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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.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
3.A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
A20
B40
C45
D55
E60
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.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
6.What is 1 + 2 + 3 + ... + 20?[3]
A190
B200
C210
D220
E420
7.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
8.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
9.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
10.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 — 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.
3.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.
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.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.
6.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.
7.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.
8.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.
9.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.
10.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.