What is the IMO pattern for Class 7?

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.

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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 7 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 7

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.
18 October is a Saturday. What day of the week is 6 November? (October has 31 days.)
1. AMonday
2. BThursday
3. CWednesday
4. DFriday
2.
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
3.
Chloe is walking south. Chloe turns left, then turns right, and finally turns left. In which direction is Chloe now travelling?
1. AWest
2. BNorth
3. CSouth
4. DEast
4.
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 1?
1. A18
2. B20
3. C17
4. D16
5.
The dashed line is a mirror. The square marked P is reflected in the mirror. Which square does its reflection land in?
1. AC2
2. BF6
3. CF7
4. DE7
6.
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
7.
In a certain month, the 9th falls on a Thursday. On what day of the week does the 24th of the same month fall?
1. AWednesday
2. BFriday
3. CSaturday
4. DSunday
8.
In a scholarship examination, Marcus ranked 29th and Aisha ranked 32nd. Among the girls, Aisha ranked 6th, and among the boys, Marcus ranked 24th. Marcus ranked 16th counting up from the bottom. Among the girls, Aisha ranked 3rd from the bottom. How many boys sat the examination?
1. A44
2. B36
3. C12
4. D37
9.
Five friends ran a race. Priya finished somewhere ahead of Zara. Chloe finished immediately ahead of Zara. Ruby finished somewhere ahead of James. Ruby finished immediately ahead of Chloe. Who finished third?
1. ARuby
2. BJames
3. CChloe
4. DPriya
10.
Which word does not belong with the others?
1. Afortnight
2. Bmetre
3. Ckilometre
4. Dmillimetre
11.
Which number comes next in this series? 6, 24, 96, 384, 1536, …
1. A6143
2. B6144
3. C3072
4. D6145
12.
Judith and Robert have two children, James and Nicole. James has two children, Zoe and Maya. Nicole has a son, Max.

Nicole is Maya's ______.
Which word fits the gap?
1. Aniece
2. Bgrandmother
3. Caunt
4. Duncle
13.
The arrows in this grid follow a rule. Which arrow belongs where the question mark is?
1. A
2. B
3. C
4. D
14.
How many triangles of any size are there in this figure?
1. A9
2. B16
3. C7
4. D15
15.
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. A11
2. B15
3. C36
4. D4

Section 2: Mathematical Reasoning

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

16.
Priya is standing in square P. Mia is standing in square Q. Which one of these squares is the same distance, in a straight line, from both of them?
1. AC7
2. BF5
3. CE8
4. DE5
17.
Two numbers add to 26, and one is 4 more than the other. What is the smaller number?
1. A15
2. B2
3. C22
4. D11
18.
This is a plan of a netball court. How many of the solid lines in this drawing are parallel to the dashed line?
1. A3
2. B5
3. C4
4. D2
19.
For any two numbers, a ✦ b means (a + b) × a. What is 2 ✦ 6?
1. A48
2. B28
3. C8
4. D16
20.
In the triangle below, what is the size of the angle marked x?
1. A26°
2. B128°
3. C64°
4. D154°
21.
Each letter of the alphabet stands for a number: A = 1, B = 2, C = 3, and so on to Z = 26. What is the value of D + D × F − C?
1. A26
2. B16
3. C45
4. D25
22.
The two lines with arrowheads on them are parallel. What is the size of the angle marked with a question mark?
1. A140°
2. B70°
3. C110°
4. D20°
23.
The shaded rectangle on this grid is enlarged by a scale factor of 2. Each square of the grid is 1 cm by 1 cm. What is the perimeter of the enlarged rectangle, in centimetres?
1. A56
2. B14
3. C22
4. D28
24.
Finn took a circular piece of paper and folded it in half three times. Finn then cut straight across the pointed corner and threw the small piece away, then opened the paper out again. What shape is the hole in the middle of the paper?
1. Aa square
2. Ba regular octagon
3. Ca regular sixteen-sided shape
4. Da triangle
25.
Find the missing number marked with the asterisk (*) in the magic square below. (Every row, column and diagonal adds to the same total.)
1. A14
2. B18
3. C13
4. D26
26.
A sequence begins 11, 14, 17, 20, … and carries on in the same way. What is the 12th term?
1. A47
2. B132
3. C41
4. D44
27.
Priya has ₹235. 20% of it is spent on a book. How much is spent on the book?
1. A₹188
2. B₹1175
3. C₹470
4. D₹47
28.
What number should replace the question mark? 8 × ? − 25 = 95
1. A9
2. B14
3. C120
4. D15
29.
Which of these fractions is not equal to 5/7?
1. A20/28
2. B15/21
3. C30/42
4. D5/14
30.
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. A6
2. B4
3. C2
4. D3
31.
Jonah started with a jar of marbles. Jonah gave away 50% to a friend, 25% to a cousin and 10% to a neighbour, each share worked out from the number Jonah started with. 30 marbles were left. How many marbles were there at the start?
1. A35
2. B200
3. C120
4. D5
32.
How many whole thousands are there in 5672418?
1. A5673
2. B567
3. C2
4. D5672
33.
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. A29
2. B24
3. C30
4. D32
34.
5 3/4 × ? = 2 7/8. What is the missing value?
1. A1
2. B1/3
3. C1/2
4. D2
35.
In the diagram below, what is the size of the angle marked x?
1. A44°
2. B34°
3. C84°
4. D53°

