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1.Today is Tuesday. What day of the week will it be in 100 days?[3]
AMonday
BTuesday
CWednesday
DThursday
EFriday
2.In a triangle, one angle is 90 degrees and another is 35 degrees. What is the third angle?[3]
A35 degrees
B45 degrees
C55 degrees
D65 degrees
E145 degrees
3.A solid block is built from unit cubes and measures 4 by 3 by 2. How many unit cubes does it contain?[3]
Text description of the figure
A rectangular block built from unit cubes, 4 cubes long, 3 cubes deep and 2 cubes tall, drawn so that both layers are visible.
A9
B12
C18
D20
E24
4.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
5.Nadia gave half her stickers to her brother, then 6 more to a friend. She has 9 left. How many stickers did she start with?[4]
A15
B21
C24
D30
E36
6.A cube 3 units on each side is built from unit cubes and painted all over the outside. How many of the small cubes have no paint on them at all?[4]
A0
B1
C6
D8
E27
7.A rectangle has an area of 36 and sides that are whole numbers. Which of these could NOT be its perimeter?[4]
A24
B26
C28
D30
E40
8.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
9.The numbers 1 to 8 are on a board. A move rubs out two of them and writes their difference, larger minus smaller. After seven moves one number is left. Can it be 1?[5]
AYes, and there are many ways
BYes, but only one way
CNo, the last number is always even
DNo, the last number is always 0
EIt depends on the order of the moves
10.Can a 10 by 10 board be covered exactly by T-shaped tiles of four squares each, with no gaps and no overlaps?[5]
AYes, and it is straightforward
BYes, but the arrangement is fiddly
CNo, because 100 is not a multiple of 4
DNo, because the two colours cannot balance
EIt depends how the tiles are turned
Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 4 · 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.D — ThursdayKA-0021Remainders and modular cycles
AI found the remainder 2 but counted the two days starting from today rather than starting from tomorrow.
BI divided 100 by 7 and used the quotient of 14, treating the leftover days as if there were none.
CI remembered there was a remainder but used a remainder of 1 instead of working it out.
EI counted 100 divided by 7 as 14 remainder 3 instead of remainder 2.
2.C — 55 degreesKA-0022Angles on lines, in triangles, in polygons
AI assumed the triangle was isosceles because it had a right angle, so I repeated the 35.
BI assumed a right-angled triangle always has two 45 degree angles.
DI subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.
EI subtracted only the 35 from 180 and forgot to take off the right angle as well.
3.E — 24KA-0038Building and counting with unit cubes
AI added the three measurements together instead of multiplying them.
BI counted one layer of 4 by 3 and forgot that the block is two layers tall.
CI read the block as 3 by 3 by 2 because the drawing hid the far column.
DI counted only the cubes whose faces I could actually see in the picture.
4.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.
5.D — 30KA-0007Working backwards
AI added the 6 and the 9 and stopped, forgetting to undo the halving at the start.
BI undid the steps in the order they were written instead of reversing the order as well as the operations.
CI doubled the 9 first and then added the 6, which reverses the steps in the wrong order.
EI doubled twice because giving half away felt like it should be undone more than once.
6.B — 1KA-0089Building and counting with unit cubes
AI assumed every small cube touches the outside somewhere.
CI counted the cubes at the centre of each face, which are painted on one side.
DI counted the corner cubes, which are the most painted rather than the least.
EI gave the total number of small cubes instead of the unpainted ones.
7.C — 28KA-0123Eliminate impossible choices by bounding
AI ruled out the square 6 by 6, forgetting that a square is a rectangle.
BI did not think to try 4 by 9, so I judged this perimeter impossible.
DI missed the 3 by 12 rectangle when listing the factor pairs.
EI stopped listing factor pairs before reaching 2 by 18.
8.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.
9.C — No, the last number is always evenKA-0098Invariants and monovariants
AI found sequences ending in small numbers and assumed 1 was among the reachable ones.
BI assumed a hard-looking question must have exactly one answer.
DI found one sequence ending in 0 and assumed every sequence must end there.
EI thought the order could change the outcome, when the quantity that decides it never changes.
10.D — No, because the two colours cannot balanceKA-0101Coloring arguments
AI checked that 100 divides by 4 and treated that as proof that a covering exists.
BI assumed a covering must exist somewhere and that I simply had not found it yet.
CI gave a reason that is not even true, since 100 really is a multiple of 4.
EI thought orientation could rescue it, but every turn of a T covers the same mixture of colours.