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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 20 points

1.A flag shape is rotated a quarter turn clockwise about its bottom-left corner. Which of the descriptions matches the result?[4]
Text description of the figure
A flag shape drawn as an upright pole with a small triangle attached to the top right of the pole, standing on a marked corner point at the bottom of the pole.
- Athe pole points right and the triangle is below it
- Bthe pole points right and the triangle is above it
- Cthe pole points left and the triangle is above it
- Dthe pole points down and the triangle is to the left
- Ethe pole points up and the triangle is on the left
2.What is 2 + 4 + 6 + ... + 100?[4]
- A1275
- B2450
- C2500
- D2550
- E5100
3.Two students are chosen from a group of six to represent the class. How many different pairs are possible?[4]
- A12
- B15
- C21
- D30
- E36
4.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
5.A mother is 32 and her child is 8. In how many years will the mother be exactly three times as old as the child?[4]
- A2
- B4
- C8
- D12
- E24

Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 1 · 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.A — the pole points right and the triangle is below itKA-0039Reflections, rotations, translations
- BI turned the pole the right way but kept the triangle on the side it started on.
- CI turned the shape anticlockwise instead of clockwise.
- DI turned the shape half a turn instead of a quarter turn.
- EI reflected the shape in a vertical line instead of rotating it.
2.D — 2550KA-0058Clever regrouping (pair to round numbers)
- AI found the sum of 1 to 50 and forgot that every term here is twice as big.
- BI used 49 pairs instead of 25, losing one pair from the count.
- CI estimated the answer as a round number rather than pairing properly.
- EI paired the terms but forgot that pairing counts every number twice, so I never halved.
3.B — 15KA-0074Selections of a few objects
- AI doubled the group size instead of counting pairs.
- CI allowed a student to be paired with themselves, adding six impossible pairs.
- DI counted each pair twice, once in each order, and forgot to halve.
- EI multiplied 6 by 6, counting every ordered pair including a student with themselves.
4.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.
5.B — 4KA-0111Age problems
- AI aged only the child and left the mother's age unchanged.
- CI looked for when the mother is four times as old rather than three times.
- DI used the age difference of 24 and halved it, without checking the ratio it gives.
- EI gave the difference between their ages, which never changes, instead of a number of years.

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