Section 3: Everyday Mathematics

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

36.
Dev is marking out the edge of a straight running track that is 8 metres long, using 5 flags spaced equally apart, with one at the very start and one at the very end. How many metres apart are they?
1. A2
2. B3
3. C5
4. D4
37.
160 books were borrowed from the class library in one term. The pie chart below shows what was borrowed. How many of them were mystery books?
1. A128
2. B96
3. C16
4. D32
38.
This graph shows the goals scored each day. What is the range of the numbers shown?
1. A14
2. B60
3. C12
4. D18
39.
A bus travels at an average speed of 48 km/h for 30 minutes. How far does it go?
1. A38 km
2. B1440 km
3. C24 km
4. D26 km
40.
Chloe is measuring a pencil stub with a ruler marked in centimetres. How long is the pencil stub, in centimetres?
1. A6.9
2. B3.9
3. C4
4. D2.9
41.
A rectangular card has a perimeter of 28 cm. One of its sides is 9 cm long. What is its area?
1. A28 cm²
2. B45 cm²
3. C54 cm²
4. D90 cm²
42.
This picture graph shows the cans collected. How many more cans are there for Ash Street than for Bay Road?
1. A35
2. B30
3. C3.5
4. D55
43.
A box measures 8 cm long, 7 cm wide and 10 cm high. What is its volume?
1. A412 cm³
2. B206 cm³
3. C100 cm³
4. D560 cm³
44.
When it is 12:00 pm in Tokyo, it is 3:00 pm in Cairo. When it is 12:00 pm in Tokyo, it is 10:00 am in Mumbai. What is the time in Mumbai when it is 8:00 pm in Cairo?
1. A3:00 pm
2. B8:00 pm
3. C3:00 am
4. D9:00 pm
45.
This graph shows Ben's bike ride away from home. For how many minutes did Ben stop during the ride?
1. A60
2. B10
3. C30
4. D20

Section 4: Achievers Section

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

46.
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. AC2
2. BA4
3. CC5
4. DC4
47.
It is a flat shape with eight straight sides and eight corners. What is the shape?
1. Apentagon
2. Bquadrilateral
3. Cheptagon
4. Doctagon
48.
A cyclist rides 24 km in 30 minutes. What is its average speed?
1. A53 km/h
2. B75 km/h
3. C48 km/h
4. D80 km/h
49.
A league has 13 clubs. Every one of them sends one letter to every other one. How many letters are there altogether?
1. A78
2. B169
3. C91
4. D79
50.
A rectangular notice measures 12 cm by 14 cm. A piece measuring 7 cm by 2 cm is cut away from one corner. What is the area of the piece that is left?
1. A14 cm²
2. B154 cm²
3. C168 cm²
4. D182 cm²

