What is the IMO pattern for Class 8?

50 multiple-choice questions for 60 marks in one hour: Logical Reasoning (15), Mathematical Reasoning (20), Everyday Mathematics (10), and 5 Achievers questions worth 3 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.

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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 8 with Answers (Free)

Section	Questions	Marks
Logical Reasoning	15	15
Mathematical Reasoning	20	20
Everyday Mathematics	10	10
Achievers Section	5	15
Total	50	60

Scholar Tests · Sample paper

Maths olympiad sample paper, Class 8

50 questions · 60 marks · 60 minutes · no negative marking

Name ______________________ Date ____________

Section 1: Logical Reasoning

Questions 1 to 15, 1 mark each. Circle the letter of the best answer.

1.
Three views of the same cube are shown below. Each of its six faces carries a different number from 1 to 6. What is the sum of all the numbers on the faces next to (touching) the face numbered 5?
1. A14
2. B11
3. C15
4. D16
2.
This solid is made of cubes stacked on a flat floor. No cube floats: each one sits on the floor or on another cube. How many cubes are there altogether, counting the ones you cannot see?
1. A5
2. B7
3. C6
4. D12
3.
The first shape changes into the second in a certain way. Which shape completes the second pair in the same way?
1. A
2. B
3. C
4. D
4.
Look at the grid below. The same rule works in every row. What number should replace the question mark?
1. A24
2. B51
3. C3
4. D23
5.
In a certain month, the 8th falls on a Friday. On what day of the week does the 20th of the same month fall?
1. AThursday
2. BTuesday
3. CSunday
4. DWednesday
6.
In a secret code, each digit is always written as the same symbol, in the same order as the digits. 4369 is written ♥ ✚ ● ▲ and 7598 is written ○ □ ▲ ★. How is 6859 written in the code?
1. A● ★ □ ▲
2. B○ ★ □ ▲
3. C▲ ▲ ▲ ●
4. D▲ □ ★ ●
7.
How many triangles of any size are there in this figure?
1. A8
2. B9
3. C4
4. D7
8.
Susan and Colin have two children, Craig and Megan. Craig has two children, Leo and Alice.

Alice is Megan's ______.
Which word fits the gap?
1. Aniece
2. Bnephew
3. Caunt
4. Dgranddaughter
9.
Which number comes next in this series? 7, 13, 20, 28, 37, …
1. A47
2. B46
3. C48
4. D57
10.
Which figure is the odd one out?
1. A
2. B
3. C
4. D
11.
If LOG is written in code as QTL, how is PIG written in the same code?
1. AUNL
2. BGIP
3. CVOM
4. DKDB
12.
Which word does not belong with the others?
1. AMediterranean
2. BCoral
3. CBaltic
4. DArctic
13.
Each row of pictures follows the same rule from left to right. Which picture belongs where the question mark is?
1. A
2. B
3. C
4. D
14.
Priya is driving south. Priya turns right, then turns right, then turns right, then turns left, and finally turns right. In which direction is Priya now travelling?
1. ASouth
2. BNorth
3. CEast
4. DWest
15.
The arrows in this grid follow a rule. Which arrow belongs where the question mark is?
1. A
2. B
3. C
4. D

Section 2: Mathematical Reasoning

Questions 16 to 35, 1 mark each. Circle the letter of the best answer.

