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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.In a triangle, one angle is 90 degrees and another is 35 degrees. What is the third angle?[3]
A35 degrees
B45 degrees
C55 degrees
D65 degrees
E145 degrees
4.A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
A20
B40
C45
D55
E60
5.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
6.A solid block is built from unit cubes and measures 4 by 3 by 2. How many unit cubes does it contain?[3]
Text description of the figure
A rectangular block built from unit cubes, 4 cubes long, 3 cubes deep and 2 cubes tall, drawn so that both layers are visible.
A9
B12
C18
D20
E24
7.Which of these arrangements of six squares cannot be folded into a closed cube?[3]
Text description of the figure
Four arrangements of six squares labelled A to D. A is a T shape, B is a straight line of six squares, C is a staircase of pairs, and D is a cross with a column of four and one square on each side.
Athe T shape
Bthe straight line of six
Cthe staircase
Dthe cross
Ethey all fold
8.A rectangle is divided by two vertical lines into three parts. How many rectangles of any size are in the picture?[3]
Text description of the figure
A wide rectangle divided by two vertical lines into three smaller rectangles side by side.
A3
B4
C6
D7
E9
9.In the number 4073, what is the value of the digit 7?[3]
A3
B7
C70
D700
E4000
10.What is 1 + 2 + 3 + ... + 20?[3]
A190
B200
C210
D220
E420
11.A tap drips about 3 times a minute. Roughly how many drips is that in one day?[3]
A180
B720
C1080
D4320
E43200
12.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
13.A floor measuring 6 by 4 units is covered exactly with tiles measuring 2 by 1, with no gaps and no overlaps. How many tiles are needed?[3]
A8
B10
C12
D24
E48
14.Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
A65
B75
C85
D95
E105
15.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
16.One minute is left. Three questions have no answer written and you cannot do any of them. Nothing is taken off for a wrong answer. What should you do?[3]
ALeave them blank, because guessing is not really doing the maths
BWrite an answer for every one of them
CAnswer only the one you nearly understand
DLeave them blank so it is clear you ran out of time
EWrite your working instead of an answer
17.How many three-digit numbers can be written using only the digits 1 and 2, with repeats allowed?[3]
A2
B3
C4
D6
E8
18.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
19.What is the remainder when 7 to the power 100 is divided by 5?[3]
A1
B2
C3
D4
E0
20.A sequence is defined by a(1) = 2 and a(n+1) = 2 a(n) - 1 for every n. What is a(6)?[3]
A33
B31
C64
D17
E63
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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 — 55 degreesKA-0022Angles on lines, in triangles, in polygons
AI assumed the triangle was isosceles because it had a right angle, so I repeated the 35.
BI assumed a right-angled triangle always has two 45 degree angles.
DI subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.
EI subtracted only the 35 from 180 and forgot to take off the right angle as well.
4.E — 60KA-0026Percentages and simple discounts
AI worked out the size of the discount and gave that as the new price instead of subtracting it.
BI treated a quarter off as half off and took the price down to 40.
CI applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.
DI subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.
5.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.
6.E — 24KA-0038Building and counting with unit cubes
AI added the three measurements together instead of multiplying them.
BI counted one layer of 4 by 3 and forgot that the block is two layers tall.
CI read the block as 3 by 3 by 2 because the drawing hid the far column.
DI counted only the cubes whose faces I could actually see in the picture.
7.B — the straight line of sixKA-0048Nets and folding, 2D to 3D
AI assumed any arrangement that is not a simple line must fail to fold.
CI thought a staircase would overlap when folded, without tracking a single face through the fold.
DI picked the cross because it looks unusual, even though it is the most familiar cube net there is.
EI checked that each arrangement had six squares and assumed six squares is enough.
8.C — 6KA-0054Counting shapes hidden inside a figure
AI counted only the three small rectangles drawn as separate cells and stopped there.
BI counted the three small rectangles and the whole one, and forgot the two made of two cells.
DI counted a rectangle made of the left and right cells, even though they are not next to each other.
EI assumed any pair of the four vertical lines makes a rectangle without checking each one.
9.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.
10.C — 210KA-0057Clever regrouping (pair to round numbers)
AI paired the numbers from the outside in but left the 20 out of every pair, so I added only up to 19.
BI estimated the total as a round number instead of working it out.
DI used eleven pairs of 20 instead of ten pairs of 21.
EI multiplied 20 by 21 and forgot that pairing counts every number twice.
11.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.
12.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.
13.C — 12KA-0086Tiling and tessellation
AI divided the floor area by 3 instead of by the tile area of 2.
BI laid tiles along the edges only and never filled the middle.
DI gave the area of the floor rather than the number of tiles that cover it.
EI multiplied the floor area by the tile area instead of dividing.
14.B — 75KA-0088Angles on lines, in triangles, in polygons
AI added the three angles wrongly, getting 295 instead of 285.
CI used an angle sum of 370, mis-remembering the total for a quadrilateral.
DI repeated one of the given angles instead of computing the missing one.
EI used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.
15.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.
16.B — Write an answer for every one of themKA-0127Never leave a blank — there is no penalty
AI treated guessing as dishonest, but the rules of the paper explicitly allow it and cost nothing.
CI answered one and left two blanks that could each have scored, at no risk.
DI tried to communicate with the marker, but only the answers are scored.
EI offered working on a paper where only the chosen letter is marked.
17.E — 8KA-0143Systematic listing
AI counted the two available digits rather than the numbers they can build.
BI counted the three positions instead of the numbers.
CI used only two of the three positions when multiplying.
DI multiplied 2 by 3, mixing the number of digits with the number of positions.
18.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.
19.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.
20.A — 33KA-0171Recursive rules
BI used the rule 2a(n) - 1 but started the sequence at 1 instead of 2.
CI doubled six times and ignored the minus one entirely.
DI stopped at a(5), one term early.
EI computed 2^6 - 1, applying the minus one only once at the very end.