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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 3 by 3 board is drawn. How many 2 by 2 squares can be found on it, if they must line up with the grid?[3]
Text description of the figure
A square board divided into a 3 by 3 arrangement of nine equal small squares.
A1
B2
C4
D6
E9
2.Sam has only 2-cent and 5-cent coins. What is the largest amount under 15 cents that he cannot make exactly?[3]
A1 cent
B3 cents
C7 cents
D9 cents
E13 cents
3.What is the angle between the hands of a clock at exactly 3 o'clock?[3]
Text description of the figure
A clock face with the hour hand pointing at 3 and the minute hand pointing at 12, with the angle between them marked.
A30 degrees
B45 degrees
C90 degrees
D120 degrees
E180 degrees
4.Toma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?[3]
A10
B14
C16
D20
E24
5.How many different two-digit numbers can be written using only the digits 1, 2 and 3, if a digit may be used twice?[3]
A3
B6
C9
D12
E27
6.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
7.Three notebooks cost 240 cents each. You pay with a 10 euro note. How many cents change do you get? One euro is 100 cents.[3]
A240
B280
C520
D720
E760
8.Which capital letter, printed plainly, has both a horizontal and a vertical line of symmetry?[3]
AA
BB
CH
DT
EZ
9.Suppose it is true that some birds cannot fly. Which of these must also be true?[3]
ANo birds can fly
BAll birds can fly
CMost birds cannot fly
DExactly one bird cannot fly
ENot all birds can fly
10.A sequence begins 7, 11, 15, 19, and continues with the same constant step. What is the 30th term?[3]
A123
B127
C120
D119
E137
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 — 4KA-0001Counting by position (sliding window)
AI split the board into separate 2 by 2 blocks and only one whole block fitted, so I answered one.
BI slid the square across the top row and found two positions, then forgot it can also move down.
DI counted the four sliding positions and then added the two whole rows of the board as well.
EI counted the nine small squares on the board instead of the 2 by 2 squares.
2.B — 3 centsKA-0010Money and change
AI found the smallest amount that cannot be made rather than the largest one.
CI did not notice that 7 is 2 plus 5, so I marked it as impossible without testing it.
DI only tried using coins of one kind at a time and never mixed the two denominations.
EI assumed odd amounts are impossible because one of the coins is even.
3.C — 90 degreesKA-0032Clock geometry: hands, angles, times
AI gave the angle for one hour mark instead of the three hour marks between the hands.
BI divided the right angle in half, as if a quarter of the clock were 45 degrees.
DI used a third of the clock face rather than a quarter of it.
EI read 3 o'clock as the hands pointing in opposite directions.
4.C — 16KA-0050Working backwards
AI added the 4 and the 6 and stopped, forgetting to undo the halving.
BI doubled the 6 first and then added the 4, reversing the steps in the wrong order.
DI doubled the total at the end rather than doubling only the amount left after the first spend.
EI doubled twice because spending half felt like it needed undoing more than once.
5.C — 9KA-0072Systematic listing
AI counted only the numbers with two identical digits, like 11, 22 and 33.
BI required the two digits to be different, even though repeats are allowed.
DI allowed a fourth digit that was not in the list.
EI counted three-digit numbers instead of two-digit ones.
6.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.
7.B — 280KA-0114Money and change
AI subtracted the cost of one notebook rather than all three.
CI bought two notebooks instead of three.
DI gave the total cost of the notebooks instead of the change.
EI converted the 10 euro note to 1000 cents but subtracted the price of only one notebook after doubling it.
8.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.
9.E — Not all birds can flyKA-0146Reading a logical statement precisely
AI read some cannot as meaning none can, which is a far stronger claim.
BI chose a statement that directly contradicts the one I was given.
CI read some as meaning a majority, when it only guarantees at least one.
DI read some as meaning exactly one, when it means at least one.
10.A — 123KA-0160Arithmetic sequences and the nth term
BI multiplied the step by 30 instead of by 29, forgetting that the first term needs no steps.
CI used 4 times 30 and forgot to add the starting value.
DI added 28 steps instead of 29, counting the gaps one short.
EI treated the first term as the step and used 7 times 30 minus something close.