NECO Senior School Certificate Examination · General Mathematics

Number, Numeration, Commercial Arithmetic and Mensuration

35 practice questions, each with the answer and an explanation.

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All 35 questions

  1. Convert the base 4 number 312₄ to base 8.
  2. In modulo 7 arithmetic, solve for x in the congruence equation: 3x ≡ 5 (mod 7).
  3. Simplify the expression involving surds completely: (√75 - √12) / √27.
  4. Solve for x in the logarithmic equation: log₁₀(x + 3) + log₁₀(x - 3) = log₁₀(16).
  5. In a secondary school of 120 final-year students, 70 study Biology, 50 study Chemistry, and 25 study both subjects. How many students study neither Biology nor Chemistry?
  6. A grain merchant purchases 40 bags of maize at ₦25,000 each. He sells 30 bags at ₦32,000 each and the remaining 10 bags at ₦28,000 each. What is his total percentage profit on the transaction?
  7. Calculate the compound interest earned on a fixed deposit of ₦80,000 invested for 2 years at an annual interest rate of 10% compounded annually.
  8. A commercial cassava milling machine bought for ₦400,000 depreciates in value at a constant rate of 15% per annum. What is the book value of the machine after 2 years?
  9. Three business partners, Kola, Musa, and Emeka, share a profit of ₦360,000 in the ratio 3 : 4 : 5. How much more money does Emeka receive than Kola?
  10. A sector of a circle of radius 14 cm subtends an angle of 60° at the center. Calculate the perimeter of the sector. (Take π = 22/7)
  11. The parallel sides of a trapezium measure 12 cm and 18 cm, and the perpendicular distance between them is 8 cm. Calculate the area of the trapezium.
  12. A solid metal cylinder has a base radius of 7 cm and a vertical height of 10 cm. Calculate its total surface area. (Take π = 22/7)
  13. Calculate the volume of a right circular cone with base radius 6 cm and vertical height 14 cm. (Take π = 22/7)
  14. Find the total surface area of a solid sphere of radius 3.5 cm. (Take π = 22/7)
  15. Round the decimal number 0.0078496 to 3 significant figures.
  16. Express the product (3.2 × 10⁴) × (5.0 × 10⁻⁷) in standard scientific notation.
  17. The first term of an Arithmetic Progression (AP) is 7 and the common difference is 4. Find the 15th term of the progression.
  18. Find the sum of the first 20 terms of the Arithmetic Progression: 3, 7, 11, 15, ...
  19. In a Geometric Progression (GP), the 2nd term is 6 and the 5th term is 162. Find the common ratio r.
  20. Evaluate the sum to infinity of the convergent Geometric Progression: 18, 6, 2, 2/3, ...
  21. If y varies directly as x and inversely as the square of z, and y = 12 when x = 3 and z = 2, find y when x = 6 and z = 4.
  22. Calculate the total surface area of a solid hemisphere of radius 7 cm. (Take π = 22/7)
  23. In a circle of radius 13 cm, a chord is drawn at a perpendicular distance of 5 cm from the center. What is the length of the chord?
  24. An electronics retailer offers a solar television for a cash price of ₦180,000. Under hire purchase, a buyer pays a 20% initial deposit followed by 12 equal monthly installments of ₦14,000. How much e…
  25. A rectangular underground concrete water reservoir measures 5.0 m long, 4.0 m wide, and 2.5 m deep. What is the maximum water capacity of this reservoir in liters? (1 m³ = 1,000 liters)
  26. A boutique hotel bill amounts to ₦80,000 before taxes. If Value Added Tax (VAT) of 7.5% and a state consumption tax of 5.0% are applied sequentially to the base bill, what is the total amount payable?
  27. A traveler exchanges $500 US Dollars for Nigerian Naira at an official exchange rate of ₦1,450 per dollar. How much Naira does he receive?
  28. A sector of a circle of radius 12 cm with an angle of 120° is folded without overlap into a hollow cone. Find the base radius of the cone formed.
  29. Calculate the area of a regular hexagon each of whose sides measures 6 cm. (Take √3 ≈ 1.732)
  30. If today is Tuesday, what day of the week will it be exactly 100 days from today?
  31. Evaluate the arithmetic expression following the order of operations (BODMAS): 3/4 + 1/2 ÷ 2/3 - 1/8.
  32. A right prism of length 15 cm has a triangular cross-section with base 8 cm and perpendicular height 6 cm. Calculate the volume of the prism.
  33. Perform the binary multiplication: 110₂ × 101₂.
  34. Find the length of the diagonal of a rectangle whose sides measure 15 cm and 8 cm.
  35. A cylindrical metallic pipe has an external radius of 5 cm, internal radius of 4 cm, and length of 14 cm. What is the volume of metal in the pipe? (Take π = 22/7)

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