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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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2.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
3.A pattern of tiles repeats: black, black, white. What colour is the 100th tile?[3]
Ablack
Bwhite
Cit depends where you start counting
Dgrey, because the pattern breaks
Ethere is no 100th tile
4.Which of these fractions lies between one third and one half?[3]
A1/5
B1/4
C2/5
D3/5
E2/3
5.One tap fills a tank in 6 hours and another fills it in 3 hours. With both running, how long does the tank take to fill?[4]
A1 hour
B2 hours
C4.5 hours
D9 hours
E3 hours
6.How many 2 by 2 squares fit on a 4 by 4 board, if they must line up with the grid?[4]
A4
B6
C8
D9
E16
7.Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?[4]
A40 percent
B37.5 percent
C75 percent
D35 percent
E30 percent
8.A drawer holds 10 red socks, 10 blue socks and 10 green socks, all mixed up in the dark. How many socks must you take out to be sure of having a matching pair?[5]
A2
B3
C4
D11
E31
9.A square sheet is folded in half, then in half again. Two holes are punched through all the layers. How many holes are there when it is unfolded?[5]
A2
B4
C6
D8
E16
10.Six friends sit around a circular table. Two seatings count as the same if one can be turned into the other by rotating the table. How many genuinely different seatings are there?[5]
A120
B720
C36
D60
E24
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 5 · 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 — 210KA-0057Clever regrouping (pair to round numbers)
AI paired the numbers from the outside in but left the 20 out of every pair, so I added only up to 19.
BI estimated the total as a round number instead of working it out.
DI used eleven pairs of 20 instead of ten pairs of 21.
EI multiplied 20 by 21 and forgot that pairing counts every number twice.
2.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.
3.A — blackKA-0108Repeating cycles and position mod n
BI got a remainder of 1 but read the last colour of the repeat rather than the first.
CI thought the pattern had no fixed first tile, even though tile one is given.
DI assumed a repeating pattern must eventually change.
EI assumed the pattern runs only for as many tiles as one repeat contains.
4.C — 2/5KA-0141Number lines and betweenness
AI compared the bottom numbers and assumed a bigger denominator means a bigger fraction.
BI saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.
DI checked that it is bigger than one third but never checked it against one half.
EI compared the top numbers only and ignored what the bottoms do to the size.
5.B — 2 hoursKA-0044Combined work rates
AI subtracted the two times from each other rather than adding the rates.
CI averaged the two times, which would only be right if the taps took turns instead of running together.
DI added the two times together, which makes the tank slower with two taps than with one.
EI used the faster tap's time alone and ignored the contribution of the slower one.
6.D — 9KA-0046Counting by position (sliding window)
AI cut the board into four separate 2 by 2 blocks instead of sliding the square one step at a time.
BI counted the three sliding positions along the top and doubled them for two rows.
CI counted the positions along the top row and down the left column and added them.
EI counted the sixteen small squares on the board rather than the 2 by 2 squares.
7.A — 40 percentKA-0165Mixtures and weighted averages
BI averaged 25 and 50 without weighting by how much of each solution there was.
CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
EI used only the acid from the weaker solution and spread it over all ten litres.
8.C — 4KA-0040The pigeonhole principle
AI answered with the lucky case, where the first two socks happen to match.
BI used the number of colours as my answer without adding one for the sock that must repeat.
DI worked from the number of socks of each colour instead of the number of colours.
EI took the whole drawer, guaranteeing a pair but far more socks than are needed.
9.D — 8KA-0134Paper folding and hole punching
AI forgot that the punch goes through every layer, not just the top one.
BI undid only one of the two folds before counting.
CI doubled twice for the folds but added the second hole instead of doubling for it too.
EI counted three folds instead of two, doubling one time too many.
10.A — 120KA-0166Counting up to symmetry
BI counted every arrangement in a row, so each circular seating got counted once for every rotation.
CI divided 720 by 20 or some other number instead of by the 6 rotations.
DI divided by 12, treating reflections as identical too, though the question only allows rotations.
EI fixed two people rather than one, dividing by an extra factor.