Junior: Kangaroo-style practice for Class 9 and 10

Junior is the Kangaroo level for Class 9 and 10. A Kiwimath Junior paper has 30 questions in three sections worth 3, 4 and 5 points, with five options each, drawn from our Level 5 questions.

It is Kangaroo-style practice, not an official paper. Try four questions here, then sit a full paper free.

Sit a Junior paper No sign-in needed to start.

Try four Junior questions

They cover all three sections. Hints come one step at a time, and nothing you pick is sent anywhere.

Junior sampleQuestion 1 of 4, worth 3 points

Find the number of ordered pairs (x, y) of positive integers with 1/x + 1/y = 1/3.

2 Strategy, not opened yet
3 Worked step, not opened yet

By Anand Prakash, who makes Kiwimath. Contest facts checked on 27 September 2026 against the organisers’ own pages (sources at the end).

What kind of questions are in a Junior paper?

Junior has 30 questions in 90 minutes in India, about three minutes each. Most questions are short, 15 words on a typical one, but each hides an idea that has to be found before any calculation starts.¹

Only 33 of the 252 questions in our Junior pool have a picture. Junior is mostly words and symbols: identities, factor pairs, counting arguments. Geometry appears as much through counting (points, lines, tilings, paths on a grid) as through angles.

The pool spreads across 6 topics with no single one above 20%. One of them, algebra meets number theory, is where equations need whole-number answers, the bridge into IOQM-style problems.

Which topics carry the points in Junior?

Our Junior pool has 252 checked questions in 6 topics. This is how they spread across the three sections. A paper draws from every row, so a topic with few questions can still appear.

Junior questions by topic and section, from Kiwimath's checked pool
Topic	3 points	4 points	5 points	All
Combinatorics	19	14	17	50
Algebra	18	17	14	49
Number Theory	16	11	17	44
Combinatorial Geometry	13	16	13	42
Algebra meets number theory	12	11	11	34
Geometry	13	5	15	33
All topics	91	74	87	252

What should a Junior child be able to do?

Algebra identities, counting and tilings, divisibility, and geometry with a clever step. Topic by topic, this is what our Junior questions ask for.

Algebra: Identities and roots of quadratics, surds, geometric sums and floor functions, used to avoid long arithmetic.
Algebra meets number theory: Equations with whole-number answers solved by factoring, such as (x − 3)(y − 3) = 9; perfect squares; zeros at the end of n!.
Combinatorics: Arrangements with repeated letters, people who must stand together, and inclusion-exclusion for “no box empty”.
Combinatorial Geometry: Triangles from points, regions made by lines, lattice paths and domino tilings.
Number Theory: Numbers with no factor in common with a given number, primes that leave a given remainder, and differences of squares.
Geometry: Chords and distances from the centre, angles of regular polygons, and areas on a grid.

How do you solve a Junior question? One worked through

This is one of the Junior samples above, a 4‑point question from our Combinatorial Geometry topic. Try it first if you like; the working is folded away below.

In how many ways can a 2×4 board be tiled by 1×2 dominoes?

What to notice first

Listing every tiling of a 2 × 4 board is possible, but easy to get wrong. Looking only at the leftmost column turns it into a pattern.

See it worked through

The leftmost column can be covered in only two ways: one upright domino, or two flat dominoes stacked across the first two columns.
One upright domino leaves a 2 × 3 board; two flat ones leave a 2 × 2 board. So the count for a board of length n is the count for n − 1 plus the count for n − 2.
A 2 × 1 board has 1 tiling and a 2 × 2 board has 2.
So a 2 × 3 board has 2 + 1 = 3 tilings, and a 2 × 4 board has 3 + 2 = 5.

The answer is D, 5.

The tempting wrong answer

The tempting answer is 8, from doubling at every column. Two flat dominoes cover two columns at once, so the choices do not simply double.

Ask: “How many tilings does a 2 × 6 board have?” (13: the counts are the Fibonacci numbers.)

Which mistakes cost marks in Junior?

Each one comes from a wrong option in our Junior samples and the note we wrote on why it tempts.

