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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 9 points

1.What is the remainder when 7 to the power 100 is divided by 5?[3]
- A1
- B2
- C3
- D4
- E0
2.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
3.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.A — 1KA-0169Remainders and modular cycles
- BI reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.
- CI read the cycle backwards and landed on the entry before the right one.
- DI used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.
- EI assumed a power that large must be divisible by 5.
2.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.
3.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.

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