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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 12 points

1.In a class of 30 students, 18 play football and 15 play chess. Exactly 7 students do both. How many students play neither?[4]
- A4
- B26
- C3
- D11
- E7
2.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
3.A pattern is built in rows. The first figure has 1 row, the second has 2 rows, and so on. In every figure, the first row has 1 dot, the second has 3 dots, the third has 5 dots, and each row after has 2 more dots than the one above it. How many dots are in the eighth figure?[4]
- A64
- B15
- C36
- D72
- E81

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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.A — 4KA-0154Inclusion–exclusion with two sets
- BI found how many students play at least one of the two and answered with that instead.
- CI added 18 and 15 to get 33, subtracted the 30 in the class, and used the 3 left over.
- DI removed the 7 from both groups and subtracted 11 and 8 from 30, taking the overlap away twice.
- EI answered with the number who play both, which is what the question gave me rather than what it asked for.
2.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.
3.A — 64KA-0156Growth patterns and figurate numbers
- BI gave the number of dots in the eighth ROW instead of the whole figure.
- CI added the row numbers 1 through 8 instead of the odd numbers of dots.
- DI multiplied 8 rows by 9, using a rough average row that is one too large.
- EI counted the rows starting from zero and used the ninth square number.

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