1. Easy (Arithmetic) - Open-ended:
What is the result of 12 × 8 ÷ 4 + 7?
Answer: 31
Explanation: Follow the order of operations (PEMDAS). First multiply 12 × 8 = 96, then divide by 4 to get 24, and finally add 7 to reach 31.
2. Medium (Algebra) - Multiple-choice:
Solve for x: 3x - 7 = 20
A) 7
B) 9
C) 11
D) 13
Answer: B) 9
Explanation: Add 7 to both sides: 3x = 27. Then divide both sides by 3 to get x = 9.
3. Medium (Geometry) - Open-ended:
A rectangle has a length that is twice its width. If the perimeter of the rectangle is 36 cm, what is its area?
Answer: 72 cm²
Explanation: Let w be the width. Then length = 2w. Perimeter formula: 2(l + w) = 36. Substitute: 2(2w + w) = 36. Simplify: 6w = 36. Solve: w = 6. So length = 12. Area = l × w = 12 × 6 = 72 cm².
4. Hard (Statistics) - Open-ended:
The mean of 5 numbers is 18. If one number is removed, the mean of the remaining 4 numbers becomes 16. What was the number that was removed?
Answer: 26
Explanation: Sum of 5 numbers = 18 × 5 = 90. Sum of 4 numbers = 16 × 4 = 64. The difference (90 - 64 = 26) is the removed number.
5. Hard (Algebra/Geometry) - Multiple-choice:
A cylinder has a volume of 100π cubic units and a height of 10 units. What is the radius of its base?
A) √10 units
B) 2 units
C) 5 units
D) 10 units
Answer: A) √10 units
Explanation: Use the formula V = πr²h. Substitute known values: 100π = π × r² × 10. Simplify: 10 = r². Take the square root of both sides: r = √10.