Student: Kangaroo-style practice for Class 11 and 12
Student is the Kangaroo level for Class 11 and 12. A Kiwimath Student paper has 30 questions in three sections worth 3, 4 and 5 points, with five options each, drawn from our Levels 6 and 7 questions.
It is Kangaroo-style practice, not an official paper. Try four questions here, then sit a full paper free.
Sit a Student paper No sign-in needed to start.
Try four Student questions
They cover all three sections. Hints come one step at a time, and nothing you pick is sent anywhere.
A function f satisfies f(x)+f(1-x)=1 for all x. What is the value of S=f!(tfrac1100)+f!(tfrac2100)+cdots+f!(99/100)?
- 2 Worked step, not opened yet
What is in a Student paper, and how is it built?
Student is the top Kangaroo level, for Class 11 and 12: 30 questions in 90 minutes in India, about three minutes each. The questions read like short olympiad problems: polynomials, functions, logarithms, modular arithmetic and triangle geometry.1
Our Student pool has 214 questions and none of them has a picture: every geometry question is given in words, and drawing the figure is part of the work. Questions are longer than at other levels, 17 words on a typical one.
The pool is built from our Level 6 and Level 7 problems, the RMO and INMO part of the climb. Many began as proofs; for a paper, each was turned into a question with one answer and five options, then checked again. Algebra and number theory make up 69% of it.
Which topics carry the points in Student?
Our Student pool has 214 checked questions in 4 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.
| Topic | 3 points | 4 points | 5 points | All |
|---|---|---|---|---|
| Algebra | 48 | 18 | 14 | 80 |
| Number Theory | 34 | 19 | 15 | 68 |
| Geometry | 24 | 14 | 3 | 41 |
| Combinatorics | 7 | 8 | 10 | 25 |
| All topics | 113 | 59 | 42 | 214 |
What should a Student child be able to do?
Polynomials, functions, logarithms, modular arithmetic and triangle geometry, built from our RMO and INMO level problems. Topic by topic, this is what our Student questions ask for.
- Algebra
- Functional equations with a symmetry to exploit, recurrences, geometric sums and inequalities such as AM-GM.
- Number Theory
- The Euclidean algorithm, the highest power of a prime dividing a number, and digit sums modulo 9.
- Geometry
- The angle bisector theorem, tangents and secants from a point, circumradius and area from two sides and an angle.
- Combinatorics
- Extremal questions (the largest set on a board or in a network with some property) and Pick’s theorem.
How do you solve a Student question? One worked through
This is one of the Student samples above, a 5‑point question from our Algebra topic. Try it first if you like; the working is folded away below.
What is 2 + 6 + 18 + ... + 2 · 3⁷?
- 2186
- 6560
- 6561
- 13120
- 19682
What to notice first
Each term is 3 times the one before, so this is a geometric sum. The only real danger is counting the terms.
See it worked through
- Write the terms as 2 × 3⁰, 2 × 3¹, 2 × 3², and so on up to 2 × 3⁷. The powers run from 0 to 7, which is 8 terms.
- A geometric sum with first term a, ratio r and n terms is a(rⁿ − 1)/(r − 1). Here that is 2(3⁸ − 1)/2 = 3⁸ − 1.
- 3⁸ = 6561, so the sum is 6560.
- A quick check with fewer terms: 2 + 6 + 18 = 26 = 3³ − 1. The pattern holds.
The answer is B, 6560.
The tempting wrong answer
The tempting option is 2186, which is 3⁷ − 1, from counting 7 terms instead of 8. Powers that start at 0 are the classic off-by-one.
Ask: “What is 1 + 3 + 9 + … + 3⁷?” (Half of 6560, which is 3280.)
Which mistakes cost marks in Student?
Each one comes from a wrong option in our Student samples and the note we wrote on why it tempts.
- Counting the terms. Exponents from 0 to 7 make 8 terms, not 7. Off-by-one errors cost more Student marks than hard ideas.
- The middle term in a pairing. Pairing f(k/100) with f(1 − k/100) gives 49 pairs, plus an unpaired middle term. Forgetting it gives 49 instead of 99/2.
- Forgetting to halve. The angle between the altitude and the bisector from a vertex is half the difference of the other two angles. Stopping at the difference doubles the answer.
How is a Student paper marked?
A Student 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.
| 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 Student 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 Student?
At this level most of the work is knowing the standard tools well. This eight-week plan assumes your child is already doing school calculus and algebra.
- Weeks 1 and 2Sessions of 45 minutes at Kiwimath Levels 6 and 7. Revise the algebra tools the papers assume: roots of polynomials, logarithms, sums that telescope.
- Weeks 3 to 5Alternate algebra and number theory sessions with one geometry session a week. In every equation, check the conditions: many wrong options come from a root that does not fit.
- Week 6Sit a full paper. Where a direct solution is long, practise working backwards from the options.
- Weeks 7 and 8A full paper each week, and read every worked solution, even for the ones you got right.
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 Student
Why is the Student level built from Level 6 and 7?
Our Levels 6 and 7 are the ones written for Class 11 and 12, so the Student questions come from there, rewritten as five-option questions and checked again. If there are not enough checked questions to fill a full paper, you get a shorter set, and the paper says so.
Does Student preparation help with RMO and INMO?
It helps with the ideas and the speed. RMO and INMO ask for written proofs, though, which a multiple-choice paper cannot practise. Our RMO page explains what RMO asks. RMO preparation.
Why do Student questions have no pictures?
Every geometry question in our Student pool is given in words, as olympiad problems usually are. Drawing a large, accurate figure is part of solving it, and often shows the answer.
Are these real Student papers?
No. They are Kangaroo-style practice made from Kiwimath’s own Level 6 and 7 questions, in the same format. Official past papers come from the organiser in your country. Where to find official past papers.
Student matches Kiwimath Levels 6 and 7
The Student papers are built from Kiwimath Levels 6 and 7, the RMO and INMO part of the climb. Everyday practice at those levels builds the same skills, one question at a time with hints.
Sit a Student 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 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