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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 rope is 3.5 metres long. A second rope is 240 centimetres long. How much longer is the first rope, in centimetres?[3]
A1.1
B11
C110
D236.5
E590
2.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
3.24 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
4.In a class of 30, 18 play football and 14 play chess. 6 play both. How many play neither?[4]
A2
B4
C8
D10
E26
5.A train covers 150 km at a steady 60 km per hour. How many minutes does the journey take?[4]
A25
B90
C150
D210
E9000
6.Everyone at a meeting shakes hands with everyone else exactly once. There are 66 handshakes in total. How many people are there?[4]
A11
B12
C22
D33
E66
7.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
8.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
9.Five beads of five different colours are threaded on a circular bracelet. Two bracelets count as the same if one can be turned or flipped into the other. How many different bracelets are there?[5]
A12
B20
C24
D60
E120
10.A jug holds 900 ml of juice. A third is poured out, then 150 ml is added. How many millilitres are in the jug?[5]
A450
B600
C750
D900
E1050
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 6 · 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 — 110KA-0029Unit conversion
AI subtracted correctly in metres but then gave the answer in metres when centimetres were asked for.
BI converted 3.5 metres to 35 centimetres instead of 350.
DI subtracted without converting at all, taking 3.5 away from 240.
EI added the two lengths instead of finding the difference between them.
2.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.
EI used a ten-sided polygon by mistake.
3.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.
4.B — 4KA-0069Inclusion–exclusion with two sets
AI added 18 and 14 without removing the overlap, then subtracted from 30.
CI subtracted the 6 who play both twice instead of once.
DI subtracted only the footballers from the class and forgot the chess players entirely.
EI found how many play at least one sport and gave that instead of how many play neither.
5.C — 150KA-0117Rate, time, distance
AI divided 150 by 60 and read the answer as minutes rather than hours.
BI used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.
DI converted 2.5 hours as two hours and fifty minutes.
EI multiplied the distance by 60 instead of dividing, then converted.
6.B — 12KA-0121Try small cases first
AI used the number of hands each person shakes rather than the number of people.
CI doubled the answer, forgetting that the halving has already been done.
DI halved 66 and treated that as the number of people.
EI gave the number of handshakes back as the number of people.
7.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.
8.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.
9.A — 12KA-0071Overcount, then correct
BI divided the 120 arrangements by 6 rather than by the 10 movements that leave a bracelet looking the same.
CI allowed for turning the bracelet but forgot it can also be flipped over.
DI halved the 120 for flipping but forgot that turning also gives the same bracelet.
EI counted every arrangement in a line, as if the bracelet had a fixed first bead.
10.C — 750KA-0137Multi-step arithmetic word problems
AI poured out half instead of a third and then forgot to add the 150 ml back.
BI poured out the third correctly but never added the 150 ml.
DI assumed the 150 ml added back was the same as the amount poured out, so nothing changed.
EI added the 150 ml to the full jug without pouring anything out first.