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Worksheet generator
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1.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
2.Which capital letter, printed plainly, has both a horizontal and a vertical line of symmetry?[3]
AA
BB
CH
DT
EZ
3.A photograph is enlarged so that each side becomes 3 times as long. How many times bigger is its area?[4]
A3 times
B6 times
C9 times
D12 times
E27 times
4.An isosceles triangle has an angle of 100 degrees. How big is each of the other two angles?[4]
A20
B40
C45
D80
E100
5.A solid is built from unit cubes. The two pictures show it from above and from the front. What is the smallest number of cubes it could be made of?[4]
Text description of the figure
Two views side by side. The view from above is a solid 2 by 2 square of four cells. The view from the front is a solid 2 by 2 square, so the solid is two columns wide and reaches two cubes high.
A4
B5
C6
D7
E8
6.How many lines of symmetry does a regular hexagon have?[4]
A2
B3
C4
D6
E12
7.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
A30
B60
C90
D120
E240
8.Two triangles are similar. The sides of the smaller are 3/5 as long as the matching sides of the larger. The smaller triangle has area 18 square cm. What is the area of the larger triangle?[4]
A30 sq cm
B50 sq cm
C45 sq cm
D10.8 sq cm
E90 sq cm
9.A room is 8 m long, 4 m wide and 2 m high. An ant walks across the floor and the walls from one bottom corner to the far top corner. What is the shortest distance in metres?[5]
Text description of the figure
The floor of a room, 8 metres by 4 metres, drawn flat, with one 8-metre-by-2-metre wall unfolded upwards from its far edge. A straight line joins the ant's starting corner on the floor to the opposite corner on the unfolded wall.
A9.2
B10
C11
D12
E14
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.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.
2.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.
3.C — 9 timesKA-0042Scaling and similar figures
AI applied the length scale factor straight to the area.
BI doubled the scale factor because area involves two dimensions, instead of squaring it.
DI multiplied the scale factor by four, as though area scaled with the number of sides.
EI cubed the scale factor, which is the rule for volume rather than area.
4.B — 40KA-0080Properties of triangles and quadrilaterals
AI subtracted 100 from 180 and then divided by four instead of by two.
CI assumed the two equal angles are always 45 degrees.
DI gave what is left after taking 100 from 180 without splitting it between the two angles.
EI made the 100 one of the equal pair, which would already exceed 180 degrees on its own.
5.C — 6KA-0081Views of a solid: top, front, side
AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
DI added an extra cube that neither view requires.
EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.
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.D — 120KA-0148Clock geometry: hands, angles, times
AI gave the angle for a single hour mark rather than the four marks between the hands.
BI counted two hour marks instead of four.
CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
EI measured the angle the long way round the clock face instead of the smaller one.
8.B — 50 sq cmKA-0164Scaling and similar figures
AI scaled the area by 5/3, using the side ratio directly instead of its square.
CI multiplied the area by 2.5, halfway between the side ratio and its square.
DI scaled by 3/5 instead of 5/3, making the larger triangle smaller.
EI multiplied by 5 and ignored the 3 in the ratio entirely.
9.B — 10KA-0082Shortest paths on and around shapes
AI measured the straight line through the middle of the room, but the ant has to stay on the surfaces.
CI unfolded the room but folded out the short wall rather than the one that makes the shortest route.
DI chose an unfolding that gives a longer straight line and did not compare it with the others.
EI walked along the edges of the room, 8 then 4 then 2, instead of cutting straight across the surfaces.
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.