Answers and working

Logical Reasoning

1.B (Thursday). From 18 October to the end of October is 13 days, plus 6 more into November = 19 days. 19 = 2 weeks and 5 days, so count 5 on from Saturday: Thursday.
2.D. In the first pair the shape is flipped over from left to right. Doing the same to the third shape gives the answer.
3.D (East). Start facing south. Then turn left, then right, then left. That ends facing east.
4.C (17). Faces seen together on a cube cannot be opposite each other, and the three views leave only one possibility: 1–3, 2–5, 4–6. So 1 is opposite 3, and the four faces touching it total 21 − 1 − 3 = 17.
5.C (F7). P is 3 squares from the mirror, so its reflection is the same distance on the other side. That is F7.
6.B. Along every row the shape stays the same and there is one more dot each step, so the missing picture is the triangle with 3 dots.
7.B (Friday). From the 9th to the 24th is 15 days. 15 = 2 full weeks and 1 day, so count 1 on from Thursday: Friday.
8.B (36). Marcus is 29th from the top and 16th from the bottom, so everyone numbers 29 + 16 − 1 = 44. The same trick on the girls gives 6 + 3 − 1 = 8 girls. Boys = 44 − 8 = 36. (The other two ranks are true but not needed.)
9.C (Chloe). The clues fix one order only: first Priya, second Ruby, third Chloe, fourth Zara, fifth James. So Chloe finished third.
10.A (fortnight). All the others are units of length; fortnight is one of the units of time.
11.B (6144). Each number is 4 times the one before it, so the next number is 6144.
12.C (aunt). Nicole is Maya's aunt. James is Maya's parent. James and Nicole are both children of Judith and Robert, so Nicole is James's sister. A parent's sister is an aunt, so Nicole is Maya's aunt and Maya is Nicole's niece.
13.D. Along each row, from left to right, every arrow is the one before it turned a quarter turn anticlockwise, so the missing arrow points left.
14.B (16). Counting size by size, from the smallest up to the biggest, finds 16 triangles.
15.B (15). Each stack reaches the floor, so add the stacks' heights: 3 + 1 + 1 + 2 + 1 + 1 + 2 + 1 + 1 + 1 + 1 = 15.

