What is the IMO pattern for Class 3?

35 multiple-choice questions for 40 marks in one hour: Logical Reasoning (10), Mathematical Reasoning (10), Everyday Mathematics (10), and 5 Achievers questions worth 2 marks each. There is no negative marking.

Is this a real IMO paper?

No. Every question is written by us in the published pattern, so it is safe to print and share. We are not connected with the Science Olympiad Foundation, which runs the IMO.

How should my child use it?

Sit it in one go with a 60-minute timer, then mark it with the answers at the end. Go back over the questions that were missed: the working shows the method for each.

Can we practise with more papers?

Yes. Sit a new paper online and every one is different. A free account includes 3 practice tests, and the India pack (₹499 for 6 months) opens unlimited tests with the answers and working.

IMO Sample Paper Class 3 with Answers (Free)

Section	Questions	Marks
Logical Reasoning	10	10
Mathematical Reasoning	10	10
Everyday Mathematics	10	10
Achievers Section	5	10
Total	35	40

Scholar Tests · Sample paper

Maths olympiad sample paper, Class 3

35 questions · 40 marks · 60 minutes · no negative marking

Name ______________________ Date ____________

Section 1: Logical Reasoning

Questions 1 to 10, 1 mark each. Circle the letter of the best answer.

1.
Which number comes next in this series? 5, 10, 20, 40, 80, …
1. A160
2. B159
3. C161
4. D240
2.
Which word does not belong with the others?
1. Amicrometre
2. Bgram
3. Ckilogram
4. Dmilligram
3.
17 October is a Friday. What day of the week is 5 November? (October has 31 days.)
1. AFriday
2. BThursday
3. CSunday
4. DWednesday
4.
If OAK is written in code as PBL, how is DOG written in the same code?
1. ADOG
2. BCNF
3. CGOD
4. DEPH
5.
Eli is taller than Omar. Yara is taller than Nia. Nia is taller than Sara. Omar is taller than Yara.
Who is the tallest?
1. ASara
2. BOmar
3. CNia
4. DEli
6.
Priya is driving south. Priya turns left, then turns right, and finally turns left. In which direction is Priya now travelling?
1. AWest
2. BNorth
3. CEast
4. DSouth
7.
Which figure is the odd one out?
1. A
2. B
3. C
4. D
8.
How many triangles of any size are there in this figure?
1. A5
2. B4
3. C7
4. D6
9.
Which shape comes next in this sequence?
1. A
2. B
3. C
4. D
10.
The shapes keep repeating in the same way. How many circles are there in the first 30 shapes?
1. A10
2. B8
3. C12
4. D9

Section 2: Mathematical Reasoning

Questions 11 to 20, 1 mark each. Circle the letter of the best answer.

11.
How many tenths are there altogether in 3.7?
1. A10
2. B37
3. C4
4. D7
12.
What fraction of the big square is shaded?
1. A5/9
2. B4/5
3. C4/9
4. D1/3
13.
A window is made of a 2 by 4 grid of small square panes. How many squares of any size can be found on it, counting the small ones and every larger square they make up?
1. A30
2. B15
3. C3
4. D11
14.
Which of these fractions is not equal to 5/9?
1. A15/27
2. B30/54
3. C50/90
4. D10/9
15.
Find the missing number marked with the asterisk (*) in the magic square below. (Every row, column and diagonal adds to the same total.)
1. A8
2. B11
3. C9
4. D17
16.
1 cube weighs the same as 2 pears. 1 pear weighs the same as 2 blocks. How many blocks weigh the same as 2 cubes?
1. A8
2. B7
3. C10
4. D9
17.
Use each of the digits 4, 1, 6 and 2 once. What is the smallest number you can make?
1. A4612
2. B1246
3. C4126
4. D1247
18.
The dashed line is a line of symmetry. One more square must be shaded so that the pattern matches on both sides of the line. Which square must be shaded?
1. AA5
2. BC5
3. CC6
4. DC7
19.
A frog starts on 8 on a number line and hops forward 5 each time: 8, 13, 18, and so on. Where does it land after 10 hops?
1. A48
2. B59
3. C63
4. D58
20.
What number should replace the question mark? ? ÷ 4 + 36 = 42
1. A6
2. B25
3. C168
4. D24

Section 3: Everyday Mathematics

Questions 21 to 30, 1 mark each. Circle the letter of the best answer.

