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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.The chart shows how many pets four children own. How many more pets does Mia own than Leo?[3]
Text description of the figure
A bar chart with four bars labelled Ana, Leo, Mia and Sam. The vertical axis is marked in steps of 2 from 0 to 10. The bars reach 4, 2, 8 and 6 respectively.
A2
B3
C6
D8
E10
3.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
4.What is the angle between the hands of a clock at exactly 3 o'clock?[3]
Text description of the figure
A clock face with the hour hand pointing at 3 and the minute hand pointing at 12, with the angle between them marked.
A30 degrees
B45 degrees
C90 degrees
D120 degrees
E180 degrees
5.One bus leaves every 12 minutes and another every 18 minutes. They leave together at 9:00. When do they next leave together?[3]
A9:06
B9:30
C9:36
D9:54
E12:36
6.Three quarters of a class of 28 travelled by bus. How many did not travel by bus?[3]
A4
B7
C12
D21
E24
7.A cafe offers 3 main courses and 2 puddings. How many different two-course meals can be ordered?[3]
Text description of the figure
A tree diagram. One starting point branches into three main courses, and each of those branches into two puddings, giving six paths in all.
A2
B5
C6
D9
E12
8.How many different two-digit numbers can be written using only the digits 1, 2 and 3, if a digit may be used twice?[3]
A3
B6
C9
D12
E27
9.A rectangle has a perimeter of 20 cm. One of its sides is 6 cm. What is its area in square centimetres?[3]
A14
B24
C40
D60
E96
10.Ana has three times as many stickers as Bo. Together they have 48. How many does Bo have?[3]
Text description of the figure
A bar model. Bo's bar is one box. Ana's bar is three boxes of the same size, drawn beneath it. A bracket spanning all four boxes is labelled 48.
A12
B16
C24
D32
E36
11.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
12.Three more than twice a number is 19. What is the number?[3]
A8
B11
C16
D22
E41
13.A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?[3]
A(1, 3)
B(1, 7)
C(5, 3)
D(7, 7)
E(7, 3)
14.In a triangle, one angle measures 30 degrees. Of the other two angles, one is exactly twice the other. What is the largest angle in the triangle?[3]
A50 degrees
B75 degrees
C100 degrees
D150 degrees
E90 degrees
15.What is the size of one interior angle of a regular twelve-sided polygon?[3]
A150 degrees
B30 degrees
C165 degrees
D1800 degrees
E144 degrees
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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.C — 6KA-0015Reading tables, charts, and graphs
AI read the vertical scale as going up in ones instead of in twos.
BI counted the gridlines between the two bar tops instead of reading the values off the scale.
DI gave Mia's total instead of the difference between Mia and Leo.
EI added the two amounts together rather than subtracting to find how many more.
3.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.
4.C — 90 degreesKA-0032Clock geometry: hands, angles, times
AI gave the angle for one hour mark instead of the three hour marks between the hands.
BI divided the right angle in half, as if a quarter of the clock were 45 degrees.
DI used a third of the clock face rather than a quarter of it.
EI read 3 o'clock as the hands pointing in opposite directions.
5.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing
AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
BI added the two intervals together rather than looking for a time that is a multiple of both.
DI found a common multiple but not the least one, landing on a later coincidence.
EI multiplied the two intervals together instead of finding their least common multiple.
6.B — 7KA-0064Fractions of a quantity
AI divided 28 by 7 instead of taking a quarter of it.
CI found three quarters of 16 by mistake, mixing up the class size.
DI found how many did travel by bus and gave that instead of how many did not.
EI subtracted the 4 quarters as if they were 4 students.
7.C — 6KA-0067Tree diagrams
AI counted the puddings only and forgot that the main course is also a choice.
BI added the number of mains to the number of puddings instead of multiplying them.
DI used three puddings as well as three mains, without reading how many puddings there are.
EI doubled the answer, as if the order of the two courses made a different meal.
8.C — 9KA-0072Systematic listing
AI counted only the numbers with two identical digits, like 11, 22 and 33.
BI required the two digits to be different, even though repeats are allowed.
DI allowed a fourth digit that was not in the list.
EI counted three-digit numbers instead of two-digit ones.
9.B — 24KA-0083Perimeter and area of rectilinear shapes
AI subtracted 6 from 20 and gave that, which is neither a side nor an area.
CI took the other side to be 20 minus 6 divided by 2, forgetting there are two sides of each length.
DI multiplied the perimeter by half the known side instead of finding the missing side first.
EI used 16 as the other side, taking 20 minus 6 plus 2 rather than working from the perimeter properly.
10.A — 12KA-0110Bar models for part–whole
BI split the 48 into three parts instead of the four the bars actually make.
CI halved the total, as if the two of them had the same number each.
DI found Bo's share correctly but then gave Ana's number instead.
EI gave Ana's total, which is three of the four boxes, rather than Bo's one.
11.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.
12.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.
13.E — (7, 3)KA-0145Grid coordinates and lattice reasoning
AI moved left instead of right, subtracting the 4 rather than adding it.
BI moved left and up, reversing both directions.
CI swapped the two coordinates round before moving.
DI moved up instead of down, adding the 2 rather than subtracting it.
14.C — 100 degreesKA-0152Angles on lines, in triangles, in polygons
AI found the smaller of the two unknown angles and stopped before doubling it.
BI split the remaining 150 degrees into two equal halves instead of a one-to-two split.
DI split the remainder evenly into 75 and 75, then doubled one of them.
EI assumed that the largest angle in a triangle like this must be a right angle.
15.A — 150 degreesKA-0170Angles on lines, in triangles, in polygons
BI found the exterior angle and answered with that instead of the interior one.
CI used 360 divided by 12 subtracted from 195, or otherwise slipped a step in the arithmetic.
DI gave the total of all twelve interior angles rather than one of them.