Confirmed exam pattern (SOF IMO, Class 3):
| Section | Questions | Marks each | Total |
|---|---|---|---|
| 1. Logical Reasoning | 10 | 1 | 10 |
| 2. Mathematical Reasoning | 10 | 1 | 10 |
| 3. Everyday Mathematics | 10 | 1 | 10 |
| 4. Achievers Section | 5 | 2 | 10 |
| Total | 35 | — | 40 |
60 minutes · No negative marking · Sections 2 and 3 share the same syllabus (Section 3 just applies it to real-life situations). The Achievers Section reuses Section 2's topics at a harder, multi-step level.
Each topic below follows the same structure:
(10 topics — these also form the syllabus for Section 1 of most other SOF Olympiads, so mastering these helps across exams.)
What it is: A pattern is a sequence — of shapes, numbers, or letters — that changes by a fixed rule. Solving it means finding the rule from the first few items, then applying it.
Worked Examples:
How to teach it: Write only the first 3–4 terms on the board and ask "what's changing, and by how much?" before revealing more terms. Physically acting out a pattern (clap-clap-stomp, clap-clap-stomp) helps students who struggle with the abstract number/shape version.
Practice Problems:
Answers: 1) 15 (add 3) · 2) 🔵 (pattern repeats every 3) · 3) 16 (differences are 1,2,3,4,5) · 4) V (going backward through the alphabet)
What it is: Analogy finds a hidden relationship ("A is to B as C is to __"). Classification sorts items into a group by a shared property and finds the one that doesn't belong.
Worked Examples:
How to teach it: For analogies, always ask students to say the relationship out loud in a full sentence first ("a shoe protects a foot") before hunting for the matching word — this stops random guessing. For classification, ask "what property do three of these share that the fourth doesn't?"
Practice Problems:
Answers: 1) Cut · 2) Cow · 3) Carrot (a vegetable; the rest are fruits) · 4) Hammer (a tool, not a profession)
What it is: Knowing each letter's fixed position (A=1 … Z=26) so you can find letters that come before, after, or a set number of steps away.
Worked Examples:
How to teach it: Keep a printed alphabet strip visible during every lesson on this topic — nearly all mistakes here are miscounting, not real confusion, and a visible strip fixes that instantly.
Practice Problems:
Answers: 1) H · 2) F · 3) F (D,E,F,G,H) · 4) B, K, R, W
What it is: A secret code replaces every letter using one fixed rule — most often "shift forward/backward by a number." Once the rule is known, any word can be coded or decoded the same way.
Worked Examples:
How to teach it: Start every new student on the "+1" rule only, using very short 3-letter words, and only add harder rules (+2, −1, reversing letter order) once they're fast and accurate at "+1."
Practice Problems:
Answers: 1) QFO · 2) PET · 3) CNF · 4) EAV
What it is: Finding a position in a line or order using clues like "Nth from the left/right" or comparison words like "taller than."
Worked Examples:
How to teach it: Physically line up 6–8 students and ask the class to work out ranks from both ends — this makes the "add both ranks, subtract 1" rule obvious rather than something to memorise blindly.
Practice Problems:
Answers: 1) 5+4−1=8 · 2) 11−6+1=6th · 3) Z · 4) 4th
What it is: Grouping sorts shapes by a shared feature. A figure matrix is a 3×3 grid with one picture missing — find the rule running across rows and down columns to work out the missing piece.
Worked Examples:
How to teach it: Before showing a full 3×3 matrix, isolate just one row and ask "what's the rule here?" then just one column and ask the same — combining both rules only after each is understood separately.
Practice Problems:
Answers: 1) {Red star, Red square} and {Blue circle, Blue triangle} · 2) 12 (following the ×3 rule: 4,8,12) · 3) an even larger circle · 4) {Triangle, Triangle} and {Circle, Square} separately, or Circle alone (0 corners) is the true odd one
What it is: A mirror image flips a picture left-to-right, as in a real mirror — this is different from rotating (turning) a picture.
Worked Examples:
How to teach it: Use an actual small mirror in class. Hold it next to a letter or simple picture and let students see the flip happen live — this topic is one of the few in the syllabus that's much harder to grasp from a still picture than from a live demonstration.
Practice Problems:
Answers: 1) A backward "E" (like Ǝ) · 2) No — mirroring flips left-right, not upside down · 3) It would show what looks like 9:00, since the hand position flips · 4) Right hand
What it is: Recognising and naming common 2D shapes and 3D solids, and counting their sides/corners (2D) or faces/edges (3D).
