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Math Kangaroo practice

Name: ______________________Date: ____________10 questions · 34 points

1.On the number line shown, the marks are equally spaced. What number does the arrow point to?[3]
Text description of the figure
A number line with equally spaced tick marks. The leftmost tick is labelled 0 and the rightmost is labelled 60, with five unlabelled ticks evenly spaced between them. An arrow points to the fourth tick from the left.
- A4
- B24
- C30
- D40
- E50
2.Today is Tuesday. What day of the week will it be in 100 days?[3]
- AMonday
- BTuesday
- CWednesday
- DThursday
- EFriday
3.In the number 4073, what is the value of the digit 7?[3]
- A3
- B7
- C70
- D700
- E4000
4.Which of these fractions lies between one third and one half?[3]
- A1/5
- B1/4
- C2/5
- D3/5
- E2/3
5.A jacket costs 80 pounds. In January the price rises by 20 percent. In February the new price falls by 20 percent. What is the price at the end of February?[3]
- A80 pounds
- B76.80 pounds
- C64 pounds
- D83.20 pounds
- E96 pounds
6.What is the remainder when 2 to the power 50 is divided by 7?[3]
- A1
- B2
- C4
- D6
- E0
7.What is the remainder when 7 to the power 100 is divided by 5?[3]
- A1
- B2
- C3
- D4
- E0
8.Which of these numbers can be divided exactly by both 4 and 9?[4]
- A96
- B117
- C132
- D144
- E153
9.The mean of four numbers is 9. Three of them are 5, 8 and 12. What is the fourth?[4]
- A9
- B10
- C11
- D12
- E13
10.What is the last digit of 3 multiplied by itself 2026 times, that is, of 3 to the power 2026?[5]
- A3
- B9
- C7
- D1
- E6

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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.C — 30KA-0006Number lines and betweenness
- AI counted the tick marks and gave the position number instead of reading the value on the scale.
- BI worked out that each gap is worth 10 but then counted only as far as the tick before the arrow.
- DI counted the tick marks rather than the gaps between them, so every gap came out one step too small.
- EI counted the gaps from the right-hand end instead of from zero.
2.D — ThursdayKA-0021Remainders and modular cycles
- AI found the remainder 2 but counted the two days starting from today rather than starting from tomorrow.
- BI divided 100 by 7 and used the quotient of 14, treating the leftover days as if there were none.
- CI remembered there was a remainder but used a remainder of 1 instead of working it out.
- EI counted 100 divided by 7 as 14 remainder 3 instead of remainder 2.
3.C — 70KA-0055Place value and digit positions
- AI gave the last digit of the number instead of looking at the 7 at all.
- BI gave the digit itself rather than what it is worth in the position it sits in.
- DI counted the positions from the left, so I read the 7 as being in the hundreds place.
- EI gave the value of the largest digit instead of the value of the 7.
4.C — 2/5KA-0141Number lines and betweenness
- AI compared the bottom numbers and assumed a bigger denominator means a bigger fraction.
- BI saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.
- DI checked that it is bigger than one third but never checked it against one half.
- EI compared the top numbers only and ignored what the bottoms do to the size.
5.B — 76.80 poundsKA-0153Percentages and simple discounts
- AI assumed a 20 percent rise and a 20 percent fall must cancel because the percentages match.
- CI applied only the fall and forgot the rise.
- DI got the size of the change right but the direction wrong.
- EI applied only the rise and forgot the fall.
6.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.
7.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.
8.D — 144KA-0063Divisibility rules: 2, 3, 4, 5, 9, 10
- AI checked that it divides by 4 and stopped without testing the 9.
- BI checked the digit sum for 9 and stopped without testing the 4.
- CI saw an even number with a digit sum of 6 and treated 6 as good enough for 9.
- EI tested 9 with the digit sum and assumed any odd multiple of 9 also divides by 4.
9.C — 11KA-0066Means, and working backwards from a mean
- AI assumed the missing number must be the mean itself.
- BI averaged the three known numbers instead of working from the total.
- DI repeated one of the numbers already given rather than computing the missing one.
- EI used a total of 37 instead of 36, adding the mean in once too often.
10.B — 9KA-0158Last-digit behavior of products and powers
- AI used the first entry of the cycle because 2026 is even, without working out where in the cycle it lands.
- CI counted the cycle starting from zero, so a remainder of 2 put me one place too far along.
- DI assumed a power that large must end in 1.
- EI multiplied 3 by 2 and used the last digit of that.

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