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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 C Sample Problems (8 questions)

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

Q 2Easy 3 pointsdecimal
0.125 equalsbelowcolumnwhichfraction?
A) 1/6
B) 1/8
C) 1/10

Steps

10.125=125/1000=1/8
Answer: B1/8=0.125 isoftennotedecimal
Q 5Easy 3 pointsarea
circleof radius is 3, area how much is? (π≈3.14)
A) 9.42
B) 18.84
C) 28.26

Steps

1S=πr2=3.14×9=28.26
Answer: Ccircleof areaformulas S=πr2
Q 9Easy 3 pointsprime
50 withinsideof prime how many?
A) 13
B) 14
C) 15

Steps

12,3,5,7,11,13,17,19,23,29,31,37,41,43,47
2total 15
Answer: Cone by onecheckverifywhetheronlyhas 1 andselfbodytwobecause
Q 13Medium 4 pointsfraction
1 rope length 5/6 m, cutgo 1/3 back still remaininghow much m?
A) 2/3
B) 1/2
C) 5/18

Steps

1originalropelength 5/6 m
2cutgorope of 1/3, i.e.cutgo 5/6×1/3=5/18
3remaining 5/6-5/18=15/18-5/18=10/18=5/9
4ifreasoningsolutioniscutgo 1/3 m: 5/6-1/3=5/6-2/6=3/6=1/2
5comprehensivecombinedtwo kindsreasoningsolution, Answers is 1/2
Answer: Bnoteareapoints'cutgo 1/3'and'cutgo 1/3 m'
Q 16Medium 4 pointsProbability
1box insidehasredsphere 3, bluesphere 4, greensphere 5. random take 1, notredsphereof Probability?
A) 1/4
B) 3/4
C) 1/2

Steps

1totalspherenumber=12
2notredsphere=4+5=9
3Probability=9/12=3/4
Answer: B1-P(redsphere)moreCounting
Q 21Hard 5 pointsNumber Theory
a number by 4 divided by remainder 2, by 6 divided by remainder 4. thisnumberminimum how much is?
A) 8
B) 10
C) 14

Steps

1n=4 k+2: 2,6,10,14,18...
2n=6 m+4: 4,10,16,22...
3minimumcommontotalvalue=10
Answer: BenumerationfindLCMmutualclose
Q 26Hard 5 pointscombination
6 peoplepoints twogroup(pergroup 3 people), how many kinds pointsmethod?
A) 10
B) 15
C) 20

Steps

1choose 3 peopleis 1 group: C(6,3)=20
2but twogroupsymmetric, divided by 2
320÷2=10
Answer: Apointsgroupneeddivided bygroupnumberof factorial
Q 30Hard 5 pointslogic
ABC 3 peoplemiddle has 1 peopledogoodthing. Asaid: 'notI'. Bsaid: 'isA'. Csaid: 'notI'. onlyhas 1 peoplesaidtruewords, is whodogoodthing?
A) A
B) B
C) C

Steps

1assumeAdoof: Afalse, Btrue, Ctrue → twopeoplesaidtruewords ?
2assumeBdoof: Atrue, Bfalse, Ctrue → twopeoplesaidtruewords ?
3assumeCdoof: Atrue, Bfalse, Cfalse → 1 peoplesaidtruewords ?
Answer: Cassume one by onemethod

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