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1.Ana adds up the first seven odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13. Is her total odd or even, and what is it?[3]
Aodd, 47
Bodd, 49
Ceven, 48
Deven, 49
Eodd, 45
2.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
3.Today is Tuesday. What day of the week will it be in 100 days?[3]
AMonday
BTuesday
CWednesday
DThursday
EFriday
4.In the number 4073, what is the value of the digit 7?[3]
A3
B7
C70
D700
E4000
5.A tap drips about 3 times a minute. Roughly how many drips is that in one day?[3]
A180
B720
C1080
D4320
E43200
6.Each shape stands for a whole number. A triangle plus a triangle plus a triangle is 12, and a triangle plus a square is 9. What is the square?[3]
A3
B4
C5
D6
E8
7.Which of these fractions lies between one third and one half?[3]
A1/5
B1/4
C2/5
D3/5
E2/3
8.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
9.What is the remainder when 2 to the power 50 is divided by 7?[3]
A1
B2
C4
D6
E0
10.What is the remainder when 7 to the power 100 is divided by 5?[3]
A1
B2
C3
D4
E0
Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 2 · 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.B — odd, 49KA-0002Parity of numbers (odd/even behavior)
AI decided that adding odd numbers always keeps the total odd, and made an arithmetic slip as well.
CI paired the numbers up and forgot that with seven numbers one is left over, so I expected an even total.
DI added correctly but then labelled 49 as even because I had already decided the pairs would make it even.
EI added only the first six numbers and stopped before including the thirteen.
2.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.
3.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.
4.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.
5.D — 4320KA-0059Estimation and order of magnitude
AI worked out the drips in an hour and stopped there.
BI multiplied by the 24 hours but forgot the 60 minutes in each one.
CI used 6 hours in a day, thinking of waking hours rather than a whole day.
EI used 600 minutes in an hour rather than 60.
6.C — 5KA-0061Operation puzzles and cryptarithms
AI solved for the triangle and gave that instead of the square.
BI found the triangle is 4 and gave that number, without going on to the second equation.
DI halved the 12 instead of dividing it by the three triangles.
EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.
7.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.
8.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.
9.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.
10.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.