Pengi Editor's Note
The Pengi editorial team selected this Think Academy 2022 Math Kangaroo analysis. The real problem walkthroughs and answer key make it a highly practical study resource for Math Kangaroo participants across all divisions.
Source: Think Academy Blog
2022 Math Kangaroo Real Questions and Analysis
In this article, you’ll find:
- A topic distribution chart for the 2022 Math Kangaroo Levels 1–4
- Key concepts tested in each topic
- A question–module mapping table
- Four real 2022 questions with solutions and common mistakes
- Study tips and resources to prepare effectively for Math Kangaroo
2022 Math Kangaroo Overview
The Math Kangaroo competition consists of a single 75-minute multiple-choice test with five answer options per question. Students can participate either online or on paper.
Scoring Structure
- Grades 1–4: 24 questions, maximum score of 96 points
- Grades 5–12: 30 questions, maximum score of 120 points
Learn more about Math Kangaroo Format and Scoring Here: Math Kangaroo FAQ and Resources: Your Ultimate Guide
Levels 1-2 Analysis
Topic Distribution
Detailed Module Summary
| Module | Question Numbers | What It Tests (Brief) |
|---|---|---|
| Spatial | 1, 2, 6, 7, 8, 12, 13, 14, 16, 18, 20, 23 | Visualization, symmetry, spatial transformations, geometric reasoning, and pattern recognition in 2D/3D shapes |
| Number | 3, 4, 5, 9, 15, 17, 19, 21, 22 | Arithmetic reasoning, number patterns, relationships between numbers, and basic operations |
| Reasoning / Logic | 10, 11, 24 | Logical deduction, sequencing, condition analysis, and strategic problem solving |
Spatial Example – Problem 13
Question:
Which option shows the view from above this stack of discs?
Solution:
From a top view, only the upper surfaces of each disc are visible as concentric circles.
Order them from top (center) to bottom (outer ring):
Top → Red → Orange → Blue → Green (bottom).
Answer (E)
Common Mistakes:
- Reversing the stacking order (bottom to top).
- Imagining a side view instead of a top-down perspective.
- Treating the discs as stacked in a line instead of concentric layers.
Number Example – Problem 9
Question:
Kanga wrote down a number and then covered each digit with a shape. She used different shapes for different digits and the same shape for the same digit. Which number could be under the shapes shown to the right?
(A) 34426 (B) 34526 (C) 34423 (D) 34424 (E) 32446
Solution:
The 2nd and 5th symbols are identical (♣), meaning those digits must be equal.
All other symbols are different, meaning the other digits are distinct.
Checking options, only 34424 satisfies these conditions.
Answer (D)
Common Mistakes:
- Ignoring that the same shape corresponds to identical digits.
- Assuming shapes correspond to digits in numerical order.
- Mixing up positions (2nd vs. 5th) when comparing.
Reasoning Example – Problem 24
Question:
There are five numbered cards on the table as shown. You may swap any two cards in a single step. What is the smallest number of steps needed to arrange the cards in increasing order?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
Solution:
Start: 3 4 1 5 2
Swap 3 and 1 → 1 4 3 5 2
Swap 4 and 2 → 1 2 3 5 4
Swap 5 and 4 → 1 2 3 4 5
Minimum swaps = 3.
Answer (C)
Common Mistakes:
- Using adjacent swaps instead of optimal direct swaps.
- Forgetting any two cards may be swapped.
- Stopping early with a partially ordered sequence (e.g., 1 2 3 5 4).
Levels 3-4 Analysis
Topic Distribution
Detailed Module Summary
| Module | Question Numbers | What It Tests (Brief) |
|---|---|---|
| Spatial | 1, 2, 8, 13, 16, 19, 20, 23 | Visualization, symmetry, 2D–3D reasoning, geometric and spatial transformations |
| Number | 5, 7, 9, 10, 14, 15, 17, 18, 21, 24 | Arithmetic reasoning, numerical patterns, algebraic thinking, measurement, and proportional relationships |
| Reasoning / Logic | 3, 4, 6, 11, 12, 22 | Logical deduction, pattern identification, and condition-based reasoning |
Real Questions and Solutions Explained
Spatial Example – Problem 13
Question:
Aladdin has a square carpet. Along each of the four sides there are the same number of dots arranged in two parallel lines. One side of the carpet is folded over (diagram shows one side folded). How many dots are on Aladdin’s carpet?
