IMO sample papers

IMO sample paper for Class 2, with answers

A free maths olympiad paper in the IMO pattern: 35 questions for 40 marks in 60 minutes, in four sections. Print it, then check the answers and working at the end.

See the answersSit a new paper online
SectionQuestionsMarks
Logical Reasoning1010
Mathematical Reasoning1010
Everyday Mathematics1010
Achievers Section510
Total3540

Scholar Tests · Sample paper

Maths olympiad sample paper, Class 2

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. 1.

    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. AG3
    2. BH2
    3. CF4
    4. DH3
  2. 2.

    The dashed line is a mirror. The square marked P is reflected in the mirror. Which square does its reflection land in?

    1. AF5
    2. BA2
    3. CD5
    4. DE5
  3. 3.

    Carlos is faster than Ben. Pia is faster than Yara. Ben is faster than Pia. Omar is faster than Carlos.
    Who is the slowest?

    1. APia
    2. BYara
    3. CBen
    4. DOmar
  4. 4.

    Which figure is the odd one out?

    1. A
    2. B
    3. C
    4. D
  5. 5.

    Which shape comes next in this sequence?

    1. A
    2. B
    3. C
    4. D
  6. 6.

    Which letter comes next in this series?   A, E, I, M, …

    1. AM
    2. BP
    3. CQ
    4. DR
  7. 7.

    The shapes keep repeating in the same way. Which shape is 12th?

    1. A
    2. B
    3. C
    4. D
  8. 8.

    Which letter comes next in this series?   F, J, N, R, …

    1. AR
    2. BU
    3. CV
    4. DZ
  9. 9.

    Five cards, each with a shape on it, were put down one at a time. Which card was put down last?

    1. A
    2. B
    3. C
    4. D
  10. 10.

    The shapes keep repeating in the same way. Which shape is 12th?

    1. A
    2. B
    3. C
    4. D

Section 2: Mathematical Reasoning

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

  1. 11.

    Use each of the digits 4, 5 and 2 once. What is the largest number you can make?

    1. A245
    2. B524
    3. C425
    4. D542
  2. 12.

    What fraction of the big square is shaded?

    1. A3/8
    2. B3/16
    3. C3/5
    4. D7/16
  3. 13.

    It has four straight sides, all four the same length, and all four of its corners are right angles. What is the shape?

    1. Akite
    2. Bsquare
    3. Crhombus
    4. Dparallelogram
  4. 14.

    1 apple weighs the same as 4 balls. How many balls weigh the same as 3 apples?

    1. A8
    2. B4
    3. C16
    4. D12
  5. 15.

    It has four straight sides and all four of its corners are right angles, but its four sides are not all the same length. What is the shape?

    1. Asquare
    2. Bparallelogram
    3. Ctrapezium
    4. Drectangle
  6. 16.

    Which number comes next in this series?   5, 10, 20, 40, 80, …

    1. A161
    2. B159
    3. C120
    4. D160
  7. 17.

    How many shaded circles are there in the picture?

    1. A2
    2. B4
    3. C1
    4. D6
  8. 18.

    A frog starts on 2 on a number line and hops forward 2 each time: 2, 4, 6, and so on. Where does it land after 4 hops?

    1. A10
    2. B11
    3. C8
    4. D12
  9. 19.

    What fraction of the big square is shaded?

    1. A5/8
    2. B1/2
    3. C9/16
    4. D19/32
  10. 20.

    How many shaded squares are there in the picture?

    1. A7
    2. B5
    3. C4
    4. D6

Section 3: Everyday Mathematics

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

  1. 21.

    How many metres are there in 6 kilometres?

    1. A1 metre
    2. B7000 metres
    3. C6000 metres
    4. D600 metres
  2. 22.

    The thermometer below shows the temperature of some water. What is the reading?

    1. A-70 °C
    2. B75 °C
    3. C70 °C
    4. D65 °C
  3. 23.

    This picture graph shows the books read. How many more books are there for Monday than for Wednesday?

    1. A4
    2. B6
    3. C1.5
    4. D46
  4. 24.

    Hugo is measuring a paperclip with a ruler marked in centimetres. How long is the paperclip, in centimetres?

    1. A2
    2. B3.3
    3. C4
    4. D2.3
  5. 25.

    This picture graph shows the books read. How many more books are there for Monday than for Thursday?

    1. A6
    2. B4
    3. C38
    4. D22
  6. 26.

    Ben is measuring a key with a ruler marked in centimetres. How long is the key, in centimetres?

    1. A2
    2. B3
    3. C3.8
    4. D5.8
  7. 27.

    Each step James takes is 80 cm long. How many steps does it take to walk 60 metres?

    1. A133 steps
    2. B76 steps
    3. C75 steps
    4. D4800 steps
  8. 28.

    Anika spins the arrow on this spinner once. Which word best describes the chance that it lands on a part marked W?

    1. Aimpossible
    2. Bunlikely
    3. Ccertain
    4. Dan even chance
  9. 29.

    The thermometer below shows the temperature of some water. What is the reading?

    1. A25 °C
    2. B29 °C
    3. C30 °C
    4. D-25 °C
  10. 30.

    Dev spins the arrow on this spinner once. Which word best describes the chance that it lands on a part marked M?

    1. Aunlikely
    2. Bcertain
    3. Clikely
    4. Dan even chance

Section 4: Achievers Section

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

  1. 31.

    Yara, Hana, Gus, Wes and Zoe are playing, and one of them has the ball.
    Yara says: "Zoe has the ball."
    Hana says: "Yara does not have the ball."
    Gus says: "Hana has the ball."
    Wes says: "Gus does not have the ball."
    Zoe says: "Yara has the ball."
    Exactly one of them is telling the truth. Who has the ball?

