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1.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
2.A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
A20
B40
C45
D55
E60
3.Eight people meet and everyone shakes hands with everyone else exactly once. How many handshakes take place?[3]
A16
B28
C36
D56
E64
4.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
5.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
6.Each shape stands for a whole number. A triangle plus a triangle plus a triangle is 12, and a triangle plus a square is 9. What is the square?[3]
A3
B4
C5
D6
E8
7.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
8.Which of these fractions lies between one third and one half?[3]
A1/5
B1/4
C2/5
D3/5
E2/3
9.How many three-digit numbers can be written using only the digits 1 and 2, with repeats allowed?[3]
A2
B3
C4
D6
E8
10.A jacket costs 80 pounds. In January the price rises by 20 percent. In February the new price falls by 20 percent. What is the price at the end of February?[3]
A80 pounds
B76.80 pounds
C64 pounds
D83.20 pounds
E96 pounds
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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 — 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.
2.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.
3.B — 28KA-0035Handshakes and pairs
AI doubled the number of people, as if each person made two handshakes in total.
CI let each person shake hands with all eight people including themselves before halving.
DI multiplied 8 by 7 and forgot that each handshake was counted from both sides.
EI multiplied 8 by 8, counting every ordered pair including a person with themselves.
4.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.
5.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.
6.C — 5KA-0061Operation puzzles and cryptarithms
AI solved for the triangle and gave that instead of the square.
BI found the triangle is 4 and gave that number, without going on to the second equation.
DI halved the 12 instead of dividing it by the three triangles.
EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.
7.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.
8.C — 2/5KA-0141Number lines and betweenness
AI compared the bottom numbers and assumed a bigger denominator means a bigger fraction.
BI saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.
DI checked that it is bigger than one third but never checked it against one half.
EI compared the top numbers only and ignored what the bottoms do to the size.
9.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.
10.B — 76.80 poundsKA-0153Percentages and simple discounts
AI assumed a 20 percent rise and a 20 percent fall must cancel because the percentages match.
CI applied only the fall and forgot the rise.
DI got the size of the change right but the direction wrong.