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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.A bag of flour holds 2.5 kg. 1750 g are used. How many grams are left?[3]
A0.75
B75
C750
D1250
E1747.5
4.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
5.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
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.A driver travels from one town to another at an average of 60 km/h and returns along the same road at an average of 40 km/h. What is the average speed for the whole journey?[4]
A48 km/h
B50 km/h
C52 km/h
D24 km/h
E100 km/h
10.A class of 12 scored an average of 8. Another class of 18 scored an average of 13. What is the average for all 30 students together?[5]
A10.5
B11
C11.5
D12
E21
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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.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.C — 750KA-0113Unit conversion
AI worked in kilograms and gave the answer in kilograms when grams were asked for.
BI converted 2.5 kg to 250 g rather than 2500 g.
DI subtracted 1750 from 3000, mis-converting 2.5 kg as three thousand grams.
EI subtracted without converting at all, taking 2.5 away from 1750.
4.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.
5.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.
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 — 48 km/hKA-0174Rate, time, distance
BI averaged the two speeds, which would only be right if equal TIME were spent at each, not equal distance.
CI weighted the two speeds by their own values instead of by the time each leg took.
DI halved the correct answer, dividing by the total distance twice.
EI added the two speeds together, which gives a number faster than either leg and so cannot be an average of them.
10.B — 11KA-0112Mixtures and weighted averages
AI averaged the two averages, ignoring that the classes are different sizes.
CI weighted the averages but used the wrong class size against each one.
DI leaned towards the larger class's average without computing the totals.
EI added the two averages together instead of combining them.