Mathematical Reasoning

16.D (E5). From E5 to P is 1 across and 3 up or down; to Q it is 3 across and 1 up or down. Both give the same straight-line distance, so E5 is the square.
17.D (11). Take the difference off the total first: 26 − 4 = 22. That is what TWO of the smaller one come to, so the smaller is 11 and the larger is 11 + 4 = 15.
18.C (4). Counting the two outside edges of the plan, 5 lines run the same way as the dashed one. A line is not parallel to itself, so that leaves 4.
19.D (16). Put 2 where a is and 6 where b is, keeping them in that order — this rule gives a different answer the other way round. That makes it (2 + 6) × 2, which comes to 16.
20.C (64°). The two ticked sides are the same length, so the two angles at the ends of the third side are equal. Between them they take up 180° − 52° = 128°, so x = 128° ÷ 2 = 64°.
21.D (25). The letters stand for D = 4, D = 4, F = 6 and C = 3. Do the multiplying first, then the adding and subtracting, and the answer is 25.
22.B (70°). The marked angle and the one asked for are in matching positions at the two crossings, so they are equal — the answer is 70°.
23.D (28). Every length is multiplied by 2, so the 3 by 4 rectangle becomes 6 by 8 and its perimeter is 2 × (6 + 8) = 28 cm.
24.B (a regular octagon). Three folds make 8 layers, and the cut takes the same corner off each one. Opened out, the hole is a regular octagon.
25.A (14). The magic total is 3 × centre = 78. The diagonal through * gives 78 − 26 − 38 = 14.
26.D (44). Each term is 3 more than the last, so the nth term is 11 + (n − 1) × 3. For n = 12: 11 + 11 × 3 = 44.
27.D (₹47). 20% means 20 out of every 100. So the amount is ₹235 × 20 ÷ 100 = ₹47.
28.D (15). Undo the operations in reverse order: 8 × ▢ − 25 = 95 gives ▢ = 15.
29.D (5/14). Multiplying the top and the bottom by the same number leaves a fraction unchanged. In 5/14 only the bottom has been multiplied (by 2), so it is not equal to 5/7.
30.D (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.
31.B (200). The shares add to 85%, so the 30 left over are the other 15%. One per cent is 30 ÷ 15 = 2, so the whole is 200.
32.D (5672). Cover the last three digits, because those are less than one thousand. What is left in front of them is 5672 whole thousands.
33.C (30). 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 13. Pairing all six squares up under that rule, and keeping the ends of every straight line of three together, leaves 13 with 17. So 13 + 17 = 30.
34.C (1/2). Turn the sentence round to get at the missing part: 2 7/8 ÷ 5 3/4 = 1/2. Put 1/2 back into the sentence and it works out to 2 7/8.
35.A (44°). OA and OE lie in a straight line, so the angles between them come to 180°. The ones printed on the diagram take up 40° + 43° + 53° = 136°, which leaves 180° − 136° = 44°, so x = 44°.

Everyday Mathematics

36.A (2). 5 flags with one at each end make 4 gaps, not 5. So each gap is 8 ÷ 4 = 2 metres.
37.D (32). The Mystery slice is 20 per cent of the chart. And 20 per cent of 160 is 160 ÷ 100 × 20 = 32.
38.A (14). The tallest column is 18 and the shortest is 4, so the range is 14.
39.C (24 km). In one hour it covers 48 km, so in one minute it covers 48 ÷ 60 km. Over 30 minutes that is 48 × 30 ÷ 60 = 24 km.
40.D (2.9). The pencil stub runs from 4 cm to 6.9 cm on the scale. A length is the difference between the two ends, so it is 6.9 − 4 = 2.9 cm.
41.B (45 cm²). Half the perimeter is one length plus one width: 28 ÷ 2 = 14 cm. So the other side is 14 − 9 = 5 cm, and the area is 9 × 5 = 45 cm².
42.A (35). One circle stands for 10 cans. Ash Street has 5.5 circles, which is 55; Bay Road has 2 circles, which is 20. The difference is 35.
43.D (560 cm³). Volume multiplies all three edges: 8 × 7 × 10 = 560 cm³.
44.A (3:00 pm). Cairo is 3 hours ahead of Tokyo and Mumbai is 2 hours behind it, so Mumbai is 5 hours behind Cairo. That makes it 3:00 pm.
45.B (10). The line is level from 20 minutes to 30 minutes, and a level line on a distance-time graph means the distance is not changing. That is 10 minutes stopped.

Achievers Section

46.D (C4). Every shaded square needs a partner the same distance on the other side of the line, in the same row. F4 has none, so its partner C4 must be shaded.
47.D (octagon). Take the clues one at a time and cross off any shape that breaks even one of them. An octagon is the only one left standing: it is the only shape that matches every part of the description at once.
48.C (48 km/h). Speed is how far it would go in one whole hour. In 30 minutes it covers 24 km, so in 60 minutes it covers 24 × 60 ÷ 30 = 48 km. Its speed is 48 km/h.
49.A (78). Each of the 13 meets 12 others, which counts 13 × 12 = 156 — but that counts every pair twice, so halve it to get 78.
50.B (154 cm²). The whole rectangle is 12 × 14 = 168 cm². The corner taken away is 7 × 2 = 14 cm². What is left is 168 − 14 = 154 cm².

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 7, with answers