21.
Jonah is measuring an eraser with a ruler marked in centimetres. How long is the eraser, in centimetres?
1. A2.9
2. B3.9
3. C2
4. D6.9
22.
Ben used a balance to compare the masses of some objects. The results are shown below. Which of these must be true?
1. AOne cube is lighter than one cone.
2. BTwo cones are heavier than one cube.
3. CTwo balls are heavier than one cone.
4. DOne ball and one cone are lighter than two cubes.
23.
This picture graph shows the cans collected. How many more cans are there for Dover Way than for Ash Street?
1. A6
2. B46
3. C4
4. D26
24.
Jonah collected data on the vehicles in a car park and graphed the results. Which statement about the vehicles is not true?
1. AAltogether 19 vehicles were counted.
2. BThere were more cars than vans.
3. CThere were 3 more petrol than diesel altogether.
4. DOne third of the vans are petrol.
25.
A train journey begins at 8:17 am and takes 2 hours 45 minutes. What time does it finish?
1. A12:02 pm
2. B5:32 am
3. C11:02 pm
4. D11:02 am
26.
A square label has an area of 576 cm². What is the distance all the way round it?
1. A94 cm
2. B24 cm
3. C96 cm
4. D48 cm
27.
Jonah collected data on the vehicles in a car park and graphed the results. Which statement about the vehicles is not true?
1. AThere were more buses than cars.
2. BOne third of the cars are diesel.
3. CAltogether 26 vehicles were counted.
4. DThere were 12 more petrol than diesel altogether.
28.
The thermometer below shows the temperature of some water. What is the reading?
1. A-24 °C
2. B24 °C
3. C26 °C
4. D22 °C
29.
How many square centimetres are there in 6 square metres?
1. A600000 cm²
2. B60 cm²
3. C60000 cm²
4. D6000 cm²
30.
Jonah spins the arrow on this spinner once. Which word best describes the chance that it lands on a part marked M?
1. Acertain
2. Blikely
3. Cunlikely
4. Dimpossible

Section 4: Achievers Section

Questions 31 to 35, 2 marks each. Circle the letter of the best answer.

31.
Five friends ran a race. Mia finished somewhere ahead of Chloe. Ruby finished somewhere ahead of Aaron. Ruby did not finish fifth. Mia finished immediately ahead of Ethan. Ruby finished immediately ahead of Chloe. Who finished third?
1. ARuby
2. BEthan
3. CMia
4. DChloe
32.
A farmyard holds only ducks and sheep. Altogether there are 48 animals and 172 legs. How many ducks are there?
1. A10
2. B38
3. C124
4. D86
33.
A league has 14 players. Every one of them plays one game against every other one. How many games are there altogether?
1. A196
2. B90
3. C105
4. D91
34.
How many triangles of any size are there in this figure?
1. A8
2. B12
3. C11
4. D6
35.
Eli, Ava, Fay, Milo and Jada are playing, and one of them has the ball.
Eli says: "Fay does not have the ball."
Ava says: "Milo does not have the ball."
Fay says: "Jada has the ball."
Milo says: "Eli has the ball."
Jada says: "Milo does not have the ball."
Exactly one of them is telling the truth. Who has the ball?
1. AMilo
2. BJada
3. CEli
4. DAva

Answers and working

Logical Reasoning

1.A (160). Each number is 2 times the one before it, so the next number is 160.
2.A (micrometre). All the others are units of mass; micrometre is one of the units of length.
3.D (Wednesday). From 17 October to the end of October is 14 days, plus 5 more into November = 19 days. 19 = 2 weeks and 5 days, so count 5 on from Friday: Wednesday.
4.D (EPH). Every letter moves 1 place forward in the alphabet, so DOG becomes EPH.
5.D (Eli). From tallest to shortest, the order is Eli, Omar, Yara, Nia, Sara. So the answer is Eli.
6.C (East). Start facing south. Then turn left, then right, then left. That ends facing east.
7.B. In every figure but one, the line starts at the middle of a side. The odd one out is the square whose line starts at a corner.
8.D (6). Counting size by size, from the smallest up to the biggest, finds 6 triangles.
9.D. At each step the shape is turned a quarter turn clockwise. One more step gives the answer.
10.A (10). Each repeat of 3 shapes has 1 circle. 30 shapes make 10 whole repeats (10) and 0 more shapes, which hold 0. So there are 10.

