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1.The L-shaped figure is made of unit squares. What is its perimeter?[3]
Text description of the figure
An L-shaped figure made of unit squares: a vertical column 3 squares tall and 1 square wide, with 2 extra squares attached along the bottom to the right, so the shape covers 5 unit squares in total.
A5
B10
C12
D14
E16
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.Bo has 24 marbles and gives a third of them to Ana. How many more marbles does Bo have than Ana now?[3]
A4
B8
C16
D24
E32
4.A sequence starts 1, 1, and every term after that is the sum of the two before it. What is the eighth term?[4]
A13
B21
C29
D34
E64
5.A train covers 150 km at a steady 60 km per hour. How many minutes does the journey take?[4]
A25
B90
C150
D210
E9000
6.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
A30
B60
C90
D120
E240
7.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
8.A drawer holds 12 red socks, 10 blue socks and 8 green socks, all mixed up. You take socks out one at a time in the dark. What is the smallest number of socks you must take to be certain of having three of the same colour?[5]
A4
B7
C9
D13
E3
9.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
10.The numbers 1 to 10 are written on a board. You repeatedly rub out any two of them and write down their positive difference instead, until a single number is left. What can be said about that final number?[5]
AIt is always odd
BIt is always even
CIt can be either odd or even
DIt is always zero
EIt is always 1
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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 — 12KA-0013Perimeter and area of rectilinear shapes
AI counted the unit squares that make up the shape, which is the area rather than the perimeter.
BI walked around the outline but skipped the two short steps at the inner corner.
DI added the perimeters of the two rectangles the shape is made of, counting the shared edge twice.
EI counted the edges of all five unit squares, which counts every internal edge as well.
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.B — 8KA-0119Find what is actually being asked
AI halved the difference, as if the question asked how many Bo should hand over to make them equal.
CI gave how many Bo has now rather than how many more he has than Ana.
DI gave the number Bo started with, without doing anything.
EI added the two amounts together instead of comparing them.
4.B — 21KA-0104Recursive rules
AI counted the two starting terms as one, so I stopped at the seventh term.
CI added the two before it but slipped once in the middle of the chain.
DI generated one term too many and gave the ninth.
EI doubled each term instead of adding the two before it.
5.C — 150KA-0117Rate, time, distance
AI divided 150 by 60 and read the answer as minutes rather than hours.
BI used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.
DI converted 2.5 hours as two hours and fifty minutes.
EI multiplied the distance by 60 instead of dividing, then converted.
6.D — 120KA-0148Clock geometry: hands, angles, times
AI gave the angle for a single hour mark rather than the four marks between the hands.
BI counted two hour marks instead of four.
CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
EI measured the angle the long way round the clock face instead of the smaller one.
7.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.
8.B — 7KA-0157The pigeonhole principle
AI thought that one more than the number of colours must give three of a kind, which only guarantees a PAIR.
CI got to two of each colour, then added one more for each colour instead of one more in total.
DI assumed the worst case meant emptying the largest pile of 12 reds first.
EI answered with the number of socks I want rather than the number I must take to be sure of them.
9.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.
10.A — It is always oddKA-0167Parity arguments
BI checked the parity of the count of numbers rather than of their sum.
CI tried two examples, got different answers, and concluded nothing is forced.
DI assumed differences must shrink all the way to nothing.
EI found one sequence of moves ending at 1 and assumed every sequence must.