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.
4.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.
5.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.
6.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.