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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.What is the angle between the hands of a clock at exactly 3 o'clock?[3]
Text description of the figure
A clock face with the hour hand pointing at 3 and the minute hand pointing at 12, with the angle between them marked.
A30 degrees
B45 degrees
C90 degrees
D120 degrees
E180 degrees
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
7.Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
A65
B75
C85
D95
E105
8.Which capital letter, printed plainly, has both a horizontal and a vertical line of symmetry?[3]
AA
BB
CH
DT
EZ
9.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)
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
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 4 · 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.C — 90 degreesKA-0032Clock geometry: hands, angles, times
AI gave the angle for one hour mark instead of the three hour marks between the hands.
BI divided the right angle in half, as if a quarter of the clock were 45 degrees.
DI used a third of the clock face rather than a quarter of it.
EI read 3 o'clock as the hands pointing in opposite directions.
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.
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.C — HKA-0142Line and rotational symmetry
AI found the vertical fold and assumed a horizontal one must work too.
BI found the horizontal fold and stopped without testing the vertical one.
DI counted the vertical fold twice rather than testing a horizontal one.
EI mistook turning the letter upside down for folding it, which is rotation rather than symmetry about a line.
9.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.
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.