16.
In a number code, each shape stands for the same number every time it is used, and a row of shapes means those numbers added together. ●●★ = 27, ●★ = 17 and ■● = 15. What number does ■●● stand for?
1. A59
2. B25
3. C3
4. D15
17.
In the diagram below, what is the size of the angle marked x?
1. A140°
2. B150°
3. C70°
4. D130°
18.
How many tenths are there altogether in 10.3?
1. A1030
2. B3
3. C13
4. D103
19.
The two lines with arrowheads on them are parallel. What is the size of the angle marked with a question mark?
1. A150°
2. B60°
3. C40°
4. D30°
20.
When a number is multiplied by 9, the answer is the same as multiplying that number by 5 and then adding 40. What is the number?
1. A3
2. B11
3. C8
4. D10
21.
Chloe writes down the digits 2, 3, 4, 5, 8 and 9. Using every digit exactly once, 3-digit numbers are made: one number from 3 of the digits and a second number from the other 3. What is the smallest difference between the two numbers?
1. A34
2. B25
3. C751
4. D43
22.
Ethan has ₹270. 20% of it is spent on a book. How much is spent on the book?
1. A₹540
2. B₹54
3. C₹1350
4. D₹216
23.
This model is built from six cubes, two shaded and four plain. It is one cube thick, and the wide face you can see is the front. Which drawing shows the model as it is seen from the back?
1. A
2. B
3. C
4. D
24.
Two of the signs below have been interchanged.
7 − (7 + 9) × (25 ÷ 5) = -51
Which two signs should be swapped to make the statement correct?
1. A+ and ÷
2. B+ and ×
3. C× and ÷
4. D− and ×
25.
Anika started with a sheet of stickers. Anika gave away 50% to a friend, 25% to a cousin and 5% to a neighbour, each share worked out from the number Anika started with. 160 stickers were left. How many stickers were there at the start?
1. A640
2. B32
3. C800
4. D200
26.
Which of these fractions is not equal to 2/5?
1. A4/10
2. B8/20
3. C12/30
4. D2/10
27.
Which of these is the largest?
1. A50%
2. B0.375
3. C9/20
4. D7/20
28.
The shaded rectangle on this grid is enlarged by a scale factor of 3. Each square of the grid is 1 cm by 1 cm. What is the area of the enlarged rectangle, in square centimetres?
1. A18
2. B30
3. C54
4. D6
29.
A solid square pyramid and a square prism stand on bases of the same size, and they are the same height. How many of the pyramids would exactly fill the prism?
1. A3
2. B2
3. C6
4. D4
30.
This solid rectangular prism has been built from identical cubes. Some of the cubes cannot be seen in the drawing. How many cubes cannot be seen?
1. A48
2. B33
3. C15
4. D24
31.
In the triangle below, what is the size of the angle marked x?
1. A63°
2. B56°
3. C126°
4. D54°
32.
A sequence begins 6, 15, 24, 33, … and carries on in the same way. What is the 16th term?
1. A96
2. B150
3. C141
4. D132
33.
A, B and C are three corners of a rectangle. What are the coordinates of the fourth corner?
1. A(3, 2)
2. B(3, 7)
3. C(3, 6)
4. D(2, 7)
34.
4 3/5 × ? = 8 1/20. What is the missing value?
1. A2
2. B4/7
3. C1 2/5
4. D1 3/4
35.
What number should replace the question mark? ? ÷ 12 + 21 = 29
1. A96
2. B348
3. C95
4. D97

Section 3: Everyday Mathematics

Questions 36 to 45, 1 mark each. Circle the letter of the best answer.

36.
Anika is measuring a sticker with a ruler marked in centimetres. How long is the sticker, in centimetres?
1. A4
2. B6.2
3. C2.2
4. D2
37.
The thermometer below shows the temperature of some water. What is the reading?
1. A19 °C
2. B-15 °C
3. C20 °C
4. D15 °C
38.
How many square centimetres are there in 9 square metres?
1. A90 cm²
2. B900000 cm²
3. C90000 cm²
4. D9000 cm²
39.
At 2:00 pm two machines start a cycle in the factory together. After that, the first starts a cycle every 12 minutes and the second every 9 minutes. At what time will they next start a cycle together?
1. A2:35 pm
2. B2:36 pm
3. C2:03 pm
4. D2:21 pm
40.
This graph shows how far Hugo and Anika walk for a given number of paces. Hugo takes 180 paces to walk from school to the library. How many paces does Anika take to walk from school to the library?
1. A60
2. B540
3. C180
4. D300
41.
This graph shows the birds counted each month. What is the range of the numbers shown?
1. A36
2. B2
3. C14
4. D16
42.
A circle has a radius of 42 cm. Taking π as 22/7, what is its area?
1. A264 cm²
2. B132 cm²
3. C22176 cm²
4. D5544 cm²
43.
A box holds 5 yellow counters and 4 green counters. Two counters are taken out one after the other, and the first is not put back. What is the chance that both are yellow?
1. A25/81
2. B5/9
3. C5/18
4. D1/2
44.
Jonah spins the arrow on this spinner once. Which word best describes the chance that it lands on a part marked W?
1. Aan even chance
2. Bunlikely
3. Ccertain
4. Dlikely
45.
A bus travels at an average speed of 45 km/h for 20 minutes. How far does it go?
1. A900 km
2. B135 km
3. C27 km
4. D15 km

Section 4: Achievers Section

Questions 46 to 50, 3 marks each. Circle the letter of the best answer.

