The questions below targets Class 7 students preparing for Mathematical Reasoning and Everyday Mathematics. These types of topics appear in Science Olympiad Foundation (SOF) exams and similar mental ability tests. The questions help students develop critical thinking, problem-solving, and numerical skills essential for competitive exams.
The content covers math topics like algebra, geometry, arithmetic, and ratios. The questions will help students sharpen their logical thinking and strengthen the math skills. It will further help them understand and use important ideas in different types of problems. This practice builds their knowledge are prepares them for SOF and other mental ability tests, giving strategies they can rely on.
40 Math & Reasoning Practice for Class 7 SOF Exams
Question 1. If the value of 5² + 3² – 4² is:
a) 20
b) 18
c) 16
d) 14
Answer:
b) 18 — 5² = 25, 3² = 9, 4² = 16; therefore, 25 + 9 – 16 = 18.
Question 2. A number x is multiplied by 3, then 4 is added to the result, and the total is divided by 2. If the final result is 10, what is the value of x?
a) 6
b) 8
c) 10
d) 12
Answer:
a) 6 — Solving (3x + 4) / 2 = 10 gives x = 6.
Question 3. Solve: 7 + 3 × (4 – 2)²
a) 15
b) 19
c) 21
d) 25
Answer:
d) 25 — Calculate inside parentheses first: (4 – 2)² = 4, then 3 × 4 = 12, and finally 7 + 12 = 25.
Question 4. Find the value of (2³ + 3²) – (4 × 2)
a) 5
b) 7
c) 9
d) 11
Answer:
b) 7 — 2³ = 8, 3² = 9, and 4 × 2 = 8; thus, 8 + 9 – 8 = 7.
Question 5. The sum of two numbers is 60, and their difference is 20. What are the two numbers?
a) 20 and 40
b) 25 and 35
c) 30 and 30
d) 10 and 50
Answer:
a) 20 and 40 — Solving x + y = 60 and x – y = 20, we get x = 40, y = 20.
Question 6. What is the result of 2⁴ ÷ 2²?
a) 2
b) 4
c) 8
d) 16
Answer:
b) 4 — Dividing powers of the same base: 2⁴ ÷ 2² = 2², which is 4.
Question 7. If the area of a square is 144 cm², what is the length of one side?
a) 10 cm
b) 11 cm
c) 12 cm
d) 13 cm
Answer:
c) 12 cm — The side length is the square root of 144, which is 12.
Question 8. A rectangle has a length of 15 cm and a width of 10 cm. What is its perimeter?
a) 25 cm
b) 50 cm
c) 75 cm
d) 30 cm
Answer:
b) 50 cm — The perimeter of a rectangle is 2 × (length + width), or 2 × (15 + 10) = 50 cm.
Question 9. If 2x – 5 = 9, what is the value of x?
a) 5
b) 6
c) 7
d) 8
Answer:
c) 7 — Solving 2x = 14 gives x = 7.
Question 10. A bag contains red and blue marbles in a ratio of 3:5. If there are 40 marbles in total, how many are red?
a) 10
b) 12
c) 15
d) 18
Answer:
a) 15 — Applying the ratio (3/8) × 40 gives 15 red marbles.
Question 11. Find the value of 15% of 200.
a) 20
b) 25
c) 30
d) 35
Answer:
b) 30 — 15% of 200 is 0.15 × 200 = 30.
Question 12. If the volume of a cube is 125 cm³, what is the length of one side?
a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
Answer:
b) 5 cm — The side length of a cube is the cube root of 125, which is 5.
Question 13. Simplify: (7 × 2) + (3² – 4)
a) 16
b) 17
c) 18
d) 19
Answer:
b) 17 — Calculate: (7 × 2) = 14 and (3² – 4) = 5, so 14 + 3 = 17.
Question 14. What is the probability of picking a heart from a standard deck of 52 cards?
a) 1/2
b) 1/4
c) 1/8
d) 1/13
Answer:
b) 1/4 — There are 13 hearts in a deck of 52 cards, so the probability is 13/52 = 1/4.
Question 15. If the sum of the angles of a polygon is 720°, how many sides does it have?
a) 4
b) 5
c) 6
d) 7
Answer:
c) 6 — The sum of angles of a polygon is (n-2) × 180°, solving gives n = 6.
Question 16. If 3² × 2³ = x, then x is:
a) 36
b) 54
c) 72
d) 108
Answer:
b) 72 — 3² = 9 and 2³ = 8, so 9 × 8 = 72.
Question 17. The perimeter of an equilateral triangle is 27 cm. What is the length of each side?
a) 7 cm
b) 8 cm
c) 9 cm
d) 10 cm
Answer:
c) 9 cm — The length of each side is 27/3 = 9 cm.
Question 18. What is the cube of 4?
a) 32
b) 48
c) 64
d) 72
Answer:
c) 64 — 4³ is 64.
Question 19. In a sequence, the first term is 6, and each term increases by 4. What is the fifth term?
a) 22
b) 24
c) 26
d) 28
Answer:
a) 22 — The fifth term is 6 + 4(4) = 22.
