Maths · Suggested Grade 6

SOF IMO Class 6 Practice 2026–27: Reasoning & Worked Answers

A wrong answer can reveal more than a rushed score. Use this original Class 6 practice set to find whether the next useful step is reading a condition, drawing a model or checking a calculation.

Original explanations and practice by BananaLearn · Published 31 October 2026 · Check your school’s teaching sequence.

On a small screen, swipe across the illustration to read every label.

The arrows show the order. To reverse the machine, undo the last operation first.
The arrows show the order. To reverse the machine, undo the last operation first.

What is confirmed for the 2026–27 exam?

The SOF website lists the remaining Level 1 IMO dates as 26 November and 10 December 2026; its first listed date, 23 October, has passed. Your school selects its exam date. Confirm your own arrangements with the school rather than treating all three dates as sittings you can freely choose. This guide was checked on 31 October 2026.

The official Class 6 syllabus page lists reasoning plus topics including patterns, lines and angles, number play, data, factors, perimeter and area, fractions, constructions, symmetry and integers. Its Level 1 pattern for Classes 5–10 has 50 questions in one hour, with four sections. This page is a short targeted practice resource, not a full-length mock and not a replacement for the official syllabus.

All questions below are original BananaLearn questions. They are not official SOF sample questions, previous-year questions, leaked questions or predictions of what will appear. No exam-coaching result or score improvement is promised.

Use the set in three passes

First, solve without looking at answers and write a brief reason. Leave a question if you cannot identify what it is asking; a guess can hide a useful learning gap. Second, open the explanation and compare the method, not just the final answer. Third, return the next day and solve a changed version without the explanation.

Use an error log with five fields: question; my method; the condition I missed; corrected method; a changed question to try tomorrow. Distinguish a reading error from a concept gap or calculation slip. A parent can ask the child to explain one correction rather than supervise an hour of identical worksheets.

Do not convert the score on this small mixed set into a predicted rank or qualifying mark. The official paper has its own content distribution and difficulty. Choose a manageable untimed first attempt before adding a time limit; speed is useful only when the child understands the method.

Worked case 1: a pattern with a changing step

Sequence: 3, 6, 11, 18, 27, __. The differences are 3, 5, 7 and 9. Continuing this intended odd-number difference pattern gives the next difference 11, so the next term is 38. Merely noticing that the values increase is not enough to select the next term.

Finite sequences can fit more than one mathematical rule. In school pattern questions, use the simplest rule supported by the given structure and answer choices, and state that rule. If an explanation says add 2 each time, check it against every adjacent pair before accepting it.

Worked case 2: identical packs without leftovers

A teacher has 36 blue counters and 48 yellow counters. She wants the greatest number of identical packs, with none left over. The number of packs must divide both 36 and 48, so use their highest common factor: 12. Each pack gets 3 blue and 4 yellow counters.

The answer depends on the question. Greatest number of packs is 12; counters in each pack is 7. Writing 7 when asked for the number of packs is a reading error even if the division was correct. A quick check is 12×3=36 and 12×4=48.

Worked case 3: area and perimeter together

A rectangle has whole-number side lengths and perimeter 30 cm. If its length is 9 cm, then 2×(9+width)=30. Hence 9+width=15 and width=6 cm. Its area is 9×6=54 cm². The perimeter is a boundary length, whereas area measures the covered surface.

A picture helps: label both lengths as 9 and the other two as unknown. Do not divide 30 by 9, and do not give the area unit as cm. Change the length to 10 cm: width becomes 5 cm and area 50 cm², even though the perimeter stays 30 cm.

Worked case 4: read a number-machine diagram

The illustration uses two operations in order: multiply by 3, then subtract 2. Input 6 gives 18−2=16. To recover the input from output 25, reverse the operations: add 2, then divide by 3. The input is 9.

The order matters. Subtracting 2 from 6 and then multiplying by 3 would give 12, which is a different machine. If a child confuses the order, trace one arrow at a time and write the intermediate number. Then test the recovered input through the original forward machine.

