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.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
2.Each shape stands for a whole number. A triangle plus a triangle plus a triangle is 12, and a triangle plus a square is 9. What is the square?[3]
A3
B4
C5
D6
E8
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.One minute is left. Three questions have no answer written and you cannot do any of them. Nothing is taken off for a wrong answer. What should you do?[3]
ALeave them blank, because guessing is not really doing the maths
BWrite an answer for every one of them
CAnswer only the one you nearly understand
DLeave them blank so it is clear you ran out of time
EWrite your working instead of an answer
5.A coin is tossed three times. In how many of the possible outcomes are there exactly two heads?[4]
A2
B3
C4
D6
E8
6.A solid is built from unit cubes. The two pictures show it from above and from the front. What is the smallest number of cubes it could be made of?[4]
Text description of the figure
Two views side by side. The view from above is a solid 2 by 2 square of four cells. The view from the front is a solid 2 by 2 square, so the solid is two columns wide and reaches two cubes high.
A4
B5
C6
D7
E8
7.All the red boxes are heavy. Box X is not heavy. What must be true?[4]
ABox X is red
BBox X is not red
CBox X is blue
DSome red boxes are light
ENothing can be said about box X
8.Each row of a grid starts 3 more than the row above. Each cell is 1 more than the one to its left. The top-left cell is 1. What is in row 4, column 3?[4]
Text description of the figure
A grid four rows by four columns. The first row reads 1, 2, 3, 4 and the second row reads 4, 5, 6, 7. The remaining rows are blank, and the cell in row 4, column 3 is shaded.
A9
B10
C12
D13
E15
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.Squares of dots grow: 1 dot, then 4, then 9, then 16. How many dots are in the seventh square?[5]
A25
B36
C42
D49
E64
Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 1 · 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.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.
2.C — 5KA-0061Operation puzzles and cryptarithms
AI solved for the triangle and gave that instead of the square.
BI found the triangle is 4 and gave that number, without going on to the second equation.
DI halved the 12 instead of dividing it by the three triangles.
EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.
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.B — Write an answer for every one of themKA-0127Never leave a blank — there is no penalty
AI treated guessing as dishonest, but the rules of the paper explicitly allow it and cost nothing.
CI answered one and left two blanks that could each have scored, at no risk.
DI tried to communicate with the marker, but only the answers are scored.
EI offered working on a paper where only the chosen letter is marked.
5.B — 3KA-0068Tree diagrams
AI read the two in exactly two heads as the answer rather than as a condition to count.
CI counted the outcomes with two or more heads, so I included the three-head one as well.
DI counted the orderings of three different objects instead of listing the eight outcomes.
EI gave the total number of possible outcomes rather than the number with exactly two heads.
6.C — 6KA-0081Views of a solid: top, front, side
AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
DI added an extra cube that neither view requires.
EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.
7.B — Box X is not redKA-0099Reading a logical statement precisely
AI read the rule backwards, as if being heavy were what makes a box red.
CI assumed not red must mean one particular other colour, when the rule says nothing about which.
DI contradicted the rule I was given rather than applying it to box X.
EI decided one fact could not settle anything, without testing what would follow if X were red.
8.C — 12KA-0105Patterns in tables and grids
AI stopped at row 3, taking two steps down from the top instead of three.
BI found where row 4 starts but forgot to move across to the third column.
DI moved three columns across instead of two, counting columns rather than steps between them.
EI took four steps of 3 downwards instead of three, counting rows rather than the gaps between them.
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.D — 49KA-0138Growth patterns and figurate numbers
AI continued the pattern to the fifth square instead of the seventh.
BI stopped one square short, giving the sixth instead of the seventh.
CI added 6 to the sixth square's 36, treating the differences as constant.
EI continued one square too far and gave the eighth.