Question 20. Solve: (5² – 2³) + (4² ÷ 2)
a) 19
b) 20
c) 21
d) 22
Answer:
d) 22 — Calculate each part separately: (5² – 2³) = 17 and (4² ÷ 2) = 5, so 17 + 5 = 22.
Question 21. If a triangle has angles measuring 45° and 55°, what is the measure of the third angle?
a) 70°
b) 80°
c) 90°
d) 100°
Answer:
b) 80° — The sum of angles in a triangle is 180°, so the third angle is 180° – (45° + 55°) = 80°.
Question 22. Solve for x if 3(x – 4) = 18.
a) 8
b) 9
c) 10
d) 11
Answer:
a) 10 — Expanding gives 3x – 12 = 18, solving for x gives x = 10.
Question 23. Find the value of (6² – 4³) + 7.
a) -9
b) -7
c) 5
d) 10
Answer:
a) -9 — 6² = 36, 4³ = 64, so 36 – 64 + 7 = -9.
Question 24. What is the average of the numbers 24, 36, and 48?
a) 30
b) 32
c) 36
d) 40
Answer:
c) 36 — The average is (24 + 36 + 48) / 3 = 36.
Question 25. If the perimeter of a square is 48 cm, what is the length of one side?
a) 10 cm
b) 12 cm
c) 15 cm
d) 18 cm
Answer:
b) 12 cm — The perimeter of a square is 4 × side, so 48 ÷ 4 = 12 cm.
Question 26. If y = 5 and z = 2, find the value of 3y + 4z.
a) 17
b) 19
c) 23
d) 26
Answer:
b) 19 — Substitute y = 5 and z = 2 to get 3(5) + 4(2) = 19.
Question 27. Simplify: (8² ÷ 4) + 3³.
a) 29
b) 33
c) 37
d) 43
Answer:
c) 37 — 8² = 64, so (64 ÷ 4) = 16, and 3³ = 27. Therefore, 16 + 27 = 37.
Question 28. If the difference between two numbers is 13 and their product is 84, what are the two numbers?
a) 21 and 8
b) 20 and 7
c) 16 and 5
d) 18 and 3
Answer:
a) 21 and 8 — The numbers that satisfy both conditions are 21 and 8.
Question 29. Calculate: 5³ – 2² × 3.
a) 100
b) 105
c) 115
d) 125
Answer:
b) 105 — 5³ = 125 and 2² × 3 = 4 × 3 = 12, so 125 – 12 = 105.
Question 30. A car travels at a speed of 60 km/h for 3 hours. What is the distance covered?
a) 160 km
b) 180 km
c) 200 km
d) 220 km
Answer:
b) 180 km — Distance = speed × time = 60 × 3 = 180 km.
Question 31. Find the HCF of 54 and 72.
a) 12
b) 18
c) 24
d) 36
Answer:
b) 18 — The highest common factor of 54 and 72 is 18.
Question 32. A rope is cut into 4 equal parts, and each part measures 6 meters. What was the original length of the rope?
a) 18 meters
b) 20 meters
c) 22 meters
d) 24 meters
Answer:
d) 24 meters — The original length is 6 × 4 = 24 meters.
Question 33. If x = -3, what is the value of 2x² – 4x + 5?
a) 23
b) 25
c) 27
d) 29
Answer:
a) 23 — Substituting x = -3, we get 2(-3)² – 4(-3) + 5 = 23.
Question 34. Simplify: (5² + 7) – (3² + 4).
a) 13
b)
15 c) 17
d) 19
Answer:
b) 15 — 5² = 25, so 25 + 7 = 32, and 3² = 9, so 9 + 4 = 13; 32 – 13 = 19.
Question 35. The perimeter of an equilateral triangle is 33 cm. What is the length of one side?
a) 10 cm
b) 11 cm
c) 12 cm
d) 13 cm
Answer:
b) 11 cm — The side length is 33 ÷ 3 = 11 cm.
Question 36. If a = 4 and b = -2, find the value of a² – b².
a) 12
b) 16
c) 18
d) 20
Answer:
c) 18 — a² = 16 and b² = 4, so 16 – 4 = 12.
Question 37. Find the value of 3³ – 4² + 7.
a) 18
b) 20
c) 24
d) 26
Answer:
a) 18 — 3³ = 27 and 4² = 16, so 27 – 16 + 7 = 18.
Question 38. A shopkeeper sold an item for $60 at a 20% profit. What was the cost price?
a) $45
b) $48
c) $50
d) $52
Answer:
c) $50 — The cost price is $60 / 1.2 = $50.
Question 39. The sum of two numbers is 80, and their ratio is 3:5. What is the smaller number?
a) 30
b) 32
c) 34
d) 36
Answer:
b) 30 — Solving 3x + 5x = 80, we get x = 10, so smaller number = 3 × 10 = 30.
Question 40. In a class, the ratio of boys to girls is 5:3. If there are 32 students in total, how many are girls?
a) 10
b) 12
c) 15
d) 18
Answer:
b) 12 — With a 5:3 ratio, there are (3/8) × 32 = 12 girls.
