Cadet: Kangaroo-style practice for Class 7 and 8
Cadet is the Kangaroo level for Class 7 and 8. A Kiwimath Cadet paper has 30 questions in three sections worth 3, 4 and 5 points, with five options each, drawn from our Level 4 questions.
It is Kangaroo-style practice, not an official paper. Try four questions here, then sit a full paper free.
Sit a Cadet paper No sign-in needed to start.
Try four Cadet questions
They cover all three sections. Hints come one step at a time, and nothing you pick is sent anywhere.
Find the remainder when 5678 is divided by 9.
- 2 Strategy, not opened yet
- 3 Worked step, not opened yet
What does a Cadet paper test that school maths does not?
Cadet has 30 questions in 90 minutes in India, about three minutes each, like Benjamin. What changes is the content: the topics are the ones olympiads build on, number theory, counting and geometry, and a fast method often matters more than a correct slow one.1
Our Cadet pool of 220 questions splits almost evenly between number theory, combinatorics and geometry, with algebra a smaller fourth. 79 questions, 36%, carry a diagram, more than at any other level, because Cadet is where geometry becomes a real part of the paper.
In our pool the 5-point section is the largest of the three. Two thirds of the algebra questions sit there: ages, coins and equations where setting up the problem is most of the work.
Which topics carry the points in Cadet?
Our Cadet pool has 220 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 |
|---|---|---|---|---|
| Combinatorics | 23 | 21 | 20 | 64 |
| Number Theory | 22 | 21 | 21 | 64 |
| Geometry | 23 | 15 | 23 | 61 |
| Algebra | 10 | 0 | 21 | 31 |
| All topics | 78 | 57 | 85 | 220 |
What should a Cadet child be able to do?
Remainders and divisibility, counting arrangements, ages and equations, and the first real geometry. Topic by topic, this is what our Cadet questions ask for.
- Number Theory
- Remainders and digit sums, divisibility tests, HCF and LCM in timetable problems, and negative numbers on the number line.
- Combinatorics
- The multiplication rule for choices, arrangements without repeats, overlaps of two groups, and probabilities as fractions in lowest terms.
- Geometry
- Angle sums of polygons, diagonals, areas of triangles and rectangles, and the 3-4-5 right triangle.
- Algebra
- Ages, coins and mixtures turned into one equation, simple inequalities, and expanding (a + b)².
How do you solve a Cadet question? One worked through
This is one of the Cadet samples above, a 5‑point question from our Algebra topic. Try it first if you like; the working is folded away below.
There are 12 coins of ₹1 and ₹5 worth ₹40 in all. How many ₹1 coins are there?
- 5
- 6
- 7
- 8
- 28
What to notice first
Two kinds of coin, a count and a total: one equation does it, but a swapping argument is quicker and needs no algebra.
See it worked through
- Pretend all 12 coins are ₹5 coins. They would be worth ₹60, which is ₹20 too much.
- Swapping one ₹5 coin for a ₹1 coin lowers the total by ₹4.
- To lose ₹20 we need 20 ÷ 4 = 5 swaps, so there are 5 coins of ₹1.
- With algebra: if x coins are ₹1, then x + 5(12 − x) = 40, so 60 − 4x = 40 and x = 5. Check: ₹5 + 7 × ₹5 = ₹40.
The answer is A, 5.
The tempting wrong answer
A slip to watch for is answering 7, the number of ₹5 coins, after solving the right equation for the wrong letter. Reading the question once more before choosing catches it.
Ask: “Could 12 such coins ever be worth ₹41?” (No: every total is 12 plus a multiple of 4.)
Which mistakes cost marks in Cadet?
Each one comes from a wrong option in our Cadet samples and the note we wrote on why it tempts.
- A remainder bigger than the divisor. Digit sums give 26 for 5678 ÷ 9, and 26 is an option. A remainder on division by 9 is always less than 9, so keep going: the answer is 8.
- A common multiple that is not the first. Runners with 12- and 16-minute laps meet at 96 and 192 minutes too. The question asks when they first meet: the LCM, 48.
- Even numbers and the last digit. An even number is decided by its last digit only. Children who make the first digit even as well undercount.
How is a Cadet paper marked?
A Cadet 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 Cadet 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 Cadet?
Cadet questions build on tools that take time to learn. Start ten weeks out if you can; this plan shows the last eight.
- Weeks 1 and 2Sessions of 30 to 40 minutes at Kiwimath Level 4. Learn and use the digit-sum rule for 3 and 9, and the LCM by listing multiples.
- Weeks 3 to 5One session a week on each of number theory, counting and geometry. In geometry, draw every figure large and mark what you know on it.
- Week 6Sit a full paper. Afterwards sort the lost points into “did not know the tool” and “knew it but slipped”. They need different fixes.
- Weeks 7 and 8A full paper each week. Before moving on from any answer, put it back into the question, especially in the 5-point section.
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 Cadet
Is Cadet the same as Class 7 and 8 school maths?
It uses the same facts, but asks them in ways school tests rarely do. Remainders, counting arrangements and angle chasing carry far more weight in Cadet than in most school syllabuses.
How much geometry does Cadet need?
More than earlier levels. Angle sums, areas of triangles and rectangles and the Pythagoras relation for simple triangles cover much of what our Cadet geometry asks. Drawing the figure to scale often shows the answer.
Does Cadet practice help with IOQM later?
Yes. The three big Cadet topics, number theory, counting and geometry, are the backbone of IOQM. Our IOQM pages explain who can sit it and what it covers. IOQM preparation.
Are these real Cadet papers?
No. They are Kangaroo-style practice made from Kiwimath’s own Level 4 questions, in the same format. Official past papers come from the organiser in your country. Where to find official past papers.
Cadet matches Kiwimath Level 4
Everyday Kiwimath practice at Level 4 builds the skills a Cadet paper tests, one question at a time, with hints and a solution after each answer.
Sit a Cadet 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