Pick what you want, print the page. The answer key comes with it, on its own sheet, and it tells you the mistake behind every wrong choice — not just which letter is right.
This exact URL always produces this exact sheet — bookmark it and the answer key will still match next term. Print with your browser; the controls and the site navigation are left off the page.
1.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
2.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
3.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
4.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
5.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
6.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
7.A pack of 24 pencils is shared equally among 4 children. Each child then gives 2 pencils to a teacher. How many pencils do the children have left altogether?[4]
A4
B6
C16
D18
E22
8.A photograph is enlarged so that each side becomes 3 times as long. How many times bigger is its area?[4]
A3 times
B6 times
C9 times
D12 times
E27 times
9.How many lines of symmetry does a regular hexagon have?[4]
A2
B3
C4
D6
E12
10.Twice a number, with 3 added, gives 17. Which of the choices is the number?[4]
A5
B7
C10
D14
E20
11.Two circles touch on the outside. One has a radius of 3 cm and the other a radius of 5 cm. How many centimetres apart are their centres?[4]
A2
B4
C8
D15
E16
12.Two triangles are similar. The sides of the smaller are 3/5 as long as the matching sides of the larger. The smaller triangle has area 18 square cm. What is the area of the larger triangle?[4]
A30 sq cm
B50 sq cm
C45 sq cm
D10.8 sq cm
E90 sq cm
13.A square sheet is folded in half top to bottom, then in half left to right. One hole is punched through all the layers. How many holes are in the unfolded sheet?[5]
Text description of the figure
Three steps in a row: a square sheet, the same sheet folded in half top to bottom into a wide rectangle, and that rectangle folded in half left to right into a small square with a single punched hole near its centre.
A1
B2
C4
D6
E8
14.A circle of radius 5 is drawn inside a square of side 10, touching all four sides. What fraction of the square is outside the circle, to the nearest tenth?[5]
Text description of the figure
A square with a circle drawn inside it, the circle touching the midpoint of each of the four sides. The region inside the square but outside the circle is shaded.
A0.1
B0.2
C0.3
D0.5
E0.8
15.Five beads of five different colours are threaded on a circular bracelet. Two bracelets count as the same if one can be turned or flipped into the other. How many different bracelets are there?[5]
A12
B20
C24
D60
E120
16.The numbers 1 to 10 stand in a row. A move swaps two neighbours. After exactly 45 moves, can the row be back in its starting order?[5]
AYes, always
BYes, if the swaps are chosen well
CNo, because 45 is not a multiple of 10
DNo, because the number of moves is odd
EIt depends which numbers are swapped
17.You reach the ten 5-point questions with 18 minutes left. What is the best plan?[5]
AStart at the first and work through in order until time runs out
BRead all ten quickly, pick the two or three that look most doable, and fill in every answer before the end
CSpend the whole time on the last question, since it is the hardest
DAnswer the ones with the shortest statements
EDivide the time evenly, about 1.8 minutes each
18.Four children stand in a line. Ana is not first. Bo stands directly behind Ana. Cal is last. Who is first?[5]
AAna
BBo
CCal
DDee
Eit cannot be decided
19.A code uses the letters A, B and C, each exactly once. How many codes do not start with A?[5]
A2
B3
C4
D6
E9
20.Six friends sit around a circular table. Two seatings count as the same if one can be turned into the other by rotating the table. How many genuinely different seatings are there?[5]
A120
B720
C36
D60
E24
Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 1 · 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.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.
2.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.
3.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.
4.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.
5.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.
6.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.
EI applied only the rise and forgot the fall.
7.C — 16KA-0019Multi-step arithmetic word problems
AI found what one child has left and gave that instead of the total for all four.
BI divided 24 by 4 and then subtracted 2 twice, mixing up per-child steps with total steps.
DI subtracted 2 pencils once from the whole pack instead of once from each of the four children.
EI subtracted the 2 before sharing, so only one lot of 2 ever came out of the total.
8.C — 9 timesKA-0042Scaling and similar figures
AI applied the length scale factor straight to the area.
BI doubled the scale factor because area involves two dimensions, instead of squaring it.
