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1.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
2.Toma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?[3]
A10
B14
C16
D20
E24
3.How many of the numbers from 1 to 20 are not multiples of 3?[3]
A6
B13
C14
D17
E20
4.In the number 4073, what is the value of the digit 7?[3]
A3
B7
C70
D700
E4000
5.A tap drips about 3 times a minute. Roughly how many drips is that in one day?[3]
A180
B720
C1080
D4320
E43200
6.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
7.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
8.A bread recipe uses flour and sugar in the ratio 5 to 3. The two together weigh 320 grams. How much of that is flour?[3]
A120 g
B160 g
C200 g
D192 g
E64 g
9.A sequence begins 7, 11, 15, 19, and continues with the same constant step. What is the 30th term?[3]
A123
B127
C120
D119
E137
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
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 5 · 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 — 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.
2.C — 16KA-0050Working backwards
AI added the 4 and the 6 and stopped, forgetting to undo the halving.
BI doubled the 6 first and then added the 4, reversing the steps in the wrong order.
DI doubled the total at the end rather than doubling only the amount left after the first spend.
EI doubled twice because spending half felt like it needed undoing more than once.
3.C — 14KA-0051Complementary counting
AI counted the multiples of 3 and gave that instead of the numbers that are not multiples.
BI counted 21 as a multiple of 3 inside the range, so I removed one too many.
DI removed only the multiples of 3 that are also even, so I subtracted three instead of six.
EI gave the size of the whole range and forgot to remove anything at all.
4.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.
5.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.
6.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.
7.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.
8.C — 200 gKA-0151Ratio as parts of a whole
AI worked out the part size correctly and then answered for the sugar instead of the flour.
BI split the 320 grams into two halves instead of into eight equal parts.
DI took three fifths of 320 rather than five eighths, using the ratio numbers as a fraction of each other.
EI divided 320 by the 5 in the ratio and stopped, treating 5 as the number of parts.
9.A — 123KA-0160Arithmetic sequences and the nth term
BI multiplied the step by 30 instead of by 29, forgetting that the first term needs no steps.
CI used 4 times 30 and forgot to add the starting value.
DI added 28 steps instead of 29, counting the gaps one short.
EI treated the first term as the step and used 7 times 30 minus something close.
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.