    1. AYara
    2. BZoe
    3. CGus
    4. DHana
  2. 32.

    How many triangles of any size are there in this figure?

    1. A4
    2. B5
    3. C10
    4. D15
  3. 33.

    A frog starts on 8 on a number line and hops forward 7 each time: 8, 15, 22, and so on. Where does it land after 7 hops?

    1. A56
    2. B58
    3. C57
    4. D50
  4. 34.

    Ava is slower than Ben. Omar is faster than Milo. Omar is slower than Uma. Ava is faster than Omar.
    Who is the slowest?

    1. AMilo
    2. BAva
    3. CUma
    4. DBen
  5. 35.

    The shapes keep repeating in the same way. How many circles are there in the first 17 shapes?

    1. A8
    2. B9
    3. C4
    4. D10

Answers and working

Logical Reasoning

  1. 1.D (H3). Every shaded square needs a partner the same distance on the other side of the line, in the same row. C3 has none, so its partner H3 must be shaded.
  2. 2.A (F5). P is 3 squares from the mirror, so its reflection is the same distance on the other side. That is F5.
  3. 3.B (Yara). From fastest to slowest, the order is Omar, Carlos, Ben, Pia, Yara. So the answer is Yara.
  4. 4.B. In every figure but one, the dot is outside the shape. The odd one out is the hexagon with its dot inside it.
  5. 5.C. At each step the shape is turned a quarter turn anticlockwise. One more step gives the answer.
  6. 6.C (Q). Each letter moves 4 places forward in the alphabet, so after M comes Q.
  7. 7.A. The pattern repeats every 3 shapes. 12 = 3 × 3 + 3, so the 12th shape is the same as the 3rd: a square.
  8. 8.C (V). Each letter moves 4 places forward in the alphabet, so after R comes V.
  9. 9.C. Wherever two cards overlap, the card on top came later. That gives the order heart, circle, square, star, triangle, so the card with the triangle was put down last.
  10. 10.C. The pattern repeats every 2 shapes. 12 = 2 × 5 + 2, so the 12th shape is the same as the 2nd: a heart.

Mathematical Reasoning

  1. 11.D (542). The largest number you can make from 4, 5 and 2 is 542.
  2. 12.A (3/8). The big square has 16 small squares. The shaded part is 6 squares. So 6 out of 16 is shaded: 3/8.
  3. 13.B (square). Take the clues one at a time and cross off any shape that breaks even one of them. A square is the only one left standing: it is the only shape that matches every part of the description at once.
  4. 14.D (12). Each apple can be swapped for 4 balls, so 3 apples weigh the same as 3 × 4 = 12 balls.
  5. 15.D (rectangle). Take the clues one at a time and cross off any shape that breaks even one of them. A rectangle is the only one left standing: it is the only shape that matches every part of the description at once.
  6. 16.D (160). Each number is 2 times the one before it, so the next number is 160.
  7. 17.A (2). Going row by row and ticking each one that fits, there are 2 shaded circles.
  8. 18.A (10). 4 hops of 2 take the frog 8 along, from 2 to 10.
  9. 19.C (9/16). The big square has 16 small squares. The shaded part is 9 squares. So 9 out of 16 is shaded: 9/16.
  10. 20.B (5). Going row by row and ticking each one that fits, there are 5 shaded squares.

Everyday Mathematics

  1. 21.C (6000 metres). There are 1000 metres in one of the kilometres, so 6 kilometres is 6 × 1000 = 6000 metres.
  2. 22.C (70 °C). The printed numbers are 20 apart with a small mark every 5 degrees. The liquid stands 2 marks below 80, so the reading is 70 °C.
  3. 23.B (6). One circle stands for 4 books. Monday has 6.5 circles, which is 26; Wednesday has 5 circles, which is 20. The difference is 6.
  4. 24.D (2.3). The paperclip runs from 4 cm to 6.3 cm on the scale. A length is the difference between the two ends, so it is 6.3 − 4 = 2.3 cm.
  5. 25.A (6). One circle stands for 4 books. Monday has 5.5 circles, which is 22; Thursday has 4 circles, which is 16. The difference is 6.
  6. 26.C (3.8). The key runs from 2 cm to 5.8 cm on the scale. A length is the difference between the two ends, so it is 5.8 − 2 = 3.8 cm.
  7. 27.C (75 steps). 60 metres is 60 × 100 = 6000 cm. Each step covers 80 cm, so it takes 6000 ÷ 80 = 75 steps.
  8. 28.B (unlikely). Two of the eight equal parts are marked W, so landing on W is unlikely.
  9. 29.A (25 °C). The printed numbers are 10 apart with a small mark every 5 degrees. The liquid stands 1 mark below 30, so the reading is 25 °C.
  10. 30.A (unlikely). Two of the six equal parts are marked M, so landing on M is unlikely.

Achievers Section

  1. 31.C (Gus). Try each child as the one with the ball and count the true statements. Only when Gus has it is exactly one statement true.
  2. 32.D (15). Counting size by size, from the smallest up to the biggest, finds 15 triangles.
  3. 33.C (57). 7 hops of 7 take the frog 49 along, from 8 to 57.
  4. 34.A (Milo). The clues do not fix the whole order, but in every order they allow, Milo is in that place.
  5. 35.A (8). Each repeat of 4 shapes has 2 circles. 17 shapes make 4 whole repeats (8) and 1 more shapes, which hold 0. So there are 8.

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

Questions parents ask

What is the IMO pattern for Class 2?
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.