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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 22 points

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.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
3.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
4.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
5.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 — 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.
3.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.
4.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.
5.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.

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