Plan the remaining preparation around evidence

Choose two weak topics from the error log, not ten new topics at once. For each, complete one worked example, three independent questions and one question with a changed condition. On a later day, mix the topics so the child has to choose the method without a heading revealing it.

If your school uses the 26 November sitting, there are several weeks to revisit mistakes rather than cram. A 10 December sitting gives a different calendar; confirm the school date first. A useful weekly rhythm is one focused practice day, one mixed review day and one short explanation check. Adjust it around schoolwork and rest.

Use the official SOF page for exam arrangements and sample-paper links. Use our library for the underlying ideas: HCF, angles, ratio, integers and data. School textbooks remain useful for prerequisites. Ask about general school-topic support if needed; this page does not claim that BananaLearn operates a dedicated SOF preparation course.

14 questions with explained answers

Try each question before revealing the answer. Explain your method, then change one detail and check whether the same reasoning still works.

  1. Using the intended difference pattern, continue 4, 9, 16, 25, __.

    Show answer and explanation

    36
    These are consecutive squares 2², 3², 4², 5²; the next is 6². The differences also continue 5,7,9,11.

  2. Find the missing input: multiply by 3, subtract 2, output 19.

    Show answer and explanation

    7
    Reverse: (19+2)÷3=7. Forward check: 7×3−2=19.

  3. What is the greatest number of identical packs from 24 red and 40 green beads, without leftovers?

    Show answer and explanation

    8 packs
    HCF(24,40)=8. Each pack contains 3 red and 5 green beads.

  4. A square has perimeter 36 cm. Find its area.

    Show answer and explanation

    81 cm²
    Each side is 36÷4=9 cm, so area=9×9. Do not square the perimeter.

  5. A 7 m by 4 m rectangle needs ribbon around its edge. How much ribbon, excluding overlap?

    Show answer and explanation

    22 m
    Perimeter=2×(7+4)=22. The word around asks for boundary length.

  6. A library lends 18 books on Monday, 24 on Tuesday and 15 on Wednesday. What is the total?

    Show answer and explanation

    57 books
    18+24+15=57. Label the total; do not average because total was requested.

  7. A turn starts facing north. Turn clockwise through 90°, then anticlockwise through 180°. Which direction now?

    Show answer and explanation

    West
    North to east, then a half-turn from east to west. Draw the compass directions if needed.

  8. Start at −3 on a number line and move 8 steps right. Where do you finish?

    Show answer and explanation

    5
    −3+8=5. Right increases the value, including while crossing zero.

  9. A ribbon is 3/4 m long. A 1/8 m piece is cut off. What remains?

    Show answer and explanation

    5/8 m
    3/4=6/8. Subtract one eighth from six eighths.

  10. A bag has 5 red, 3 blue and 2 yellow counters. Which colour is most likely on a random draw?

    Show answer and explanation

    Red
    Five red counters exceed the count of either other colour. The probability is 5/10 if each counter is equally likely.

  11. What is the smallest positive integer divisible by both 6 and 8?

    Show answer and explanation

    24
    List multiples or use prime factors: 6=2×3 and 8=2³, so LCM=2³×3.

  12. Two adjacent angles on a straight line are 65° and x°. Find x.

    Show answer and explanation

    115°
    They add to 180°. Subtract 65 from 180; this is not a full 360° turn.

  13. A rectangle has area 48 cm² and length 8 cm. Find its perimeter.

    Show answer and explanation

    28 cm
    Width=48÷8=6 cm. Then perimeter=2×(8+6)=28 cm. Finding the width is only the first step.

  14. A machine doubles a number, then adds 5. The output is 29. What was the input?

    Show answer and explanation

    12
    Reverse: (29−5)÷2=12. Doubling 12 and adding 5 returns 29.

Keep the ideas connected

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Examples, diagrams and questions are original BananaLearn work. They are not copied textbook solutions, official exam questions or an endorsed assessment. Grade labels are suggestions, not a promise about every school’s syllabus.

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