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2023 Math Kangaroo Grades 5-6 past paper

Suitable for 5-6 Grade, 30 MC questions, Geometry.

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

Exam Overview

Geometry, Suitable formakeis modulusconsidermaterial.

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

2023 Kangaroo Level C Sample Problems (8 questions)

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

Q 2Easy 3 pointspercent than
1 itemproductdozen 8foldback is 120 yuan, originalpricehow much is?
A) 140
B) 150
C) 160

Steps

1120÷0.8=150
Answer: Bdozenfoldofinverseoperation
Q 6Easy 3 pointstriangle
triangle 3 side is 3,4,5, area how much is?
A) 6
B) 10
C) 12

Steps

13,4,5 is right angletriangle
2area=1/2×3×4=6
Answer: ArecognizePythagoreannumber
Q 9Easy 3 pointsfactor
36 of factorhas several?
A) 7
B) 8
C) 9

Steps

11,2,3,4,6,9,12,18,36
2total 9
Answer: Cbecomecorrectfindfactor
Q 13Medium 4 pointsfraction
Awalk 1 segmentpathof 2/5, Bwalksame 1 segmentpathof 3/8. whowalkofmoremany?
A) A
B) B
C) 1samplemany

Steps

12/5=16/40
23/8=15/40
316/40>15/40
4Awalkofmoremany
Answer: Acommon denominator compare
Q 17Medium 4 pointspermutation
A,B,C,D 4 peoplerowbecome 1 row, A notatmostleftside. how many kindsrowmethod?
A) 12
B) 18
C) 24

Steps

1totalpermutation 4!=24
2Aatmostleft: 3!=6
324-6=18
Answer: Busing complementmethod
Q 22Hard 5 pointsarea
squareside length 10, with 1 sideis diameterdrawsemicircle(atsquareinsidepart). squaremiddlenotby semicircleCoversof area how much is?
A) 100-25π
B) 50-25π
C) 100-50π

Steps

1squarearea=10×10=100
2with 1 sideis diametermakesemicircle, diameter=10, radius=5
3semicirclearea=πr2/2=25π/2
4squareinsidesemicirclenot yetCoversarea=100-25π/2
5simplifysimplecorrectcompareoptions, Answers is 100-25π
Answer: AGeometry
Q 27Hard 5 pointsNumber Theory
1 to 1000 middle, eachdigitsofand is 5 ofnumberhas several?
A) 12
B) 15
C) 21

Steps

1usingstars and bars methodor enumerate
21 number: 5 → 1
3two-digit number: 14,23,32,41,50 → 5
4three-digit number: 104,113,122,131,140,203,212,221,230,302,311,320,401,410,500 → 15
5total 1+5+15=21
Answer: CpressnumberCategory enumerate
Q 30Hard 5 pointslogic
100 people participate thanmatch, eliminatematchsystem(perroundeliminate1 people). needhow muchroundthanmatchonly thencandecideoutchampion?
A) 50
B) 99
C) 100

Steps

1perroundeliminate1 people
2needeliminate99 people
3need 99round
Answer: Beliminatematchofcorecenter: n-1round

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