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2026 Math Kangaroo Grades 5-6 past paper

Suitable for 5-6 Grade, 30 MC questions, Geometry54%.

Sample ProblemsDownload PDF
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30 Questions
75 Minutes
3/4/5 Tiered Scoring
No Calculator
Exam Overview

Exam Overview

2026 years Competition overall Difficulty improve, Geometry54%, multi-step comprehensive reasoning increases.

DDifficulty

  • 3 pointsQ 1-10
  • 4 pointsQ 11-20
  • 5 pointsQ 21-30

TTopics

  • Fraction Operations25%
  • Geometry25%
  • Number Theory20%
  • Combinatorics15%
  • Logic15%

AAwards

Super Gold
Top 1%
90+
Gold
Top 5%
80+
Silver
Top 15%
65+
Bronze
Top 30%
50+
Sample Problems

2026 Kangaroo Level C Sample Problems (30 questions)

Selected problems across difficulty tiers — click an option to check your answer

Q 1Easy 3 pointsfraction
3/4 - 1/3 = ?
A) 1/6
B) 5/12
C) 2/3

Steps

19/12-4/12=5/12
Answer: Bcommon denominator
Q 5Easy 3 pointsarea
trianglebase 10 cmheight 6 cm, area?
A) 16
B) 30
C) 60

Steps

1?×10×6=30
Answer: Bareaformulas
Q 9Easy 3 pointsdivisible
1-40 middlecandivisible by both 2 and 3 numbers divisible byhas several?
A) 5
B) 6
C) 7

Steps

1i.e.6 of multiple: 6,12,18,24,30,36
Answer: BLCM
Q 13Medium 4 pointsGeometry
circleof diameterexpand 2 times, areaexpandseveral times?
A) 2
B) 4
C) 8

Steps

1areaand radiussquaredirectly proportional than→4 times
Answer: Bratio relationship
Q 17Medium 4 pointsfraction application
240 pages of a book#read on day one 1/4, #read on day two remaining 1/3. still remainingseveral pages?
A) 80
B) 100
C) 120

Steps

1240×?=60 remaining 180, 180×?=60 remaining 120
Answer: Cnote'remaining of'
Q 22Hard 5 pointscombination
from 6 peoplemiddlechoose 3 people participate thanmatchhow many ways to choose?
A) 15
B) 18
C) 20

Steps

1C(6,3)=20
Answer: CCombinatorics
Q 26Hard 5 pointsNumber Theory
a number divided by 5 remainder 3, divided by 7 remainder 5. minimum how much is?
A) 31
B) 33
C) 38

Steps

1enumeration: 5 a+3 and 7 b+5 minimum common value 33
Answer: Benumeration
Q 2Easy 3 pointsfraction
1/2+1/3 = ?
A) 2/5
B) 5/6
C) 1/6

Steps

13/6+2/6=5/6
Answer: Bcommon denominatoradd
Q 3Easy 3 pointsarea
squareside length 7 area?
A) 14
B) 28
C) 49

Steps

172=49
Answer: Carea
Q 4Easy 3 pointsoperation
36×25 = ?
A) 800
B) 900
C) 1000

Steps

136×25=900
Answer: Bmultiplymethod
Q 6Easy 3 pointsGeometry
isosceles triangletwo baseangleeach 50°vertex angle?
A) 50°
B) 80°
C) 100°

Steps

1180-100=80°
Answer: Binsideangleand
Q 7Easy 3 pointsNumber Theory
1-50 middle 5 of multiplehas several?
A) 8
B) 9
C) 10

Steps

15,10,...,50→10
Answer: Cmultiple counting
Q 8Easy 3 pointsvolume
cuboid 5×4×3 volume?
A) 12
B) 30
C) 60

Steps

15×4×3=60
Answer: Cvolume
Q 10Easy 3 pointsfraction
3/5 convert to percent?
A) 30%
B) 50%
C) 60%

Steps

13÷5=0.6=60%
Answer: Cfraction convert to percent
Q 11Medium 4 pointsarea
parallelogrambase 12 height 7 area?
A) 19
B) 42
C) 84

Steps

112×7=84
Answer: Careaformulas
Q 12Medium 4 pointsNumber Theory
72 of factorhas several?
A) 10
B) 11
C) 12

Steps

11,2,3,4,6,8,9,12,18,24,36,72→12
Answer: Cfactor
Q 14Medium 4 pointsoperation
2.5×4 = ?
A) 8
B) 10
C) 12

Steps

110
Answer: Bdecimalmultiplymethod
Q 15Medium 4 pointsGeometry
circleradius 3 perimeter? (π≈3.14)
A) 9.42
B) 18.84
C) 28.26

Steps

12πr≈18.84
Answer: Bcircleperimeter
Q 16Medium 4 pointsfraction
a book 240 pages read 5/8 still remainingseveral pages?
A) 90
B) 120
C) 150

Steps

1240×3/8=90
Answer: Afraction application
Q 18Medium 4 pointscombination
4 peoplemiddlechoose 2 people form teams how many ways?
A) 4
B) 6
C) 12

Steps

1C(4,2)=6
Answer: BCombinatorics
Q 19Medium 4 pointsarea
trapezoidon 6 below 10 height 4 area?
A) 24
B) 32
C) 64

Steps

1(6+10)×4÷2=32
Answer: Btrapezoidarea
Q 20Medium 4 pointsNumber Theory
24 and 32 of LCM?
A) 48
B) 64
C) 96

Steps

1LCM=96
Answer: CLCM
Q 21Hard 5 pointsGeometry
rhombusdiagonal 10 and 8 area?
A) 18
B) 40
C) 80

Steps

110×8÷2=40
Answer: Brhombusarea
Q 23Hard 5 pointsoperation
0.125×80 = ?
A) 8
B) 10
C) 12

Steps

10.125=1/8→80÷8=10
Answer: Bdecimal clever calculation
Q 24Hard 5 pointscombination
using 0,1,2,3 composedifferent three-digit numberhas several?
A) 12
B) 16
C) 18

Steps

1hundreds digit 3 kinds×tens digit 3 kinds×units digit 2 kinds=18
Answer: Cpermutation
Q 25Hard 5 pointsNumber Theory
a number divided by 3 remainder 2 divided by 5 remainder 3 minimum is?
A) 8
B) 13
C) 23

Steps

1enumerate 3 k+2 and 5 m+3→8
Answer: Amiddlecountryremaining
Q 28Hard 5 pointslogic
10 peoplethanmatchper twopeopleplays one match how many matches total?
A) 20
B) 45
C) 90

Steps

1C(10,2)=45
Answer: BCombinatorics
Q 29Hard 5 pointsarea
right angletriangleslopeside 131 right angleside 5 another right angleside? area?
A) 25
B) 30
C) 60

Steps

1anotherside 12→?×5×12=30
Answer: BPythagorean+area
Q 27Hard 5 pointsGeometry
positive triangleside length 6 area? (√3≈1.73)
A) 9√3
B) 18
C) 15.59

Steps

1(√3/4)×36=9√3
Answer: Apositive trianglearea
Q 30Hard 5 pointslogic
ABCD 4 people 1 peoplebroke the vase. Asaid'notI', Bsaid'is C', Csaid'is D', Dsaid'C is wrong'. only 1 peoplelied who broke it?
A) A
B) B
C) C

Steps

1assume Cfragment: Atrue Btrue Cfalse D true→only 1 false?
Answer: Cassume one by one

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