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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 9 points

1.A sequence begins 7, 11, 15, 19, and continues with the same constant step. What is the 30th term?[3]
- A123
- B127
- C120
- D119
- E137
2.What is the remainder when 2 to the power 50 is divided by 7?[3]
- A1
- B2
- C4
- D6
- E0
3.Two towns are 300 km apart. A car leaves each town at the same moment driving toward the other, one at 60 km/h and the other at 90 km/h. How long until they meet?[3]
- A2 hours
- B3 hours 20 minutes
- C4 hours
- D5 hours
- E1 hour

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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 — 123KA-0160Arithmetic sequences and the nth term
- BI multiplied the step by 30 instead of by 29, forgetting that the first term needs no steps.
- CI used 4 times 30 and forgot to add the starting value.
- DI added 28 steps instead of 29, counting the gaps one short.
- EI treated the first term as the step and used 7 times 30 minus something close.
2.C — 4KA-0161Remainders and modular cycles
- AI assumed the cycle ends on 1 at every exponent that is a multiple of 2.
- BI used a remainder of 1 rather than 2 when dividing 50 by 3.
- DI doubled my way to 2 cubed = 8 and used 8 minus 2.
- EI assumed a large power of 2 must eventually be divisible by 7.
3.A — 2 hoursKA-0162Rate, time, distance
- BI used only the slower car's speed and divided 300 by 90 the wrong way round.
- CI averaged the two speeds to 75 km/h and divided 300 by it, which ignores that both cars move at once.
- DI divided 300 by 60, using only the slower car.
- EI halved the distance to 150 and then divided by 150, applying the closing speed twice.

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