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FMO 2026 - Grade 7 - Preliminary - Paper 01

Question 1

Which figure should fill the cell with the question mark?

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Question 2

There were some people on a train. At the first stop, one third got off. At the second stop, three eighths of the remaining people got off. Finally 15 people remained. How many were on the train originally?
  1. 60
  2. 72
  3. 120
  4. 36
  5. 48

Question 3

Isabella has the four different number cards shown. She combines two cards to form a two-digit prime number. At most how many different prime numbers can she form?

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  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 4

Ethan surveyed the hobbies of boys and girls in his class. Based on the bar chart, which hobby is second most popular?

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Boys = Nam; Girls = Nữ.
  1. Video games
  2. Singing
  3. Dancing
  4. Swimming
  5. Painting

Question 5

Liam finds half a pizza in the fridge. He wants to cut from its centre to eat two fifths of this half and leave the rest for his brother. What angle should his piece have?

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  1. 75°
  2. 100°
  3. 82°
  4. 80°
  5. 72°

Question 6

Carry out the three operations in the direction of the arrows. Find the number in the cloud with the question mark.

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  1. 15
  2. 17
  3. 11
  4. 13
  5. 14

Question 7

Mr Jimmy has 120 litres of red paint and 75 litres of blue paint. He fills each kind into full buckets of equal volume. If the bucket volume is as large as possible, how many buckets does he need?
  1. 11
  2. 8
  3. 15
  4. 13
  5. 5

Question 8

Solve the digit puzzle and find A + B + C.

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  1. 18
  2. 16
  3. 17
  4. 20
  5. 19

Question 9

Vivian folds a square sheet in half twice and cuts along the red line as shown. What does the remaining paper look like after unfolding?

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Question 10

Hellen can spend all her money on 6 bottles of milk and 7 loaves of bread, or on 8 bottles of milk and 4 loaves of bread. If she buys only bread, at most how many loaves can she buy?
  1. 15
  2. 16
  3. 17
  4. 18
  5. 19

Question 11

The pie chart divides a class into excellent, good, fair and poor performance levels. Excellent students outnumber poor students by 18. How many good students are there?

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  1. 30
  2. 36
  3. 40
  4. 42
  5. 54

Question 12

The seven-digit number 2023FMO is divisible by 2, 5 and 9. Find the greatest possible value of F × M. (F, M and O denote digits.)
  1. 11
  2. 30
  3. 24
  4. 20
  5. 56

Question 13

Dylan stacks 18 identical cubes of side length 1 cm as shown. Find the total surface area of the solid.

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  1. 58 cm²
  2. 52 cm²
  3. 54 cm²
  4. 56 cm²
  5. 60 cm²

Question 14

It is 8:30 a.m. on a standard clock. Jane’s clock gains 4 minutes every true hour. What will it show when the correct time is 2:30 p.m. the next day?

Necessary intended convention: Jane’s clock is also set correctly to 8:30 a.m. at the start; the source does not explicitly state this synchronization.
  1. 2:06 p.m.
  2. 12:30 p.m.
  3. 4:30 p.m.
  4. 2:54 p.m.
  5. 4:18 p.m.

Question 15

Find the missing value in the coin equations.

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  1. 369
  2. 396
  3. 389
  4. 398
  5. 360

Question 16

A box contains 18 white, 22 blue, 16 red and 25 black marbles. At least how many marbles must be drawn at random to guarantee 20 of one colour?
  1. 74
  2. 80
  3. 77
  4. 72
  5. 73

Question 17

Following the pattern of the sequence below, how many odd numbers are among its first 2023 terms?

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  1. 674
  2. 1348
  3. 1012
  4. 1349
  5. 675

Question 18

Kylie draws five identical circles touching as shown. Joining the centres of the four outer circles forms a square of area 32 cm². Find the shaded area, using π = 3.14.

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  1. 25.12 cm²
  2. 25.32 cm²
  3. 23.34 cm²
  4. 23.32 cm²
  5. 25.14 cm²

Question 19

Based on the pattern below, how many matches are in Figure 10?

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The supplied key disagrees with the displayed pattern; answer using the figure as printed. See the solution for the comparison.
  1. 135
  2. 145
  3. 155
  4. 165
  5. None of the above

Question 20

Morgan cycles from home to a party. At 10 km/h he would arrive 30 minutes late; at 18 km/h he would arrive 10 minutes early. What speed gets him there on time?

Intended comparison made explicit: the route and departure time are the same in both cases.
  1. 14 km/h
  2. 15 km/h
  3. 12 km/h
  4. 16 km/h
  5. 13 km/h