Worked Examples:
How to teach it: Have real objects on hand (a ball for sphere, a dice/box for cube, a cone-shaped party hat) so 3D shapes aren't just flat drawings — students often confuse a drawn cube with a square until they've held an actual cube.
Practice Problems:
Answers: 1) 6 · 2) 4 · 3) Sphere (a ball) · 4) 6
What it is: A small, simple shape is hidden inside a larger, busier drawing, and must be found by tracing lines carefully.
Worked Examples:
How to teach it: Give students a highlighter to trace the hidden shape directly on the page rather than just pointing — the act of tracing catches lines the eye alone misses, and it is far more effective than "just look carefully."
Practice Problems:
Answers: 1) Four straight lines meeting at right angles, even if formed by different triangles' edges · 2) False — size can vary · 3) A highlighter/coloured pencil to trace lines · 4) Yes
What it is: "Days and dates" uses the fact that a week always has 7 days to find what day a future/past date falls on. "Possible combinations" counts every possible pairing from two or more groups by multiplying the group sizes.
Worked Examples:
How to teach it: For days/dates, use a real wall calendar and physically count forward in weeks. For combinations, draw a simple grid (one group across the top, the other down the side) and count the boxes — this "grid method" prevents students from missing or double-counting combinations.
Practice Problems:
Answers: 1) Monday (14 days later = exactly 2 weeks) · 2) 11÷7=1 week+4 days → Friday+4=Tuesday · 3) 2×3=6 · 4) 4×2=8
(Same syllabus for both sections — Section 2 asks it as a reasoning puzzle, Section 3 asks it as a real-life situation. 12 topics.)
What it is: Reading and writing numbers both as digits (numerals, e.g. 245) and in words (number names, e.g. "two hundred forty-five"), up to 4-digit numbers.
Worked Examples:
How to teach it: The most common student error is writing "9009" as "9990" or similar — always say the number aloud digit-by-digit (nine-thousand, zero-hundred, zero-tens, nine) while writing it, so the zeros aren't skipped.
Practice Problems:
Answers: 1) Three thousand four hundred fifty-six · 2) 7020 · 3) Five thousand five · 4) 4404
What it is: Understanding place value (thousands, hundreds, tens, ones) so you can compare, order, and break apart 4-digit numbers.
Worked Examples:
How to teach it: Use a simple place-value chart (Thousands | Hundreds | Tens | Ones columns) on the board for every number until students can do it mentally — comparing digit-by-digit from the left is the key skill, not guessing by "which number looks bigger."
Practice Problems:
Answers: 1) 700 (hundreds place) · 2) 6243 · 3) 4000+0+50+9 · 4) 3210, 3201, 3021
What it is: Addition, subtraction, multiplication, and division with numbers appropriate for Class 3 (typically up to 4-digit numbers for +/−, and small multiplication/division facts).
Worked Examples:
How to teach it: For addition/subtraction with carrying/borrowing, always align digits by place value in a column and work right to left, saying each step aloud ("5 plus 4 is 9, write 9" etc.) — most errors come from misaligned columns, not from not knowing the facts.
Practice Problems:
Answers: 1) 5689 · 2) 2544 · 3) 54 · 4) 7
What it is: A fraction represents a part of a whole (e.g. 1/2 = one of two equal parts). Class 3 focuses on simple fractions like halves, thirds, and quarters, and comparing them.
Worked Examples:
How to teach it: Always use a physical object (a paper circle folded into halves/quarters, or real fruit cut into pieces) before moving to numbers on a page — fractions are one of the hardest abstract ideas at this age, and a hands-on model makes "bigger denominator = smaller piece" intuitive.
Practice Problems:
Answers: 1) 3 oranges · 2) 1/3 · 3) 10 sweets · 4) 2/6 = 1/3
What it is: Measuring how long/tall/far something is, using units like centimetres (cm) and metres (m), where 1 m = 100 cm.
Worked Examples:
How to teach it: Bring an actual metre ruler/tape and have students measure real classroom objects — this builds a physical sense of "how long is a metre" that no worksheet can substitute for.
Practice Problems:
Answers: 1) 300 cm · 2) 4.5 m · 3) 1 m (100 cm) is longer · 4) 4 m 20 cm (2m+1m=3m, 30cm+90cm=120cm=1m20cm, total 4m 20cm)
What it is: Measuring how heavy something is, using grams (g) and kilograms (kg), where 1 kg = 1000 g.
Worked Examples:
How to teach it: If a kitchen or classroom weighing scale is available, let students weigh a few familiar objects — the surprise of "that's heavier/lighter than I thought" is a strong memory hook for the unit sizes.
