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1.Ana adds up the first seven odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13. Is her total odd or even, and what is it?[3]
Aodd, 47
Bodd, 49
Ceven, 48
Deven, 49
Eodd, 45
2.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
3.Eight people meet and everyone shakes hands with everyone else exactly once. How many handshakes take place?[3]
A16
B28
C36
D56
E64
4.One bus leaves every 12 minutes and another every 18 minutes. They leave together at 9:00. When do they next leave together?[3]
A9:06
B9:30
C9:36
D9:54
E12:36
5.A rectangle is divided by two vertical lines into three parts. How many rectangles of any size are in the picture?[3]
Text description of the figure
A wide rectangle divided by two vertical lines into three smaller rectangles side by side.
A3
B4
C6
D7
E9
6.Which of these fractions lies between one third and one half?[3]
A1/5
B1/4
C2/5
D3/5
E2/3
7.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
8.In a triangle, one angle measures 30 degrees. Of the other two angles, one is exactly twice the other. What is the largest angle in the triangle?[3]
A50 degrees
B75 degrees
C100 degrees
D150 degrees
E90 degrees
9.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
10.A sequence is defined by a(1) = 2 and a(n+1) = 2 a(n) - 1 for every n. What is a(6)?[3]
A33
B31
C64
D17
E63
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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.B — odd, 49KA-0002Parity of numbers (odd/even behavior)
AI decided that adding odd numbers always keeps the total odd, and made an arithmetic slip as well.
CI paired the numbers up and forgot that with seven numbers one is left over, so I expected an even total.
DI added correctly but then labelled 49 as even because I had already decided the pairs would make it even.
EI added only the first six numbers and stopped before including the thirteen.
2.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.
3.B — 28KA-0035Handshakes and pairs
AI doubled the number of people, as if each person made two handshakes in total.
CI let each person shake hands with all eight people including themselves before halving.
DI multiplied 8 by 7 and forgot that each handshake was counted from both sides.
EI multiplied 8 by 8, counting every ordered pair including a person with themselves.
4.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing
AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
BI added the two intervals together rather than looking for a time that is a multiple of both.
DI found a common multiple but not the least one, landing on a later coincidence.
EI multiplied the two intervals together instead of finding their least common multiple.
5.C — 6KA-0054Counting shapes hidden inside a figure
AI counted only the three small rectangles drawn as separate cells and stopped there.
BI counted the three small rectangles and the whole one, and forgot the two made of two cells.
DI counted a rectangle made of the left and right cells, even though they are not next to each other.
EI assumed any pair of the four vertical lines makes a rectangle without checking each one.
6.C — 2/5KA-0141Number lines and betweenness
AI compared the bottom numbers and assumed a bigger denominator means a bigger fraction.
BI saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.
DI checked that it is bigger than one third but never checked it against one half.
EI compared the top numbers only and ignored what the bottoms do to the size.
7.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.
8.C — 100 degreesKA-0152Angles on lines, in triangles, in polygons
AI found the smaller of the two unknown angles and stopped before doubling it.
BI split the remaining 150 degrees into two equal halves instead of a one-to-two split.
DI split the remainder evenly into 75 and 75, then doubled one of them.
EI assumed that the largest angle in a triangle like this must be a right angle.
9.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.
10.A — 33KA-0171Recursive rules
BI used the rule 2a(n) - 1 but started the sequence at 1 instead of 2.
CI doubled six times and ignored the minus one entirely.
DI stopped at a(5), one term early.
EI computed 2^6 - 1, applying the minus one only once at the very end.