Stage 01 · Year 5–6 · Age 9–11
Primary Stage — The Primary Kangaroo, Where the British Maths Pathway Begins
The Primary Kangaroo is the single UKMT competition at primary level: a twenty-problem multiple-choice paper sat each March in Year 5 and Year 6. It is the first formal mathematics competition most British schoolchildren encounter, and it serves as the on-ramp to the Junior stage from age twelve onwards.
Primary Kangaroo at a glance
Primary stage
problems
duration
(age 9–11)
Overview
What the Primary Kangaroo Is, and Who It Is For
The Primary Kangaroo is a national mathematics competition for British students in Year 5 and Year 6, sat each March (typically a one-week window, 19–26 March) and run by the UK Mathematics Trust. It is the lone event in the Primary stage of the UKMT pipeline, and is designed to identify the strongest mathematical thinkers in upper primary classrooms before they move into Year 7 and the much busier Junior stage.
The Primary Kangaroo is sat in schools across the United Kingdom within a one-week window in March (typically 19–26 March). Schools register their participating students with UKMT in advance and pay a per-student entry fee; the paper is administered by the school’s teaching staff using materials sent by UKMT, and answer sheets are returned for centralised marking. Results are returned to schools in early spring of the following year.
The paper itself is twenty multiple-choice problems sat over forty-five minutes. There is no calculator allowed, and students mark answers on a UKMT answer sheet. Problems are graded in difficulty from straightforward arithmetic and pattern-recognition at the start of the paper to substantially more demanding combinatorics and geometry at the end, where students typically need to combine two or three pieces of school-taught mathematics in a single argument. Positive marking only — there is no penalty for incorrect answers.
Unlike at the older stages, there is no Olympiad follow-on for the Primary Kangaroo. The paper stands alone. Every participant receives a Certificate of Success, and the top scorers are recognised with “Best in Class” and “Best in Year” rosettes — there is no Gold/Silver/Bronze percentile certificate system at Primary level (that begins with the Junior Mathematical Challenge in Year 7). There is no further sitting at Primary level — strong Primary Kangaroo scorers naturally roll forward into the Junior Mathematical Challenge in Year 7.
The Primary Kangaroo’s design intent is broad: get younger students used to competitive mathematics in a low-stakes, well-structured setting, and identify a strong cohort that can be encouraged into the Junior pipeline the following year. For most British schools that participate, the Primary Kangaroo is the first formal mathematics competition any of their students will sit.
Format
Primary Kangaroo — Paper Format and Marking
A single forty-five-minute, twenty-problem multiple-choice paper, sat in March of each academic year (a one-week window, typically 19–26 March). No calculator permitted. Positive marking throughout — there is no penalty for incorrect answers.
Primary Kangaroo · PK
Format at a glance
- SatMarch, a one-week window each year (typically 19–26 March)
- Duration45 minutes from start to finish
- Problems20 multiple-choice, graded in difficulty
- CalculatorNot permitted
- MarkingCentralised UKMT marking; results in spring
- AwardsCertificate of Success for all participants; "Best in Class" and "Best in Year" rosettes for top scorers
- EligibilityUK students in Year 5–6, registered through their school
- EntryThrough school registration with UKMT; per-student fee
Problem Style
A Representative Primary Kangaroo Problem
Primary Kangaroo problems tend to be short, vivid and reward careful counting or pattern-recognition over mechanical arithmetic. The hardest questions at the end of the paper combine two or three pieces of school-taught mathematics in a single argument. Below is a representative problem in the Primary Kangaroo style.
Problem (in Primary Kangaroo style)
Anna writes down all the whole numbers from 1 to 50 in a list, then crosses out every multiple of 3 and every multiple of 5. How many numbers remain on her list?
What the question rewards
This question tests a Year 5 student’s ability to combine two simple counting principles: count the multiples of 3, count the multiples of 5, but subtract the multiples of 15 (which were counted twice). It is an early introduction to the inclusion-exclusion principle in a friendly form, with all the arithmetic well within Year 5 capability.
A strong student would set up the calculation cleanly: 16 multiples of 3, 10 multiples of 5, 3 multiples of 15, so the count of crossed-out numbers is 16 + 10 − 3 = 23, leaving 50 − 23 = 27 numbers on the list. A clean argument earns full marks; a guess at one of the multiple-choice options does not.
The Primary Kangaroo paper has a dozen problems at roughly this level, with the final three or four substantially harder. The aim is broad accessibility at the easier end and a clear ceiling at the harder end so that the top-scoring students stand out.
What Comes Next
After the Primary Kangaroo — the Junior Stage
There is no Olympiad follow-on at Primary level. Strong Primary Kangaroo students naturally move into Year 7 and the Junior stage of the UKMT pipeline, which carries three events — the Junior Mathematical Challenge, the Junior Kangaroo follow-on, and the Junior Mathematical Olympiad. The JMO is the first written Olympiad in the pipeline.
Frequently Asked
Five Questions about the Primary Kangaroo
Five questions parents most often ask about the Primary Kangaroo. All answers are verified against UKMT primary-stage publications.
- Who can sit the Primary Kangaroo?
- The Primary Kangaroo is open to UK students in Year 5 and Year 6, equivalent to ages 9 to 11. Students sit the paper in their own school during the national sitting window in March (typically the week of 19–26 March). Schools register their participating students with UKMT and pay a per-student entry fee. Younger students at exceptional ability levels may also be entered at the school’s discretion, but this is rare.
- How long is the paper, and is a calculator allowed?
- The Primary Kangaroo paper is forty-five minutes long and consists of twenty multiple-choice problems. No calculator is permitted; students work with pencil and paper only and mark their final answer choices on a UKMT answer sheet which is returned for centralised marking. Positive marking is used throughout — there is no penalty for incorrect answers.
- What kinds of problems appear on the paper?
- Problems range from straightforward arithmetic and pattern-recognition at the start of the paper to substantially more demanding combinatorics, number-pattern, and elementary geometry questions at the end. The hardest problems typically require combining two or three pieces of school-taught mathematics in a single argument. The aim is broad accessibility at the easier end and a clear ceiling at the harder end.
- Are there awards or certificates?
- Yes, but the Primary Kangaroo does not use the Gold/Silver/Bronze percentile system found at older stages. Every participant receives a Certificate of Success, and the top scorers are recognised with “Best in Class” and “Best in Year” rosettes. Schools also receive notification from UKMT highlighting their strongest students. The Gold/Silver/Bronze certificate system begins with the Junior Mathematical Challenge in Year 7.
- What comes next after the Primary Kangaroo?
- There is no Olympiad follow-on at Primary level. Strong Primary Kangaroo students naturally move into the Junior stage in Year 7, sitting the Junior Mathematical Challenge in April of Year 7 or Year 8, and progressing into the Junior Kangaroo and Junior Mathematical Olympiad if their JMC score is strong enough to invite follow-on entry.
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Get Advice on Entering the Primary Kangaroo from Outside the UK
For parents in international schools and overseas British-curriculum primary settings, the WhatsApp advisor can help with school registration questions, eligibility, and what to expect on Primary Kangaroo sitting day. Written exchanges in English or Chinese welcomed.