Ordered or unordered pairs. When a question says ordered pairs, (4, 12) and (12, 4) are different answers. Reading that one word decides between 2 and 3.
Factor pairs of the wrong parity. For n² + 40 to be a square, the two factors of 40 must both be even or both odd. Every factor pair counted gives 4; only 2 of them work.
Subtracting twice. In inclusion-exclusion, cases with two empty boxes are taken away twice. Forgetting to add them back gives 147 instead of 150.

How is a Junior paper marked?

A Junior paper has 30 questions in three sections of 10. Every question has five options, A to E, and exactly one is right. The sections get harder as you go, and so they are worth more.

What each answer is worth
A right answer	3 points in the first section, 4 in the second, 5 in the third.
A wrong answer	Loses a quarter of that question’s points: ¾, 1 or 1¼.
A blank	Nothing gained, nothing lost.
Starting points	You start with 30, one for each question, so no score can fall below zero. The top score is 150.

Kiwimath marks its practice papers this way. Math Kangaroo India, the organiser in India, takes 1 mark off for each wrong answer and gives no starting points, so its Junior top score is 120. Why a blind guess is worth nothing on average, and when guessing starts to pay, is on the Kangaroo-style practice page.

How should my child prepare for Junior?

Junior and IOQM preparation overlap, so this eight-week plan serves both.

Weeks 1 and 2Sessions of 40 minutes at Kiwimath Level 5. Revise identities, factoring and the counting rules until they come without thinking.
Weeks 3 to 5For each counting or tiling question, try the smallest cases first and look for the pattern before reaching for a formula.
Week 6Sit a full paper. Use rough estimates to cross out options first, and record how often that alone found the answer.
Weeks 7 and 8A full paper each week, then read the worked solution even for the questions you got right: a shorter method is worth learning.

For the real contest, check the dates, the rules and the time allowed with Math Kangaroo India or the organiser in your country. Our Math Kangaroo guide covers the official marking and where the past papers are.

All six levels

Pre-EcolierClass 1 and 2Kiwimath Level 124 questions
EcolierClass 3 and 4Kiwimath Level 224 questions
BenjaminClass 5 and 6Kiwimath Level 330 questions
CadetClass 7 and 8Kiwimath Level 430 questions
JuniorClass 9 and 10Kiwimath Level 530 questions
StudentClass 11 and 12Kiwimath Levels 6 and 730 questions

Questions parents ask about Junior

Is Junior useful for IOQM preparation?

Very. Junior covers the same four areas as IOQM at a gentler level, and multiple-choice practice builds the speed IOQM needs. Everyday Kiwimath Level 5 practice serves both. IOQM preparation.

Why are there so few diagrams in Junior?

At this level geometry is often about counting, such as lines, points and tilings, and the algebra questions need no picture at all. A child should draw their own sketch for any question that describes a shape.

What if my child finds the 5-point questions impossible?

That is common at the start. Make sure the first two sections are secure, because they carry most of the paper’s questions, then add one 5-point question a day with its worked solution.

Are these real Junior papers?

No. They are Kangaroo-style practice made from Kiwimath’s own Level 5 questions, in the same format. Official past papers come from the organiser in your country. Where to find official past papers.

Junior matches Kiwimath Level 5

Everyday Kiwimath practice at Level 5 builds the skills a Junior paper tests, one question at a time, with hints and a solution after each answer.

Sit a Junior paper Free during early access.

Sources

Kiwimath is not connected with Math Kangaroo, Math Kangaroo India or Kangourou sans Frontières. Our papers are Kangaroo-style practice made from Kiwimath’s own questions; no question is taken from a real Kangaroo paper. Contest facts were checked on 27 September 2026 against these pages. If something here differs from what the organiser says, trust the organiser, and write to hello@kiwimaths.com so we can fix it.

Contest categoriesMath Kangaroo India, the organiser in India
Scoring systemMath Kangaroo India, the organiser in India
Exam datesMath Kangaroo India, the organiser in India
Kangourou sans FrontièresThe international association behind the contest
Free sample questions and answer keysMath Kangaroo USA, the organiser in the United States