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2024 Math Kangaroo Grades 7-8 past paper

Suitable for 7-8 Grade, 30 MC questions, AlgebraGeometry.

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

  • Algebra25%
  • Geometry20%
  • Number Theory20%
  • Probability15%
  • combination20%

AAwards

Super Gold
Top 1%
90+
Gold
Top 5%
80+
Silver
Top 15%
65+
Bronze
Top 30%
50+
Sample Problems

2024 Kangaroo Level D Sample Problems (8 questions)

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

Q 3Easy 3 pointsequation
solutionequationgroup x+y=10, x-y=4, x=?
A) 5
B) 6
C) 7

Steps

1twoexpressionmutualadd: 2 x=14
2x=7
Answer: Caddsubtracteliminateyuanmethod
Q 6Easy 3 pointsGeometry
waitsidetriangleperanglehow much is°?
A) 45°
B) 60°
C) 90°

Steps

1180°÷3=60°
Answer: Bwaitsidetriangle 3 angleequal
Q 10Easy 3 pointsdivisible
1-100 middle, divisible by 2 and 3 at the same time numbers divisible byhas several?
A) 16
B) 33
C) 50

Steps

1i.e.6 of multiple
2100÷6=16(takeinteger)
Answer: Adivisible by both 2 and 3 divisible=by 6 divisible
Q 14Medium 4 pointsProbability
roll1dice two times, two timespointnumbersameof Probability?
A) 1/36
B) 1/6
C) 1/3

Steps

1#1 times arbitrary
2#2 times and#1 times same: 1/6
3Probability=1/6
Answer: Baloneset upthingitemProbability
Q 18Medium 4 pointsnumbercolumn
arithmetic sequence#1 term=3, #5 term=19, common difference how much is?
A) 3
B) 4
C) 5

Steps

1a?=a?+4 d
219=3+4 d
3d=4
Answer: Barithmetic sequencegeneral term
Q 24Hard 5 pointsAlgebra
if x2-5 x+6=0, find x?2+x?2.
A) 13
B) 19
C) 25

Steps

1x?+x?=5, x?x?=6
2x?2+x?2=(x?+x?)2-2 x?x?
3=25-12=13
Answer: AVietacertainreasoning+completelysquare
Q 27Hard 5 pointsGeometry
circleof insideconnectpositive hexagonside lengthand radiusof relationship?
A) side length=radius
B) side length=2 timesradius
C) side length=radius/2

Steps

1positive hexagonpermiddlecenterangle=60°
2shapebecomeof triangle iswaitsidetriangle
3side length=radius
Answer: Apositive hexagon ofspecialspecialpropertyprime
Q 30Hard 5 pointscombination
from 1-10 middlechoose 4 number, needfindmaximumvalueand minimumvalueofdifferenceexactly is 5. how many kindschoosemethod?
A) 30
B) 40
C) 60

Steps

1from 1~10 middlechoose 4 number, maximum-minimum=5
2minimumvaluem, maximumvaluem+5, thenm+5≤10, m≤5
3mcantake 1,2,3,4,5 total 5 kinds
4middlebetween 2 numberfromm+1 tom+4 middlechoose, totalC(4,2)=6 kinds
5totalnumber=5×6=30
Answer: CdeterminerangebackCombinatorics

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