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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.
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1.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)
2.24 pencils and 36 erasers are shared into identical gift bags, using every item. What is the largest number of bags possible?[4]
A4
B6
C12
D18
E72
3.One pipe fills a pool in 12 hours and another fills it in 4 hours. With both running, how many hours does the pool take to fill?[4]
A3
B4
C6
D8
E16
4.A rectangle measures 30 cm by 0.4 m. What is its area in square centimetres?[4]
A0.12
B12
C120
D1200
E12000
5.Four beads - one red, one green, one blue, one yellow - are threaded on a circular bracelet. Two bracelets are the same if one can be rotated into the other. How many different bracelets are there?[5]
A3
B4
C6
D12
E24
6.Seven cups all stand upside down. In one move you must turn over exactly two cups. Can all seven ever stand the right way up?[5]
AYes, in 4 moves
BYes, in 7 moves
CYes, but it takes many moves
DIt depends which two cups you pick
ENo, it is impossible
7.On the street grid shown you may only walk right or down. One junction is closed. How many routes go from the top-left corner to the bottom-right corner?[5]
Text description of the figure
A grid of streets with junctions arranged 4 across and 4 down. The junction one step right and one step down from the top-left corner is marked closed with a cross.
A8
B10
C12
D18
E20
8.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
9.Can a 10 by 10 board be covered exactly by T-shaped tiles of four squares each, with no gaps and no overlaps?[5]
AYes, and it is straightforward
BYes, but the arrangement is fiddly
CNo, because 100 is not a multiple of 4
DNo, because the two colours cannot balance
EIt depends how the tiles are turned
10.A machine turns 3 into 7, 5 into 11 and 8 into 17. What does it turn 12 into?[5]
A19
B21
C24
D25
E29
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 9 · 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.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.
2.C — 12KA-0062Factors, multiples, LCM and GCD by listing
AI found a number that divides both but not the largest one, stopping at the first that worked.
BI used the difference between 36 and 24 divided by 2 rather than a common factor.
DI used a factor of 36 without checking that it also divides 24.
EI found the least common multiple instead of the greatest common divisor.
3.A — 3KA-0116Combined work rates
BI gave the faster pipe's time on its own, forgetting the slower one helps as well.
CI halved the slower pipe's time rather than adding the two rates.
DI averaged the two times, which would only be right if the pipes took turns.
EI added the two times, which makes two pipes slower than one - an impossible answer.
4.D — 1200KA-0128Check units and re-read before bubbling
AI worked entirely in metres and gave the answer in square metres.
BI multiplied 30 by 0.4 without converting the metres to centimetres at all.
CI converted 0.4 m to 4 cm rather than 40 cm.
EI converted 0.4 m to 400 cm, moving the decimal point one place too far.
5.C — 6KA-0025Counting up to symmetry
AI also treated bracelets that are mirror images as the same, but only rotations were allowed.
BI divided the number of beads by itself rather than dividing the number of arrangements by the number of rotations.
DI divided the 24 arrangements by 2 instead of by the 4 rotations of a circle of four beads.
EI counted every arrangement in a line and forgot that rotating a bracelet gives the same bracelet.
6.E — No, it is impossibleKA-0028Parity arguments
AI found a sequence that turned over most of the cups and assumed the last one could be fixed somehow.
BI matched the number of moves to the number of cups without checking whether the target is reachable at all.
CI assumed that with enough moves any arrangement can be reached.
DI thought the choice of which cups to flip could change whether the target is reachable.
7.A — 8KA-0031Counting paths on a grid
BI assumed closing one junction removes about half the routes and halved the total of 20.
CI counted the routes that pass through the closed junction and gave that instead of the ones that avoid it.
DI subtracted only the 2 routes that reach the closed junction, not all the routes that continue through it.
EI counted every route on the open grid and forgot to remove the ones through the closed junction.
8.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.
9.D — No, because the two colours cannot balanceKA-0101Coloring arguments
AI checked that 100 divides by 4 and treated that as proof that a covering exists.
BI assumed a covering must exist somewhere and that I simply had not found it yet.
CI gave a reason that is not even true, since 100 really is a multiple of 4.
EI thought orientation could rescue it, but every turn of a T covers the same mixture of colours.
10.D — 25KA-0106Inferring a rule from examples
AI used the rule add 4, which fits the first example but not the others.
BI found a rule from two examples only and never tested it against the third.
CI doubled the input and forgot the extra one that every example needs.
EI used double and add five, which fits none of the examples exactly.