DI multiplied the scale factor by four, as though area scaled with the number of sides.
EI cubed the scale factor, which is the rule for volume rather than area.
9.D — 6KA-0085Line and rotational symmetry
AI checked only the vertical and horizontal folds and stopped there.
BI counted the lines through opposite corners and forgot the ones through opposite edges.
CI assumed a hexagon behaves like a rectangle with a couple of extra folds.
EI counted each line twice, once from each end.
10.B — 7KA-0131Back-solve from the answer choices
AI tested the first choice, got 13, and picked it anyway because it was close.
CI added the 3 to 17 instead of subtracting it, then halved the 20 that gave me.
DI subtracted 3 from 17 and gave that without halving it.
EI added 3 to 17 instead of undoing the addition by subtracting it.
11.C — 8KA-0147Circles: radius, diameter, and touching circles
AI subtracted the radii, which is the answer when one circle sits inside the other.
BI averaged the two radii instead of adding them.
DI multiplied the radii together rather than adding them.
EI added the two diameters instead of the two radii.
12.B — 50 sq cmKA-0164Scaling and similar figures
AI scaled the area by 5/3, using the side ratio directly instead of its square.
CI multiplied the area by 2.5, halfway between the side ratio and its square.
DI scaled by 3/5 instead of 5/3, making the larger triangle smaller.
EI multiplied by 5 and ignored the 3 in the ratio entirely.
13.C — 4KA-0020Paper folding and hole punching
AI forgot that the punch goes through every layer at once, not just the top one.
BI undid only one of the two folds before counting the holes.
DI doubled for the first fold and then added two more rather than doubling a second time.
EI counted a fold that was never made, doubling three times instead of twice.
14.B — 0.2KA-0052Area by subtraction (shaded regions)
AI estimated by eye from the four corner pieces without comparing them to the whole square.
CI used a diameter of 5 instead of a radius of 5 when working out the circle's area.
DI assumed the circle covers half the square because it touches all four sides.
EI found the fraction covered by the circle and gave that instead of the fraction outside it.
15.A — 12KA-0071Overcount, then correct
BI divided the 120 arrangements by 6 rather than by the 10 movements that leave a bracelet looking the same.
CI allowed for turning the bracelet but forgot it can also be flipped over.
DI halved the 120 for flipping but forgot that turning also gives the same bracelet.
EI counted every arrangement in a line, as if the bracelet had a fixed first bead.
16.D — No, because the number of moves is oddKA-0097Parity arguments
AI assumed enough moves can undo anything, without asking what each move preserves.
BI tried a few sequences that nearly worked and assumed a better choice would finish the job.
CI reached for the number of items rather than for what a single swap actually changes.
EI thought the choice of swaps could change the outcome, when every swap has the same effect.
17.B — Read all ten quickly, pick the two or three that look most doable, and fill in every answer before the endKA-0130Managing the 5-point block
AI worked in order, so a hard early question could eat the time meant for easier later ones.
CI assumed the hardest question is worth the most, but every question in this block scores the same.
DI used length as a proxy for difficulty, which is not reliable in this block.
EI spread the time equally, which is too little for the questions I could do and wasted on the ones I could not.
18.D — DeeKA-0136Ordering and ranking from clues
AI ignored the very first clue, which rules Ana out of the front directly.
BI put Bo at the front, but Bo must have Ana immediately in front of him.
CI forgot that Cal is fixed at the back of the line.
EI stopped once two arrangements seemed possible, without testing whether the second one actually fits every clue.
19.C — 4KA-0140The multiplication principle
AI counted the codes that do start with A rather than the ones that do not.
BI counted the letters available for the first position instead of counting whole codes.
DI counted every arrangement of the three letters and forgot the restriction.
EI allowed letters to repeat, which the words each exactly once rule out.
20.A — 120KA-0166Counting up to symmetry
BI counted every arrangement in a row, so each circular seating got counted once for every rotation.
CI divided 720 by 20 or some other number instead of by the 6 rotations.
DI divided by 12, treating reflections as identical too, though the question only allows rotations.
EI fixed two people rather than one, dividing by an extra factor.