46.
The same rule turns every number in the top row into the number directly below it. What number belongs in the cell marked with a question mark?
1. A76
2. B196
3. C17
4. D199
47.
A bag holds 4 red marbles and 7 blue marbles. Two marbles are taken out one after the other, and the first is not put back. What is the chance that both are red?
1. A4/11
2. B6/55
3. C16/121
4. D3/10
48.
The net below is folded to make a cube. What is the total of the number on the shaded square and the number on the face that ends up opposite it?
1. A31
2. B29
3. C26
4. D24
49.
Anika is measuring a sticker with a ruler marked in centimetres. How long is the sticker, in centimetres?
1. A4
2. B2
3. C6.1
4. D2.1
50.
Jonah wants to post some art supplies. The brush has a mass of 900 grams, the paint tin has a mass of 250 grams, the sketchpad has a mass of 1400 grams and the easel has a mass of 500 grams. Which group has a total mass as close as possible to 1800 grams?
1. Athe paint tin and easel
2. Ball 4 items
3. Cthe brush, paint tin and sketchpad
4. Dthe brush, sketchpad and easel

Answers and working

Logical Reasoning

1.C (15). Faces seen together on a cube cannot be opposite each other, and the three views leave only one possibility: 1–5, 2–6, 3–4. So 5 is opposite 1, and the four faces touching it total 21 − 5 − 1 = 15.
2.B (7). Each stack reaches the floor, so add the stacks' heights: 2 + 2 + 1 + 1 + 1 = 7.
3.A. In the first pair the shape is with the black and white parts swapped. Doing the same to the third shape gives the answer.
4.D (23). In every row, the third number is the first two added together. In the row with the question mark that gives 23.
5.D (Wednesday). From the 8th to the 20th is 12 days. 12 = 1 full week and 5 days, so count 5 on from Friday: Wednesday.
6.A (● ★ □ ▲). Read each clue place by place to find every digit's symbol. Coding 6859 gives ● ★ □ ▲.
7.A (8). Counting size by size, from the smallest up to the biggest, finds 8 triangles.
8.A (niece). Alice is Megan's niece. Craig is Alice's parent. Craig and Megan are both children of Susan and Colin, so Megan is Craig's sister. A parent's sister is an aunt, so Megan is Alice's aunt and Alice is Megan's niece.
9.A (47). The gaps grow: +6, +7, +8, and so on, each gap 1 bigger than the last, so the next number is 47.
10.B. All but one are the same picture turned round. The odd one out is the figure that is flipped over, not turned.
11.A (UNL). Every letter moves 5 places forward in the alphabet, so PIG becomes UNL.
12.D (Arctic). All the others are seas; Arctic is one of the oceans.
13.D. Along every row the shaded part moves 3 slices clockwise each step, so the missing picture is the bottom row's middle picture with its shaded slice moved 3 slices clockwise.
14.C (East). Start facing south. Then turn right, then right, then right, then left, then right. That ends facing east.
15.D. Along each column, from top to bottom, every arrow is the one before it turned an eighth of a turn anticlockwise, so the missing arrow points down and to the right.

