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2015

2015 Math Kangaroo Grades 5-6 past paper

Suitable for 5-6 Grade, 30 MC questions.

Sample ProblemsDownload PDF
Scan for 2015 Level E (Grades 9-10) PDF

Scan to get 2015 Level E (Grades 9-10) PDF + Answers

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

Exam Overview

2015 years Competitionstrongadjustspacebetweenthinkobjectforceand Logic ofconcludecombined.

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

2015 Kangaroo Level E Sample Problems (8 questions)

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

Q 3Easy 3 pointsNumber Theory
2^5 = ?
A) 32
B) 16
C) 64

Steps

12x2x2x2x2=32
Answer: APowers
Q 8Easy 3 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 13Medium 4 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 18Medium 4 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 23Hard 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 26Hard 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 30Hard 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

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