Mathematical Reasoning

11.B (37). Each whole one holds 10 tenths, so 3 wholes are 30 tenths. Add the 7 already there: 30 + 7 = 37.
12.C (4/9). The big square has 9 small squares. The shaded part is 4 squares. So 4 out of 9 is shaded: 4/9.
13.D (11). Take the sizes one at a time: a square of side k can sit in (2 − k + 1) × (4 − k + 1) positions. Adding those up from k = 1 to 2 gives 11.
14.D (10/9). Multiplying the top and the bottom by the same number leaves a fraction unchanged. In 10/9 only the top has been multiplied (by 2), so it is not equal to 5/9.
15.A (8). The magic total is 3 × centre = 51. The diagonal through * gives 51 − 17 − 26 = 8.
16.A (8). 2 cubes weigh the same as 4 pears, and each pear is 2 blocks, so the answer is 4 × 2 = 8.
17.B (1246). The smallest number you can make from 4, 1, 6 and 2 is 1246.
18.B (C5). Every shaded square needs a partner the same distance on the other side of the line, in the same row. D5 has none, so its partner C5 must be shaded.
19.D (58). 10 hops of 5 take the frog 50 along, from 8 to 58.
20.D (24). Undo the operations in reverse order: ▢ ÷ 4 + 36 = 42 gives ▢ = 24.

Everyday Mathematics

21.A (2.9). The eraser runs from 2 cm to 4.9 cm on the scale. A length is the difference between the two ends, so it is 4.9 − 2 = 2.9 cm.
22.B (Two cones are heavier than one cube.). The pictures say one cube and one ball are lighter than two cones; one cube is lighter than one ball and one cone. Put together, they make it certain that two cones are heavier than one cube, whatever the objects weigh.
23.A (6). One circle stands for 4 cans. Dover Way has 6.5 circles, which is 26; Ash Street has 5 circles, which is 20. The difference is 6.
24.C (There were 3 more petrol than diesel altogether.). Checked against the columns, three of the four statements hold. "There were 3 more petrol than diesel altogether" does not. The difference is 5.
25.D (11:02 am). Add the hours first: 8:17 am plus 2 hours is 10:17 am. Then the 45 minutes. That takes the minutes past 60, so an hour carries, and it finishes at 11:02 am.
26.C (96 cm). A square's sides are all equal, so each side is the number that multiplies by itself to make 576, which is 24 cm. Round all four sides is 4 × 24 = 96 cm.
27.D (There were 12 more petrol than diesel altogether.). Checked against the columns, three of the four statements hold. "There were 12 more petrol than diesel altogether" does not. The difference is 10.
28.B (24 °C). The printed numbers are 10 apart with a small mark every 2 degrees. The liquid stands 2 marks above 20, so the reading is 24 °C.
29.C (60000 cm²). One metre is 100 cm, so one square metre is 100 × 100 = 10 000 cm². That makes 6 square metres 6 × 10 000 = 60000 cm².
30.B (likely). Six of the eight equal parts are marked M, so landing on M is likely.

Achievers Section

31.A (Ruby). The clues fix one order only: first Mia, second Ethan, third Ruby, fourth Chloe, fifth Aaron. So Ruby finished third.
32.A (10). If all 48 had two legs there would be 96 legs, but there are 172 — 76 extra. Each sheep adds two extra legs, so there are 38 sheep and 10 ducks. The answer is 10.
33.D (91). Each of the 14 meets 13 others, which counts 14 × 13 = 182 — but that counts every pair twice, so halve it to get 91.
34.B (12). Counting size by size, from the smallest up to the biggest, finds 12 triangles.
35.A (Milo). Try each child as the one with the ball and count the true statements. Only when Milo has it is exactly one statement true.

Written by Scholar Tests in the published IMO pattern. Not an SOF paper; we are not connected with the Science Olympiad Foundation.

IMO sample paper for Class 3, with answers