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1.Sam has only 2-cent and 5-cent coins. What is the largest amount under 15 cents that he cannot make exactly?[3]
A1 cent
B3 cents
C7 cents
D9 cents
E13 cents
2.A rope is 3.5 metres long. A second rope is 240 centimetres long. How much longer is the first rope, in centimetres?[3]
A1.1
B11
C110
D236.5
E590
3.Three more than twice a number is 19. What is the number?[3]
A8
B11
C16
D22
E41
4.A pack of 24 pencils is shared equally among 4 children. Each child then gives 2 pencils to a teacher. How many pencils do the children have left altogether?[4]
A4
B6
C16
D18
E22
5.Ravi cycles 12 km at 24 km per hour, then walks 6 km at 4 km per hour. How many minutes does the whole journey take?[4]
A30
B90
C105
D120
E150
6.There are 5 boxes with 12 pencils in each. 17 pencils are given away and the rest are shared equally between 2 children. How many does each child get?[4]
A21
B21.5
C26
D43
E60
7.One pipe fills a pool in 12 hours and another fills it in 4 hours. With both running, how many hours does the pool take to fill?[4]
A3
B4
C6
D8
E16
8.A train covers 150 km at a steady 60 km per hour. How many minutes does the journey take?[4]
A25
B90
C150
D210
E9000
9.Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?[4]
A40 percent
B37.5 percent
C75 percent
D35 percent
E30 percent
10.One tap fills a tank in 6 hours. A second tap fills the same tank in 4 hours. Both taps are opened together on an empty tank. How long does it take to fill?[5]
A2 hours 24 minutes
B5 hours
C10 hours
D2 hours
E1 hour 12 minutes
Math Kangaroo Star · 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 — 3 centsKA-0010Money and change
AI found the smallest amount that cannot be made rather than the largest one.
CI did not notice that 7 is 2 plus 5, so I marked it as impossible without testing it.
DI only tried using coins of one kind at a time and never mixed the two denominations.
EI assumed odd amounts are impossible because one of the coins is even.
2.C — 110KA-0029Unit conversion
AI subtracted correctly in metres but then gave the answer in metres when centimetres were asked for.
BI converted 3.5 metres to 35 centimetres instead of 350.
DI subtracted without converting at all, taking 3.5 away from 240.
EI added the two lengths instead of finding the difference between them.
3.A — 8KA-0144Translating a sentence into an equation
BI subtracted 8 from 19 rather than working the two steps backwards.
CI subtracted the 3 from 19 and gave that without halving it.
DI added the 3 to 19 instead of subtracting it.
EI doubled 19 and added 3, applying the machine forwards instead of undoing it.
4.C — 16KA-0019Multi-step arithmetic word problems
AI found what one child has left and gave that instead of the total for all four.
BI divided 24 by 4 and then subtracted 2 twice, mixing up per-child steps with total steps.
DI subtracted 2 pencils once from the whole pack instead of once from each of the four children.
EI subtracted the 2 before sharing, so only one lot of 2 ever came out of the total.
5.D — 120KA-0036Rate, time, distance
AI worked out the cycling leg and gave that as the answer, forgetting the walk entirely.
BI worked out the walking leg and gave that as the answer, forgetting the cycling entirely.
CI wrote half an hour as 15 minutes instead of 30 and added it to the 90 minute walk.
EI rounded the cycling leg up to a whole hour instead of keeping it as half an hour.
6.B — 21.5KA-0115Multi-step arithmetic word problems
AI halved the 60 pencils before giving any away.
CI subtracted 17 from one box of 12 rather than from the whole 60.
DI gave the number of pencils left over rather than what each child gets.
EI gave the starting number of pencils without doing either of the steps.
7.A — 3KA-0116Combined work rates
BI gave the faster pipe's time on its own, forgetting the slower one helps as well.
CI halved the slower pipe's time rather than adding the two rates.
DI averaged the two times, which would only be right if the pipes took turns.
EI added the two times, which makes two pipes slower than one - an impossible answer.
8.C — 150KA-0117Rate, time, distance
AI divided 150 by 60 and read the answer as minutes rather than hours.
BI used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.
DI converted 2.5 hours as two hours and fifty minutes.
EI multiplied the distance by 60 instead of dividing, then converted.
9.A — 40 percentKA-0165Mixtures and weighted averages
BI averaged 25 and 50 without weighting by how much of each solution there was.
CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
EI used only the acid from the weaker solution and spread it over all ten litres.
10.A — 2 hours 24 minutesKA-0159Combined work rates
BI averaged the two times, but two taps together must be faster than either one alone.
CI added the two times, which would be right for filling two tanks one after the other.
DI halved the smaller of the two times, guessing that two taps must simply be twice as fast as one.
EI found 2 hours 24 minutes correctly and then halved it a second time.