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2024 Math Kangaroo Grades 5-6 past paper

Suitable for 5-6 Grade, 30 MC questions, Number Theory.

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

Exam Overview

Number Theory, outappearmanyneedcreatepropertythinkingdimensionof comprehensive problem.

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

2024 Kangaroo Level E Sample Problems (8 questions)

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

Q 2Easy 3 pointsNumber Theory
gcd(48,36) x lcm(48,36) = ?
A) 48x36
B) 1728
C) 432

Steps

1gcd x lcm = product = 48x36
Answer: Agcd and lcm
Q 5Easy 3 pointsProbability
Flip 3 coins. Probability all heads?
A) 1/8
B) 1/4
C) 3/8

Steps

1(1/2)^3=1/8
Answer: AIndependent events
Q 9Easy 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 13Medium 4 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 16Medium 4 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 21Hard 5 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 26Hard 5 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 30Hard 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

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