(A) 48 (B) 44 (C) 40 (D) 36 (E) 32
Solution:
Let each side show \(n\) dots per line.
One border line then has \(4n-4\) dots (the four corners are shared),
and there are two such parallel lines,
so the total is \(2(4n-4)=8n-8\).
From the diagram we read \(n=6\).
Hence total dots \(=8\times6-8=40\).
Answer (C)
Common Mistakes:
- Computing \(4\times2\times n\) and double-counting the four corners.
- Misreading “two lines” as “two dots” per side.
- Letting the fold change the counting logic (the fold hides, but does not change totals).
Number Example – Problem 9
Question:
Five cars numbered 1, 2, 3, 4, and 5 move in the same direction in the order 1–2–3–4–5. First, the last car passes the two cars ahead of it. Next, the second-to-last car passes the two cars ahead of it. Finally, the middle car passes the two cars ahead of it. In what order are the cars now?
(A) 1, 2, 3, 5, 4 (B) 2, 1, 3, 5, 4 (C) 2, 1, 5, 3, 4 (D) 3, 1, 4, 2, 5 (E) 4, 1, 2, 5, 3
Solution:
Start: 1–2–3–4–5.
Step 1: Car 5 passes two cars (3 and 4) → 1–2–5–3–4.
Step 2: Second-to-last is car 3 → passes 2 and 5 → 1–3–2–5–4.
Step 3: Middle is car 2 → passes 1 and 3 → 2–1–3–5–4.
Answer (B)
Common Mistakes:
- Not updating the order after each pass.
- Reading “passes the two cars ahead of it” as “passes any two cars in total.”
- Using the original “middle” car in the last step instead of the new middle.
Reasoning Example – Problem 11
Question:
During my vacation, I sent the five postcards shown below to my friends.
- There are no ducks on Mike’s card.
- Cara’s card has the sun on it.
- There are exactly two living creatures on Paula’s card.
- Lexi’s card has a dog on it.
- There are kangaroos on Heather’s card.
Which card did Mike get?
Solution:
We analyze each statement systematically:
- Heather’s card must have kangaroos → (B).
- Lexi’s card has a dog → (E).
- Cara’s card has the sun → could be (A) or (D), but (A) has no animals. Keep open.
- Paula’s card has exactly two living creatures → (C) fits (ladybug + fly).
- Mike’s card has no ducks, so not (D).
Now assign remaining:
- (B) Heather → kangaroo.
- (E) Lexi → dog.
- (C) Paula → two living creatures.
- (D) Cara → has the sun.
- Remaining card (A) has no ducks and no sun → fits Mike.
Answer: (A)
Common Mistakes:
- Forgetting to exclude cards already assigned before assigning the next.
- Ignoring negative clues such as “no ducks.”
- Misinterpreting “exactly two living creatures” (not decorations like the sun or waves).
2022 Math Kangaroo Answer Key
| Question | Level 1 & 2 | Level 1 & 2 |
|---|---|---|
| 1 | B | A |
| 2 | E | B |
| 3 | B | C |
| 4 | B | C |
| 5 | D | E |
| 6 | B | D |
| 7 | B | A |
| 8 | E | C |
| 9 | A | B |
| 10 | E | C |
| 11 | A | A |
| 12 | D | B |
| 13 | A | E |
| 14 | D | B |
| 15 | C | E |
| 16 | E | B |
| 17 | D | B |
| 18 | A | D |
| 19 | C | E |
| 20 | D | E |
| 21 | C | C |
| 22 | C | B |
| 23 | A | A |
| 24 | C | D |
Best Resources to Prepare for Math Kangaroo
MK Past Papers & 100 Questions Pack
Get instant access to real MK past papers and 100 carefully selected questions — perfect for focused prep!
Math Kangaroo Resource Pack
Free Download: Levels 1–2 & 3–4
Past Exams (2023–2025) & 100-Question Practice Collection
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Recommended Reading
- 2023 Math Kangaroo Real Questions and Analysis
- Math Kangaroo 2025 Results: Scores, Awards & Rankings
- Math Kangaroo: Solutions for 2025 and Preparation for 2026
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