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1.Today is Tuesday. What day of the week will it be in 100 days?[3]
AMonday
BTuesday
CWednesday
DThursday
EFriday
2.In a triangle, one angle is 90 degrees and another is 35 degrees. What is the third angle?[3]
A35 degrees
B45 degrees
C55 degrees
D65 degrees
E145 degrees
3.A rope is 3.5 metres long. A second rope is 240 centimetres long. How much longer is the first rope, in centimetres?[3]
A1.1
B11
C110
D236.5
E590
4.One bus leaves every 12 minutes and another every 18 minutes. They leave together at 9:00. When do they next leave together?[3]
A9:06
B9:30
C9:36
D9:54
E12:36
5.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
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.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 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
9.Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
A65
B75
C85
D95
E105
10.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
11.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
12.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
13.Which capital letter, printed plainly, has both a horizontal and a vertical line of symmetry?[3]
AA
BB
CH
DT
EZ
14.Three more than twice a number is 19. What is the number?[3]
A8
B11
C16
D22
E41
15.A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?[3]
A(1, 3)
B(1, 7)
C(5, 3)
D(7, 7)
E(7, 3)
16.In a triangle, one angle measures 30 degrees. Of the other two angles, one is exactly twice the other. What is the largest angle in the triangle?[3]
A50 degrees
B75 degrees
C100 degrees
D150 degrees
E90 degrees
17.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
18.What is the remainder when 2 to the power 50 is divided by 7?[3]
A1
B2
C4
D6
E0
19.What is the remainder when 7 to the power 100 is divided by 5?[3]
A1
B2
C3
D4
E0
20.What is the size of one interior angle of a regular twelve-sided polygon?[3]
A150 degrees
B30 degrees
C165 degrees
D1800 degrees
E144 degrees
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.D — ThursdayKA-0021Remainders and modular cycles
AI found the remainder 2 but counted the two days starting from today rather than starting from tomorrow.
BI divided 100 by 7 and used the quotient of 14, treating the leftover days as if there were none.
CI remembered there was a remainder but used a remainder of 1 instead of working it out.
EI counted 100 divided by 7 as 14 remainder 3 instead of remainder 2.
2.C — 55 degreesKA-0022Angles on lines, in triangles, in polygons
AI assumed the triangle was isosceles because it had a right angle, so I repeated the 35.
BI assumed a right-angled triangle always has two 45 degree angles.
DI subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.
EI subtracted only the 35 from 180 and forgot to take off the right angle as well.
3.C — 110KA-0029Unit conversion
AI subtracted correctly in metres but then gave the answer in metres when centimetres were asked for.
BI converted 3.5 metres to 35 centimetres instead of 350.
DI subtracted without converting at all, taking 3.5 away from 240.
EI added the two lengths instead of finding the difference between them.
4.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing
AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
BI added the two intervals together rather than looking for a time that is a multiple of both.
DI found a common multiple but not the least one, landing on a later coincidence.
EI multiplied the two intervals together instead of finding their least common multiple.
5.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.
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.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.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.
9.B — 75KA-0088Angles on lines, in triangles, in polygons
AI added the three angles wrongly, getting 295 instead of 285.
CI used an angle sum of 370, mis-remembering the total for a quadrilateral.
DI repeated one of the given angles instead of computing the missing one.
EI used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.
10.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.
11.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.
12.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.
13.C — HKA-0142Line and rotational symmetry
AI found the vertical fold and assumed a horizontal one must work too.
BI found the horizontal fold and stopped without testing the vertical one.
DI counted the vertical fold twice rather than testing a horizontal one.
EI mistook turning the letter upside down for folding it, which is rotation rather than symmetry about a line.
14.A — 8KA-0144Translating a sentence into an equation
BI subtracted 8 from 19 rather than working the two steps backwards.
CI subtracted the 3 from 19 and gave that without halving it.
DI added the 3 to 19 instead of subtracting it.
EI doubled 19 and added 3, applying the machine forwards instead of undoing it.
15.E — (7, 3)KA-0145Grid coordinates and lattice reasoning
AI moved left instead of right, subtracting the 4 rather than adding it.
BI moved left and up, reversing both directions.
CI swapped the two coordinates round before moving.
DI moved up instead of down, adding the 2 rather than subtracting it.
16.C — 100 degreesKA-0152Angles on lines, in triangles, in polygons
AI found the smaller of the two unknown angles and stopped before doubling it.
BI split the remaining 150 degrees into two equal halves instead of a one-to-two split.
DI split the remainder evenly into 75 and 75, then doubled one of them.
EI assumed that the largest angle in a triangle like this must be a right angle.
17.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.
18.C — 4KA-0161Remainders and modular cycles
AI assumed the cycle ends on 1 at every exponent that is a multiple of 2.
BI used a remainder of 1 rather than 2 when dividing 50 by 3.
DI doubled my way to 2 cubed = 8 and used 8 minus 2.
EI assumed a large power of 2 must eventually be divisible by 7.
19.A — 1KA-0169Remainders and modular cycles
BI reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.
CI read the cycle backwards and landed on the entry before the right one.
DI used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.
EI assumed a power that large must be divisible by 5.
20.A — 150 degreesKA-0170Angles on lines, in triangles, in polygons
BI found the exterior angle and answered with that instead of the interior one.
CI used 360 divided by 12 subtracted from 195, or otherwise slipped a step in the arithmetic.
DI gave the total of all twelve interior angles rather than one of them.