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2026 Math Kangaroo Grades 7-8 past paper

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

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

Exam Overview

2026 years Competition overall Difficulty improve, Geometry54%, multi-step comprehensive reasoning increases.

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

2026 Kangaroo Level D Sample Problems (30 questions)

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

Q 2Easy 3 pointsAlgebra
5 x-3=2 x+9, x=?
A) 3
B) 4
C) 5

Steps

13 x=12,x=4
Answer: Bmovetermcombinedand
Q 6Easy 3 pointsGeometry
right angletriangletwo right angleside 6 and 8, slopeside?
A) 10
B) 12
C) 14

Steps

1√(36+64)=10
Answer: APythagorean theorem
Q 10Easy 3 pointsdivisible
100 withinsidecandivisible by both 3 and 5 numbers divisible byhas several?
A) 5
B) 6
C) 7

Steps

115 of multiple: 15,30,45,60,75,90
Answer: BLCM(3,5)=15
Q 14Medium 4 pointsProbability
middle 4 red 3 blue 2 greensphere take 1 notredsphereof Probability?
A) 4/9
B) 5/9
C) 2/3

Steps

1notred 5/totalnumber 9
Answer: Bcomplementmethod
Q 19Medium 4 pointsnumbercolumn
arithmetic sequencefirstterm 5 common difference 3#10 term?
A) 29
B) 32
C) 35

Steps

15+9×3=32
Answer: Bgeneral term
Q 23Hard 5 pointsGeometry
positive hexagonside length 4 area? (√3≈1.73)
A) 24√3
B) 48
C) 36√3

Steps

16×(√3/4×16)=24√3
Answer: A6 waitsidetriangle
Q 27Hard 5 pointsAlgebra
a+b=8, ab=15, finda2+b2
A) 29
B) 34
C) 49

Steps

1(a+b)2-2 ab=64-30=34
Answer: Bcompletelysquarechangeshape
Q 1Easy 3 pointsoperation
(-3)2 = ?
A) -9
B) -6
C) 9

Steps

1negative numbersquare is positive
Answer: Cpower operation
Q 3Easy 3 pointsequation
x/3=7, x=?
A) 3
B) 10
C) 21

Steps

1x=21
Answer: C1 yuanequation
Q 4Easy 3 pointsGeometry
squarediagonaltakesquare pointsbecomeseveral triangle?
A) 2
B) 3
C) 4

Steps

12 right angletriangle
Answer: Adiagonal
Q 5Easy 3 pointsoperation
3.6+2.4×2 = ?
A) 8.4
B) 12
C) 7.2

Steps

12.4×2=4.8+3.6=8.4
Answer: Aoperationsequenceorder
Q 7Easy 3 pointsarea
circleradius 5 area? (π≈3.14)
A) 31.4
B) 78.5
C) 157

Steps

1π×25≈78.5
Answer: Bcirclearea
Q 8Easy 3 pointsNumber Theory
100 withinsidemaximumprime?
A) 89
B) 93
C) 97

Steps

197 is prime
Answer: Cprimedeterminecertain
Q 9Easy 3 pointsProbability
roll dice getnumber>4 of Probability?
A) 1/6
B) 1/3
C) 1/2

Steps

15,6→2/6=1/3
Answer: BCountingProbability
Q 11Medium 4 pointsequation
2(x+3)=14, x=?
A) 2
B) 4
C) 5

Steps

1x+3=7→x=4
Answer: Bgoparenthesisnumber
Q 12Medium 4 pointsGeometry
triangle 3 side 3,4,5 iswhat triangle?
A) waitside
B) right angle
C) obtuse angle

Steps

132+42=52→right angle
Answer: BPythagoreaninversecertainreasoning
Q 13Medium 4 pointsNumber Theory
GCD(45,60) = ?
A) 5
B) 15
C) 30

Steps

115
Answer: Bmaximumcommonfactor
Q 15Medium 4 pointsoperation
(-2)3+42 = ?
A) 8
B) 24
C) -8

Steps

1-8+16=8
Answer: Apower operation
Q 16Medium 4 pointsGeometry
positive pentagoninsideangleand?
A) 360°
B) 450°
C) 540°

Steps

1(5-2)×180=540°
Answer: Cinsideangleand formulas
Q 17Medium 4 pointsProbability
middle 5 red 3 whitetake 2 at least 1 redProbability?
A) 5/8
B) 15/28
C) 25/28

Steps

11-C(3,2)/C(8,2)=1-3/28=25/28
Answer: Ccomplementmethod
Q 18Medium 4 pointsnumbercolumn
arithmetic sequencea?=7,a?=19 common difference?
A) 2
B) 3
C) 4

Steps

14 d=12→d=3
Answer: Bwaitdifferencepropertyprime
Q 20Medium 4 pointsAlgebra
if3 a+2 b=20,a=4 thenb=?
A) 2
B) 4
C) 6

Steps

112+2 b=20→b=4
Answer: Bsubstituteinto
Q 21Hard 5 pointsGeometry
cylinderbasefaceradius 3 height 5 volume? (π≈3.14)
A) 47.1
B) 141.3
C) 282.6

Steps

1πr2h≈141.3
Answer: Bcylindervolume
Q 24Hard 5 pointsNumber Theory
2?×5? = ?
A) 10?
B) 101?
C) 10?

Steps

1(2×5)?=10?
Answer: Aexponentmethodthen
Q 25Hard 5 pointsequation
x2-7 x+12=0 of two ofand?
A) 5
B) 7
C) 12

Steps

1Vietacertainreasoning→and=7
Answer: BVietacertainreasoning
Q 26Hard 5 pointscombination
8 peoplemiddlechoose 2 peoplerespectivelywhenpositivepairgrouplength how many ways?
A) 28
B) 56
C) 72

Steps

1P(8,2)=56
Answer: Bpermutationnumber
Q 28Hard 5 pointsGeometry
squareinsidecutcircleareaand squareareathan? (π≈3.14)
A) π/2
B) π/4
C) π/8

Steps

1(πr2)/(4 r2)=π/4
Answer: Binsidecutcircle
Q 29Hard 5 pointsnumbercolumn
12+22+32+...+102 = ?
A) 330
B) 385
C) 505

Steps

1n(n+1)(2 n+1)/6=385
Answer: Bsquareand formulas
Q 22Hard 5 pointsProbability
roll3die and is 10 of Probability?
A) 1/8
B) 1/12
C) 1/6

Steps

1satisfy itemof combination 27 kinds/216=1/8
Answer: Aenumeratecounting
Q 30Hard 5 pointscombination
1-10 choose 3 makeandis even how many ways?
A) 40
B) 50
C) 60

Steps

13 evenC(5,3)=10+1 even 2 oddC(5,1)×C(5,2)=50→total 60
Answer: Coddevenpointsanalysis

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