Mathematical Reasoning

16.B (25). The three clues give ■ = 5, ● = 10, ★ = 7. So ■●● is 5 + 10 + 10 = 25.
17.A (140°). The angles at O go all the way round, so they come to 360°. The ones printed on the diagram take up 70° + 150° = 220°, which leaves 360° − 220° = 140°, so x = 140°.
18.D (103). Each whole one holds 10 tenths, so 10 wholes are 100 tenths. Add the 3 already there: 100 + 3 = 103.
19.D (30°). The marked angle and the one asked for are on opposite sides of the crossing line, between the two parallel lines, so they are equal — the answer is 30°.
20.D (10). Multiplying by 9 rather than by 5 adds 9 − 5 = 4 lots of the number. Those 4 lots come to 40, so the number is 40 ÷ 4 = 10.
21.B (25). Putting the two closest digits at the front and running the tails in opposite directions gives 523 and 498, and 523 − 498 = 25.
22.B (₹54). 20% means 20 out of every 100. So the amount is ₹270 × 20 ÷ 100 = ₹54.
23.A. The model is one cube thick, so going round to the back swaps left and right and changes nothing else. The back view is the front view mirrored side to side.
24.B (+ and ×). Swapping + and × everywhere gives 7 − (7 × 9) + (25 ÷ 5) = -51, which is correct.
25.C (800). The shares add to 80%, so the 160 left over are the other 20%. One per cent is 160 ÷ 20 = 8, so the whole is 800.
26.D (2/10). Multiplying the top and the bottom by the same number leaves a fraction unchanged. In 2/10 only the bottom has been multiplied (by 2), so it is not equal to 2/5.
27.A (50%). As decimals: 50% = 0.5, 0.375 = 0.375, 9/20 = 0.45, 7/20 = 0.35. The largest is 50%.
28.C (54). Every length is multiplied by 3, so the area is multiplied by 3 × 3 = 9. That makes 6 × 9 = 54 square centimetres.
29.A (3). A pyramid on the same base and the same height as a prism is a third of it, so 3 of them fill the prism exactly.
30.C (15). Three faces are showing, so peel one layer off each of them. What is left is a 5 by 3 by 1 block entirely inside, which is 15 cubes.
31.D (54°). The two ticked sides are the same length, so the two angles at the ends of the third side are equal. Each of them is 63°, and the three angles come to 180°, so x = 180° − 63° − 63° = 54°.
32.C (141). Each term is 9 more than the last, so the nth term is 6 + (n − 1) × 9. For n = 16: 6 + 15 × 9 = 141.
33.B ((3, 7)). The fourth corner lines up with C across and with B up, so it is (3, 7).
34.D (1 3/4). Turn the sentence round to get at the missing part: 8 1/20 ÷ 4 3/5 = 1 3/4. Put 1 3/4 back into the sentence and it works out to 8 1/20.
35.A (96). Undo the operations in reverse order: ▢ ÷ 12 + 21 = 29 gives ▢ = 96.

Everyday Mathematics

36.C (2.2). The sticker runs from 4 cm to 6.2 cm on the scale. A length is the difference between the two ends, so it is 6.2 − 4 = 2.2 cm.
37.D (15 °C). The printed numbers are 20 apart with a small mark every 5 degrees. The liquid stands 1 mark below 20, so the reading is 15 °C.
38.C (90000 cm²). One metre is 100 cm, so one square metre is 100 × 100 = 10 000 cm². That makes 9 square metres 9 × 10 000 = 90000 cm².
39.B (2:36 pm). The smallest number that both 12 and 9 divide into is 36. So they meet again 36 minutes after 2:00 pm, which is 2:36 pm.
40.A (60). 180 paces puts Hugo at 30 metres. Reading 30 metres back down Anika's line gives 60 paces.
41.C (14). The tallest column is 16 and the shortest is 2, so the range is 14.
42.D (5544 cm²). The area of a circle is π × r × r. That is 22/7 × 42 × 42, and the 7 cancels into one of the 42s, so it comes to 5544 cm².
43.C (5/18). The first draw is 5 out of 9. One yellow is now gone, so the second is 4 out of 8. Both must happen, so multiply: 5/9 × 4/8 = 5/18.
44.A (an even chance). Three of the six equal parts are marked W, so landing on W is an even chance.
45.D (15 km). In one hour it covers 45 km, so in one minute it covers 45 ÷ 60 km. Over 20 minutes that is 45 × 20 ÷ 60 = 15 km.

Achievers Section

46.D (199). The rule is: multiply the number by itself, then add 3. It works on every column — 1 × 1 + 3 = 4 — so the missing number is 14 × 14 + 3 = 199.
47.B (6/55). The first draw is 4 out of 11. One red is now gone, so the second is 3 out of 10. Both must happen, so multiply: 4/11 × 3/10 = 6/55.
48.C (26). Two squares that are joined along an edge, or that meet at a corner, always end up side by side on the cube, so none of those can be opposite 14. Pairing all six squares up under that rule, and keeping the ends of every straight line of three together, leaves 14 with 12. So 14 + 12 = 26.
49.D (2.1). The sticker runs from 4 cm to 6.1 cm on the scale. A length is the difference between the two ends, so it is 6.1 − 4 = 2.1 cm.
50.C (the brush, paint tin and sketchpad). The brush, paint tin and sketchpad come to 2550 g, which is 750 g from 1800 g — closer than any of the others.

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 8, with answers