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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.In a triangle, one angle is 90 degrees and another is 35 degrees. What is the third angle?[3]
A35 degrees
B45 degrees
C55 degrees
D65 degrees
E145 degrees
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
7.Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
A65
B75
C85
D95
E105
8.A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?[3]
A(1, 3)
B(1, 7)
C(5, 3)
D(7, 7)
E(7, 3)
9.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
10.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
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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.C — 55 degreesKA-0022Angles on lines, in triangles, in polygons
AI assumed the triangle was isosceles because it had a right angle, so I repeated the 35.
BI assumed a right-angled triangle always has two 45 degree angles.
DI subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.
EI subtracted only the 35 from 180 and forgot to take off the right angle as well.
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.
7.B — 75KA-0088Angles on lines, in triangles, in polygons
AI added the three angles wrongly, getting 295 instead of 285.
CI used an angle sum of 370, mis-remembering the total for a quadrilateral.
DI repeated one of the given angles instead of computing the missing one.
EI used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.
8.E — (7, 3)KA-0145Grid coordinates and lattice reasoning
AI moved left instead of right, subtracting the 4 rather than adding it.
BI moved left and up, reversing both directions.
CI swapped the two coordinates round before moving.
DI moved up instead of down, adding the 2 rather than subtracting it.
9.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.
10.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.