What is the IMO pattern for Class 4?

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 4 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 4

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.
How many triangles of any size are there in this figure?
1. A2
2. B4
3. C3
4. D5
2.
Which number comes next in this series? 3, 6, 12, 24, 48, …
1. A96
2. B72
3. C97
4. D95
3.
27 May is a Sunday. What day of the week is 5 June? (May has 31 days.)
1. AMonday
2. BFriday
3. CThursday
4. DTuesday
4.
Theo, Ben and Kai are playing, and one of them has the ball.
Theo says: "Kai has the ball."
Ben says: "Kai has the ball."
Kai says: "Theo does not have the ball."
Exactly one of them is telling the truth. Who has the ball?
1. AKai
2. BBen
3. CTheo
4. DRaj
5.
Five friends ran a race. Chloe finished first. Mia finished fifth. Ruby finished somewhere ahead of Zara. Ruby finished immediately ahead of Aaron. Who finished third?
1. ARuby
2. BAaron
3. CZara
4. DMia
6.
If TOP is written in code as UPQ, how is SUN written in the same code?
1. ASUN
2. BNUS
3. CTVO
4. DUWP
7.
Which letter comes next in this series? F, H, J, L, …
1. AN
2. BL
3. CM
4. DO
8.
Which word does not belong with the others?
1. Akilometre
2. Bmillimetre
3. Cmetre
4. Dkilogram
9.
Which shape comes next in this sequence?
1. A
2. B
3. C
4. D
10.
The dashed line is a mirror. The square marked P is reflected in the mirror. Which square does its reflection land in?
1. AF1
2. BB6
3. CE1
4. DE2

Section 2: Mathematical Reasoning

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

11.
A window is made of a 2 by 2 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. A4
2. B9
3. C6
4. D5
12.
Use each of the digits 8, 5 and 3 once. What is the largest number you can make?
1. A358
2. B853
3. C583
4. D835
13.
How many whole thousands are there in 6139045?
1. A61390
2. B6139
3. C6140
4. D613
14.
Two crowds come to 8, and one is 4 more than the other. What is the bigger crowd?
1. A4
2. B6
3. C2
4. D5
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. A11
2. B10
3. C15
4. D9
16.
1 marble weighs the same as 3 pears. How many pears weigh the same as 2 marbles?
1. A7
2. B9
3. C5
4. D6
17.
What fraction of the big square is shaded?
1. A5/32
2. B1/8
3. C3/16
4. D1/16
18.
What number should replace the question mark? 8 × ? + 10 = 98
1. A88
2. B11
3. C12
4. D14
19.
It has three straight sides. Exactly two of them are the same length, and the two angles at the ends of the third side are equal. What is the shape?
1. Ascalene triangle
2. Btrapezium
3. Ckite
4. Disosceles triangle
20.
Which of these fractions is not equal to 17/21?
1. A170/210
2. B68/84
3. C102/126
4. D17/42

Section 3: Everyday Mathematics

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

21.
Ben spins the arrow on this spinner once. Which word best describes the chance that it lands on a part marked M?
1. Alikely
2. Ban even chance
3. Cunlikely
4. Dimpossible
22.
The thermometer below shows the temperature of some water. What is the reading?
1. A-10 °C
2. B15 °C
3. C5 °C
4. D10 °C
23.
This picture graph shows the books read. How many more books are there for Tuesday than for Wednesday?
1. A30
2. B22
3. C14
4. D12
24.
Chloe used a balance to compare the masses of some objects. The results are shown below. Which of these must be true?
1. ATwo cones weigh the same as one cube.
2. BOne cone is lighter than one cube and one ball.
3. COne cube is lighter than one ball and one cone.
4. DOne cube is lighter than one ball.
25.
A swimming carnival starts at 3:23 pm and finishes at 6:13 pm. How long does it last?
1. A3 hours 50 minutes
2. B2 hours
3. C2 hours 50 minutes
4. D2 hours 10 minutes
26.
Elena is measuring a leaf with a ruler marked in centimetres. How long is the leaf, in centimetres?
1. A3.4
2. B3
3. C2.4
4. D5.4
27.
A rectangular place mat has a perimeter of 48 cm. One of its sides is 10 cm long. What is its area?
1. A140 cm²
2. B150 cm²
3. C48 cm²
4. D280 cm²
28.
This picture graph shows the books read. How many more books are there for Monday than for Tuesday?
1. A2
2. B0.5
3. C4
4. D12
29.
How many square centimetres are there in 7 square metres?
1. A70000 cm²
2. B70 cm²
3. C700000 cm²
4. D7000 cm²
30.
Elena collected data on the juice cartons in a shop and graphed the results. Which statement about the cartons is not true?
1. AThere were more apple cartons than pear cartons.
2. BThere were 10 more large than small altogether.
3. CAltogether 52 cartons were counted.
4. DOne third of the orange cartons are large.

