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1.Ana adds up the first seven odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13. Is her total odd or even, and what is it?[3]
Aodd, 47
Bodd, 49
Ceven, 48
Deven, 49
Eodd, 45
2.Four road signs are shown. Exactly one of them has two lines of symmetry. Which one is it?[3]
Text description of the figure
Four outlined shapes side by side, labelled A to D: a plain rectangle, an isosceles triangle, a five-pointed star, and an arrow pointing right.
Athe rectangle
Bthe isosceles triangle
Cthe star
Dthe arrow
Enone of them
3.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
4.The first three patterns are made of dots and follow a rule. How many dots will the fifth pattern have?[3]
Text description of the figure
Three dot patterns in a row. The first has one column of 2 dots with a single dot above it, making 3. The second has two columns of 2 dots with a single dot above, making 5. The third has three columns of 2 dots with a single dot above, making 7.
A9
B10
C11
D13
E14
5.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
6.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
7.How many of the numbers from 1 to 20 are not multiples of 3?[3]
A6
B13
C14
D17
E20
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.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
10.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
11.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
12.A pattern of tiles repeats: black, black, white. What colour is the 100th tile?[3]
Ablack
Bwhite
Cit depends where you start counting
Dgrey, because the pattern breaks
Ethere is no 100th tile
13.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
14.Bo has 24 marbles and gives a third of them to Ana. How many more marbles does Bo have than Ana now?[3]
A4
B8
C16
D24
E32
15.A cat walks 3 m north, then 4 m east, then 3 m south. How many metres is it now from where it started?[3]
A0
B3
C4
D7
E10
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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.B — odd, 49KA-0002Parity of numbers (odd/even behavior)
AI decided that adding odd numbers always keeps the total odd, and made an arithmetic slip as well.
CI paired the numbers up and forgot that with seven numbers one is left over, so I expected an even total.
DI added correctly but then labelled 49 as even because I had already decided the pairs would make it even.
EI added only the first six numbers and stopped before including the thirteen.
2.A — the rectangleKA-0004Line and rotational symmetry
BI found the vertical fold that works and assumed a second one must work as well without testing it.
CI saw that the star looks very symmetric and picked it without counting how many lines of symmetry it actually has.
DI counted the horizontal fold and then counted the vertical one too, even though the two halves do not match.
EI only tested vertical folds on every shape and concluded that no shape had two lines.
3.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.
4.C — 11KA-0008Continuing a visual pattern
AI continued the pattern to the fourth stage and stopped one stage early.
BI counted only the columns of two and forgot the single dot sitting on top of each pattern.
DI continued the pattern one stage too far and gave the sixth pattern instead of the fifth.
EI doubled the third pattern's count, assuming the pattern doubles rather than grows by a fixed amount.
5.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.
6.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.
7.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.
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 — 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.
10.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.
11.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.
12.A — blackKA-0108Repeating cycles and position mod n
BI got a remainder of 1 but read the last colour of the repeat rather than the first.
CI thought the pattern had no fixed first tile, even though tile one is given.
DI assumed a repeating pattern must eventually change.
EI assumed the pattern runs only for as many tiles as one repeat contains.
13.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.
14.B — 8KA-0119Find what is actually being asked
AI halved the difference, as if the question asked how many Bo should hand over to make them equal.
CI gave how many Bo has now rather than how many more he has than Ana.
DI gave the number Bo started with, without doing anything.
EI added the two amounts together instead of comparing them.
15.C — 4KA-0120Draw the diagram
AI assumed the walk was a loop because the north and south distances match.
BI gave one of the distances walked rather than the distance from the start.
DI added the two different directions together instead of drawing where the cat ends up.
EI added up the whole distance walked, which is not the same as the distance from the start.