Practice Problems:
Answers: 1) 3000 g · 2) 1 kg 500 g · 3) 1 kg (1000 g) is heavier · 4) 1050 g = 1 kg 50 g
What it is: Measuring how much liquid a container holds, using millilitres (ml) and litres (l), where 1 l = 1000 ml.
Worked Examples:
How to teach it: Use a measuring jug with water and everyday containers (a cup, a small bottle) to physically show how many "cups" fill a litre — capacity is much easier to grasp by pouring than by reading numbers.
Practice Problems:
Answers: 1) 2000 ml · 2) 2 l 500 ml · 3) 1 l (1000 ml) holds more · 4) 1200 ml = 1 l 200 ml
What it is: Reading temperature using a thermometer, in degrees Celsius (°C), and understanding hot vs. cold in everyday contexts.
Worked Examples:
How to teach it: If a real (or toy) thermometer is available, show how the liquid rises with heat (e.g., holding it near a warm hand vs. leaving it in cool air) — this makes "higher number = hotter" concrete rather than a rule to memorise.
Practice Problems:
Answers: 1) Hotter · 2) 0°C · 3) 100°C · 4) 8°C
What it is: Reading clocks (analog and digital), understanding hours/minutes, and simple time calculations.
Worked Examples:
How to teach it: Use a real or paper clock with movable hands — physically moving the hands to "add 45 minutes" or "add 2 hours" builds the skill far faster than doing it purely with numbers.
Practice Problems:
Answers: 1) 5:15 · 2) 1:00 · 3) 6:15 · 4) 45 minutes
What it is: Counting money (coins and notes), and simple addition/subtraction involving rupees and paise (or the local currency's equivalent units).
Worked Examples:
How to teach it: Play-money or real coins for a simple "classroom shop" activity (pricing pencils, erasers, etc., and having students "buy" them) makes this topic feel real rather than abstract.
Practice Problems:
Answers: 1) ₹40 · 2) ₹115 · 3) ₹20 · 4) ₹33
What it is: Basic shapes (recognising and naming 2D shapes and simple 3D solids) and very basic ideas of position (inside/outside, above/below).
Worked Examples:
How to teach it: Overlap this lesson with the "Geometrical Shapes" reasoning topic (A8) — since the content is nearly identical, teaching them together saves time and reinforces the same shapes from two angles (naming vs. spotting them in puzzles).
Practice Problems:
Answers: 1) 4 · 2) Cone · 3) Above · 4) 4
What it is: Reading and interpreting simple data shown in pictographs (picture-based charts) and basic bar graphs.
Worked Examples:
How to teach it: Before reading any pre-made graph, have the class create their own simple pictograph from a real classroom count (e.g., favourite fruit, by show of hands) — building a graph from scratch makes reading someone else's graph far easier afterward.
Practice Problems:
Answers: 1) 20 pencils (4×5) · 2) Riya · 3) Tuesday · 4) 12 units (6×2)
The Achievers Section reuses everything in Part B, but asks it in a harder, often two-step way. Recognising the pattern below is the single best way to prepare.
Pattern 1 — Combine two facts: "A shop sells pencils at ₹8 each. If Rani buys 3 pencils and pays with a ₹50 note, how much change does she get?" (combines multiplication B3 + money B10: 3×8=24, 50−24=26 → ₹26 change)
Pattern 2 — Compare two quantities: "Ravi's pencil is 12 cm long. Meena's pencil is 1 m − 88 cm long. Whose pencil is longer?" (combines length units B5: 1 m − 88 cm = 100−88=12 cm — they are equal in length!)
Pattern 3 — Multi-step word problem: "A bottle holds 2 litres. If Anil pours out 750 ml, then adds back 300 ml, how much water is in the bottle now?" (combines capacity B7: 2000−750+300 = 1550 ml = 1 l 550 ml)
Pattern 4 — Data + reasoning together: "A pictograph shows 4 symbols for Class A and 3 for Class B, with each symbol = 6 students. How many more students are in Class A than Class B?" (combines data handling B12 + subtraction: 4×6=24, 3×6=18, 24−18=6 more students)
How to teach this section: Once a student can solve a Part B topic confidently on its own, immediately follow up with a version that combines it with one other topic (money+multiplication, length+subtraction, etc.) — that habit alone is what the Achievers Section is testing.
Once a topic is understood here, move to the matching IMO Class 3 mock exam questions built earlier in this conversation to practice it under timed conditions.