Section 4: Achievers Section

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

31.
Pia, Uma, Yara, Sara and Theo are playing, and one of them has the ball.
Pia says: "I do not have the ball."
Uma says: "Sara has the ball."
Yara says: "I have the ball."
Sara says: "Uma has the ball."
Theo says: "Yara does not have the ball."
Exactly one of them is telling the truth. Who has the ball?
1. ASara
2. BPia
3. CUma
4. DTheo
32.
Five friends ran a race. Zara finished immediately ahead of Aaron. Ethan finished first. Ethan finished immediately ahead of Tom. Chloe did not finish fifth. Who finished third?
1. AChloe
2. BAaron
3. CZara
4. DEthan
33.
A league has 15 players. Every one of them plays one game against every other one. How many games are there altogether?
1. A105
2. B225
3. C106
4. D210
34.
A straight driveway is 1,752 m long. There is a tree every 12 m along it, including one at each end. How many trees are there?
1. A147
2. B148
3. C157
4. D135
35.
Find the missing number marked with the asterisk (*) in the magic square below. (Every row, column and diagonal adds to the same total.)
1. A10
2. B15
3. C9
4. D8

Answers and working

Logical Reasoning

1.B (4). Counting size by size, from the smallest up to the biggest, finds 4 triangles.
2.A (96). Each number is 2 times the one before it, so the next number is 96.
3.D (Tuesday). From 27 May to the end of May is 4 days, plus 5 more into June = 9 days. 9 = 1 weeks and 2 days, so count 2 on from Sunday: Tuesday.
4.B (Ben). Try each child as the one with the ball and count the true statements. Only when Ben has it is exactly one statement true.
5.B (Aaron). The clues fix one order only: first Chloe, second Ruby, third Aaron, fourth Zara, fifth Mia. So Aaron finished third.
6.C (TVO). Every letter moves 1 place forward in the alphabet, so SUN becomes TVO.
7.A (N). Each letter moves 2 places forward in the alphabet, so after L comes N.
8.D (kilogram). All the others are units of length; kilogram is one of the units of mass.
9.A. At each step the shape is turned a quarter turn anticlockwise. One more step gives the answer.
10.C (E1). P is 3 squares from the mirror, so its reflection is the same distance on the other side. That is E1.

Mathematical Reasoning

11.D (5). Take the sizes one at a time: a square of side k can sit in (2 − k + 1) × (2 − k + 1) positions. Adding those up from k = 1 to 2 gives 5, which on a square grid is just 1² + 2² + … + 2².
12.B (853). The largest number you can make from 8, 5 and 3 is 853.
13.B (6139). Cover the last three digits, because those are less than one thousand. What is left in front of them is 6139 whole thousands.
14.B (6). Take the difference off the total first: 8 − 4 = 4. That is what TWO of the smaller one come to, so the smaller is 2 and the larger is 2 + 4 = 6.
15.D (9). The magic total is 3 × centre = 45. The diagonal through * gives 45 − 15 − 21 = 9.
16.D (6). Each marble can be swapped for 3 pears, so 2 marbles weigh the same as 2 × 3 = 6 pears.
17.B (1/8). The big square has 16 small squares. The shaded part is 2 squares. So 2 out of 16 is shaded: 1/8.
18.B (11). Undo the operations in reverse order: 8 × ▢ + 10 = 98 gives ▢ = 11.
19.D (isosceles triangle). Take the clues one at a time and cross off any shape that breaks even one of them. An isosceles triangle is the only one left standing: it is the only shape that matches every part of the description at once.
20.D (17/42). Multiplying the top and the bottom by the same number leaves a fraction unchanged. In 17/42 only the bottom has been multiplied (by 2), so it is not equal to 17/21.

Everyday Mathematics

21.D (impossible). 0 of the four equal parts are marked M, so landing on M is impossible.
22.D (10 °C). The printed numbers are 20 apart with a small mark every 5 degrees. The liquid stands 2 marks below 20, so the reading is 10 °C.
23.C (14). One circle stands for 4 books. Tuesday has 5.5 circles, which is 22; Wednesday has 2 circles, which is 8. The difference is 14.
24.B (One cone is lighter than one cube and one ball.). The pictures say two balls are heavier than one cone; one cube is heavier than one cone. Put together, they make it certain that one cone is lighter than one cube and one ball, whatever the objects weigh.
25.C (2 hours 50 minutes). Count on in two steps rather than subtracting the two times as though they were numbers. From 3:23 pm to 5:23 pm is 2 hours, and from there to 6:13 pm is another 50 minutes. Altogether that is 2 hours 50 minutes.
26.C (2.4). The leaf runs from 3 cm to 5.4 cm on the scale. A length is the difference between the two ends, so it is 5.4 − 3 = 2.4 cm.
27.A (140 cm²). Half the perimeter is one length plus one width: 48 ÷ 2 = 24 cm. So the other side is 24 − 10 = 14 cm, and the area is 10 × 14 = 140 cm².
28.A (2). One circle stands for 4 books. Monday has 3 circles, which is 12; Tuesday has 2.5 circles, which is 10. The difference is 2.
29.A (70000 cm²). One metre is 100 cm, so one square metre is 100 × 100 = 10 000 cm². That makes 7 square metres 7 × 10 000 = 70000 cm².
30.B (There were 10 more large than small altogether.). Checked against the columns, three of the four statements hold. "There were 10 more large than small altogether" does not. The difference is 8.

Achievers Section

31.B (Pia). Try each child as the one with the ball and count the true statements. Only when Pia has it is exactly one statement true.
32.A (Chloe). The clues fix one order only: first Ethan, second Tom, third Chloe, fourth Zara, fifth Aaron. So Chloe finished third.
33.A (105). Each of the 15 meets 14 others, which counts 15 × 14 = 210 — but that counts every pair twice, so halve it to get 105.
34.A (147). 1,752 ÷ 12 = 146, so there are 146 gaps. Something stands at both ends, so there is one more tree than gaps: 146 + 1 = 147.
35.C (9). The magic total is 3 × centre = 45. The diagonal through * gives 45 − 15 − 21 = 9.

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 4, with answers