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1.A 3 by 3 board is drawn. How many 2 by 2 squares can be found on it, if they must line up with the grid?[3]
Text description of the figure
A square board divided into a 3 by 3 arrangement of nine equal small squares.
A1
B2
C4
D6
E9
2.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
3.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
4.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
5.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
6.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
7.Which of these is true of every rectangle?[3]
Aall four sides are the same length
Bthe diagonals cross at right angles
Cit has four lines of symmetry
Dthe angles add to 180 degrees
Ethe two diagonals are the same length
8.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
9.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
10.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.C — 4KA-0001Counting by position (sliding window)
AI split the board into separate 2 by 2 blocks and only one whole block fitted, so I answered one.
BI slid the square across the top row and found two positions, then forgot it can also move down.
DI counted the four sliding positions and then added the two whole rows of the board as well.
EI counted the nine small squares on the board instead of the 2 by 2 squares.
2.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.
3.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.
4.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.
5.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.
6.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.
7.E — the two diagonals are the same lengthKA-0079Properties of triangles and quadrilaterals
AI confused a rectangle with a square, which is only one special kind of rectangle.
BI remembered a fact about squares and rhombuses and applied it to every rectangle.
CI counted the two diagonals as lines of symmetry, which only works for a square.
DI used the angle sum of a triangle on a four-sided shape.
8.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.
9.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.
10.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.