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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 F Sample Problems (30 questions)

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

Q 1Easy 3 pointsNumber Theory
How many multiples of 3 from 1 to 100?
A) 33
B) 34
C) 30

Steps

1⌊100/3⌋=33
Answer: ADivisibility
Q 5Easy 3 pointsCombinatorics
How many 3-digit numbers with distinct digits from 1,2,3,4?
A) 24
B) 12
C) 64

Steps

14x3x2=24
Answer: APermutation
Q 9Easy 3 pointsGeometry
Pick 4 of 8 cube vertices that are coplanar. How many ways?
A) 12
B) 6
C) 8

Steps

16 faces + 6 diagonal sections = 12
Answer: BCube sections
Q 13Medium 4 pointsLogic
12 balls, one fake (different weight). Min balance weighings to find it?
A) 3
B) 4
C) 2

Steps

13^3=27>12, 3 weighings suffice
Answer: AInformation theory
Q 17Medium 4 pointsProbability
Bag: 3 red, 2 white balls. Draw 2, both red probability?
A) 3/10
B) 1/2
C) 3/5

Steps

1C(3,2)/C(5,2)=3/10
Answer: AClassical probability
Q 22Hard 5 pointsNumber Theory
Two primes p,q sum to 20. Max value of pq?
A) 51
B) 91
C) 96

Steps

1(3,17),(7,13) -> 7x13=91 max
Answer: BPrime property
Q 26Hard 5 pointsNumber Theory
How many multiples of 3 from 1 to 50?
A) 16
B) 17
C) 15

Steps

1⌊50/3⌋=16
Answer: ADivisibility
Q 2Easy 3 pointsGeometry
Right triangle legs 3 and 4. Hypotenuse?
A) 5
B) 6
C) 7

Steps

13²+4²=25, √25=5
Answer: APythagorean
Q 3Easy 3 pointsCombinatorics
3 books on a shelf. How many arrangements?
A) 6
B) 3
C) 9

Steps

13!=6
Answer: APermutation
Q 4Easy 3 pointsNumber Theory
gcd(12,18)?
A) 6
B) 3
C) 2

Steps

112=2²·3, 18=2·3², gcd=2·3=6
Answer: Agcd
Q 6Easy 3 pointsSequence
2,4,8,16,... 6th term?
A) 64
B) 32
C) 128

Steps

12^n, 6th=2^6=64
Answer: AGeometric
Q 7Easy 3 pointsGeometry
Square side 4. Area?
A) 16
B) 8
C) 4

Steps

14²=16
Answer: ASquare area
Q 8Easy 3 pointsCombinatorics
Choose a team of 2 from 5 people. How many ways?
A) 10
B) 20
C) 5

Steps

1C(5,2)=10
Answer: ACombination
Q 10Easy 3 pointsNumber Theory
How many primes below 100?
A) 25
B) 24
C) 26

Steps

1There are 25 primes below 100
Answer: APrimes
Q 11Medium 4 pointsProbability
Draw one card from 52. Probability it is an Ace?
A) 1/13
B) 1/4
C) 1/52

Steps

14 aces / 52 cards = 1/13
Answer: AClassical probability
Q 12Medium 4 pointsGeometry
Circle radius 2. Area?
A) 4π
B) 2π
C) π

Steps

1πr²=4π
Answer: ACircle area
Q 14Medium 4 pointsCombinatorics
4 people around a circular table. How many seatings?
A) 6
B) 24
C) 12

Steps

1(n-1)!=3!=6
Answer: ACircular permutation
Q 15Medium 4 pointsNumber Theory
How many multiples of 5 from 100 to 200?
A) 21
B) 20
C) 19

Steps

1(200-100)/5+1=21
Answer: ADivisibility
Q 16Medium 4 pointsSequence
1,1,2,3,5,8,... 8th term?
A) 21
B) 13
C) 34

Steps

1Fibonacci: 1,1,2,3,5,8,13,21
Answer: AFibonacci
Q 18Medium 4 pointsProbability
Two independent events each 1/2. Both occur?
A) 1/4
B) 1/2
C) 1

Steps

11/2 x 1/2 = 1/4
Answer: AIndependent
Q 19Medium 4 pointsGeometry
Rectangle 6 by 4. Perimeter?
A) 20
B) 24
C) 10

Steps

12(6+4)=20
Answer: APerimeter
Q 20Medium 4 pointsNumber Theory
2^5 = ?
A) 32
B) 16
C) 64

Steps

12x2x2x2x2=32
Answer: APowers
Q 21Hard 5 pointsCombinatorics
5 people stand in a row. How many ways if A and B must be adjacent?
A) 24
B) 48
C) 120

Steps

1Tie A,B as one unit: 4! x 2! = 48
Answer: BBundling
Q 23Hard 5 pointsGeometry
Ratio of inscribed regular hexagon area to circle area?
A) 2/3
B) 3√3/(2π)
C) √3/π

Steps

1Hexagon area=6(√3/4)r²=3√3r²/2, circle=πr², ratio=3√3/(2π)
Answer: BRegular hexagon
Q 24Hard 5 pointsNumber Theory
How many integers 1-100 are divisible by neither 3 nor 5?
A) 53
B) 47
C) 54

Steps

1100-⌊100/3⌋-⌊100/5⌋+⌊100/15⌋=100-33-20+6=53
Answer: AInclusion-exclusion
Q 25Hard 5 pointsProbability
Two dice rolled. Probability the sum is 8?
A) 5/36
B) 1/6
C) 7/36

Steps

1Sum 8: (2,6)(3,5)(4,4)(5,3)(6,2)=5 outcomes, 5/36
Answer: AClassical probability
Q 28Hard 5 pointsCounting
Choose 3 balls from 10 distinct balls. How many ways?
A) 120
B) 720
C) 210

Steps

1C(10,3)=10x9x8/(3x2x1)=120
Answer: ACombination
Q 29Hard 5 pointsSequence
10th term of 3,7,11,...?
A) 39
B) 43
C) 47

Steps

1a10=a1+9d=3+9x4=39
Answer: AArithmetic sequence
Q 27Hard 5 pointsGeometry
Triangle sides 5,12,13. Inradius?
A) 2
B) 3
C) 6

Steps

1Right triangle, area=30, semiperimeter=15, r=area/s=2
Answer: AIncircle
Q 30Hard 5 pointsCombinatorics
4 people shake hands once each. Total handshakes?
A) 6
B) 12
C) 24

Steps

1C(4,2)=6
Answer: ACombination

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