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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 bag of flour holds 2.5 kg. 1750 g are used. How many grams are left?[3]
A0.75
B75
C750
D1250
E1747.5
3.Three notebooks cost 240 cents each. You pay with a 10 euro note. How many cents change do you get? One euro is 100 cents.[3]
A240
B280
C520
D720
E760
4.The chart shows how many books four children read. How many did they read altogether?[3]
Text description of the figure
A bar chart with four bars labelled Ana, Bo, Cal and Dee. The vertical axis is marked in steps of 5 from 0 to 25. The bars reach 10, 25, 5 and 15.
A11
B25
C45
D55
E60
5.Three more than twice a number is 19. What is the number?[3]
A8
B11
C16
D22
E41
6.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
7.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
8.One tap fills a tank in 6 hours and another fills it in 3 hours. With both running, how long does the tank take to fill?[4]
A1 hour
B2 hours
C4.5 hours
D9 hours
E3 hours
9.A mother is 32 and her child is 8. In how many years will the mother be exactly three times as old as the child?[4]
A2
B4
C8
D12
E24
10.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
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 4 · 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 — 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.
3.B — 280KA-0114Money and change
AI subtracted the cost of one notebook rather than all three.
CI bought two notebooks instead of three.
DI gave the total cost of the notebooks instead of the change.
EI converted the 10 euro note to 1000 cents but subtracted the price of only one notebook after doubling it.
4.D — 55KA-0118Reading tables, charts, and graphs
AI read the axis as going up in ones and added the gridline heights instead of the values.
BI gave the tallest bar rather than the total of all four.
CI added only three of the four bars, missing the shortest one.
EI read the shortest bar as 10 rather than 5, because the axis steps in fives.
5.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.
6.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.
7.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.
8.B — 2 hoursKA-0044Combined work rates
AI subtracted the two times from each other rather than adding the rates.
CI averaged the two times, which would only be right if the taps took turns instead of running together.
DI added the two times together, which makes the tank slower with two taps than with one.
EI used the faster tap's time alone and ignored the contribution of the slower one.
9.B — 4KA-0111Age problems
AI aged only the child and left the mother's age unchanged.
CI looked for when the mother is four times as old rather than three times.
DI used the age difference of 24 and halved it, without checking the ratio it gives.
EI gave the difference between their ages, which never changes, instead of a number of years.
10.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.