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1.Two similar triangles have areas of 9 and 25 square units. A side of the smaller one is 6 units. How long is the matching side of the larger one?[4]
A8
B10
C12
D15
E18
2.A sequence starts at 3. Each term after that is double the one before it, minus 1. What is the sixth term?[4]
A17
B33
C65
D96
E129
3.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
4.There are 5 boxes with 12 pencils in each. 17 pencils are given away and the rest are shared equally between 2 children. How many does each child get?[4]
A21
B21.5
C26
D43
E60
5.Everyone at a meeting shakes hands with everyone else exactly once. There are 66 handshakes in total. How many people are there?[4]
A11
B12
C22
D33
E66
6.Which of these numbers has exactly 6 different whole-number factors, counting 1 and the number itself?[4]
A12
B15
C16
D25
E27
7.Ana has exactly 5 coins, each worth either 2 cents or 5 cents. Which of these could NOT be her total?[4]
A13
B16
C19
D21
E25
8.What is the units digit of 3 multiplied by itself 100 times, that is 3 to the power 100?[4]
A1
B3
C7
D9
Eit cannot be found without a calculator
9.A photograph measures 8 cm by 12 cm. It is enlarged so that the shorter side becomes 20 cm, and the shape is not distorted. How long is the longer side of the enlargement?[4]
A24 cm
B30 cm
C32 cm
D4.8 cm
E18 cm
10.Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?[4]
A40 percent
B37.5 percent
C75 percent
D35 percent
E30 percent
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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 — 10KA-0087Scaling and similar figures
AI added the difference between the areas' square roots to the side rather than multiplying by their ratio.
CI doubled the side because the larger area is roughly double the smaller.
DI used the ratio of the areas as if it were the ratio of the lengths, then adjusted.
EI multiplied the side by the ratio of the areas divided by three, mixing up which ratio applies to lengths.
2.C — 65KA-0103Recursive rules
AI stopped at the fourth term, counting the starting number as the first step rather than the first term.
BI generated one term too few, giving the fifth term instead of the sixth.
DI doubled six times and subtracted 1 only once at the end.
EI generated one term too many, giving the seventh instead of the sixth.
3.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.
4.B — 21.5KA-0115Multi-step arithmetic word problems
AI halved the 60 pencils before giving any away.
CI subtracted 17 from one box of 12 rather than from the whole 60.
DI gave the number of pencils left over rather than what each child gets.
EI gave the starting number of pencils without doing either of the steps.
5.B — 12KA-0121Try small cases first
AI used the number of hands each person shakes rather than the number of people.
CI doubled the answer, forgetting that the halving has already been done.
DI halved 66 and treated that as the number of people.
EI gave the number of handshakes back as the number of people.
6.A — 12KA-0122Back-solve from the answer choices
BI assumed a number with two different prime factors always has six factors.
CI counted the factors of 16 as six by including a number twice.
DI assumed a square number has six factors without listing them.
EI counted the powers of 3 up to 27 and thought there were six of them.
7.D — 21KA-0132Eliminate impossible choices by bounding
AI did not try one five and four twos, so I judged this total impossible.
BI missed the combination of two fives and three twos.
CI stopped listing after two fives and never reached three fives and two twos.
EI forgot the case where every coin is a five, which is allowed by the wording.
8.A — 1KA-0149Last-digit behavior of products and powers
BI assumed every power of 3 ends in 3.
CI found the cycle 3, 9, 7, 1 but counted its positions from zero, landing one step early.
DI used a remainder of 2 instead of 0 when dividing 100 by the cycle length of 4.
EI assumed a number this large has no reachable last digit, rather than looking for a repeat.
9.B — 30 cmKA-0155Scaling and similar figures
AI kept the difference of 4 cm between the two sides instead of keeping their ratio.
CI added 20 to 12 rather than scaling 12.
DI used the scale factor upside down and multiplied 12 by 8/20 instead of 20/8.
EI multiplied 12 by 1.5, the ratio between the original sides, instead of by the enlargement factor.
10.A — 40 percentKA-0165Mixtures and weighted averages
BI averaged 25 and 50 without weighting by how much of each solution there was.
CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
EI used only the acid from the weaker solution and spread it over all ten litres.