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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.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
2.A bag holds 5 black and 6 white stones. You repeatedly remove two stones: if they match you put a black one in, if they differ you put a white one in. What colour is the last stone?[5]
Ablack
Bwhite
Cit depends on the order of the moves
Dthe bag never gets down to one stone
Ewhite if the first two stones match
3.A number is 4 more than a third of itself. Which of the choices is that number?[5]
A3
B6
C8
D12
E18
4.Five children sit in a row. Two of them are twins who insist on sitting next to each other. In how many orders can the five sit?[5]
A12
B24
C48
D60
E120
5.A box holds 4 red, 5 blue and 6 green balls, mixed up. How many must be taken out without looking to be sure of having 3 of the same colour?[5]
A3
B6
C7
D9
E13
6.One hundred apples are packed into twelve boxes. What is the largest number n for which you can always be sure that some box holds at least n apples?[5]
A8
B9
C10
D12
E100
7.The numbers 1 to 10 stand in a row. A move swaps two neighbours. After exactly 45 moves, can the row be back in its starting order?[5]
AYes, always
BYes, if the swaps are chosen well
CNo, because 45 is not a multiple of 10
DNo, because the number of moves is odd
EIt depends which numbers are swapped
8.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
9.What is the value of (1 - 1/2) x (1 - 1/3) x (1 - 1/4) x ... x (1 - 1/10)?[5]
A1/10
B1/9
C1/2
D9/10
E1
10.You reach the ten 5-point questions with 18 minutes left. What is the best plan?[5]
AStart at the first and work through in order until time runs out
BRead all ten quickly, pick the two or three that look most doable, and fill in every answer before the end
CSpend the whole time on the last question, since it is the hardest
DAnswer the ones with the shortest statements
EDivide the time evenly, about 1.8 minutes each
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.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.
2.A — blackKA-0043Invariants and monovariants
BI noticed there are more white stones than black ones and guessed the majority colour would survive.
CI tried a few orders, saw different-looking positions along the way, and assumed the ending must vary too.
DI did not notice that every move takes two stones out and puts one back, so the count falls by exactly one each time.
EI assumed the first move settles the outcome instead of looking for a quantity that no move can change.
3.B — 6KA-0045Back-solve from the answer choices
AI tested the smallest choice first and stopped at the first one that felt about right.
CI read a third of itself as three times itself and solved the wrong equation.
DI reversed the comparison, finding a number whose third is 4 less than itself in the wrong direction.
EI picked the largest choice because dividing by three made me expect a big starting number.
4.C — 48KA-0070Counting with restrictions
AI treated the twins as one child and forgot they can also swap places with each other.
BI glued the twins together into a single block but then forgot that the block can be arranged with the others in more ways than I counted.
DI halved the 120 total, assuming the twins are together in exactly half the arrangements.
EI counted every arrangement of five children and forgot the twins' condition entirely.
5.C — 7KA-0077The pigeonhole principle
AI answered with the luckiest case, where the first three balls happen to match.
BI found the worst case of two of each colour and forgot to take one more.
DI multiplied the three colours by the three balls I need, rather than thinking about the worst case.
EI worked from the number of balls of each colour rather than from the number of colours.
6.B — 9KA-0095The extremal principle
AI divided 100 by 12 and rounded down instead of up.
CI rounded the division to a convenient number without checking that a packing with a smaller maximum exists.
DI gave the number of boxes as the answer rather than a number of apples.
EI described the case where one box holds everything, which is possible but not guaranteed.
7.D — No, because the number of moves is oddKA-0097Parity arguments
AI assumed enough moves can undo anything, without asking what each move preserves.
BI tried a few sequences that nearly worked and assumed a better choice would finish the job.
CI reached for the number of items rather than for what a single swap actually changes.
EI thought the choice of swaps could change the outcome, when every swap has the same effect.
8.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.
9.A — 1/10KA-0125Spot the trick vs. decide to grind
BI cancelled the chain but stopped one factor early, leaving a 9 on the bottom.
CI worked out the first bracket and assumed the rest made no difference.
DI gave the last bracket on its own instead of the whole product.
EI assumed everything cancels completely, leaving nothing behind.
10.B — Read all ten quickly, pick the two or three that look most doable, and fill in every answer before the endKA-0130Managing the 5-point block
AI worked in order, so a hard early question could eat the time meant for easier later ones.
CI assumed the hardest question is worth the most, but every question in this block scores the same.
DI used length as a proxy for difficulty, which is not reliable in this block.
EI spread the time equally, which is too little for the questions I could do and wasted on the ones I could not.